PH  Bryant^ 


This  book  is  due  on  the  date  indicated 
below  and  is  subject  to  an  overdue 
fine  as  posted  at  the  circulation  desk. 


EXCEPTION:  Date  due  will  be 
earlier  if  this  item  is  RECALLED. 


^ 


150M/01 -92-941 680 


FOEEST  MENSUEATION 


BY 


HERMAN   HAUPT   CHAPMAN,  M.F. 

Harriman   Professor   of  Forest   Management, 
Yale   University 


NEW  YORK 

JOHN    WILEY    &    SONS,   Inc. 

London:  CHAPMAN  &  HALL,  Limited 
1921 


Copyright,  1921 
By  HERMAN  HAUPT  CHAPMAN 


PRESS  or 

BRAUNWORTH  fit   CO. 

BOOK  MAWUFACTURERI 

BROOKLYN,   N.   V. 


TO 

IN   RECOGNITIOX   OF    HIS    LIFELONG    SERVICE 

IN    PROMOTING    FOREST    EDUCATION 

AND    IN    DEVELOPING    A    HIGH    STANDARD 

OF   PROFESSIONAL    FORESTRY    IN    AMERICA 


PREFACE 


This  text  is  intended  as  a  thorough  discussion  of  the  measurement 
of  the  volume  of  felled  timber,  in  the  form  of  logs  or  other  products; 
of  the  measurement  of  the  volume  of  standing  timber;  and  of  the 
growth  of  trees,  stands  of  timber  and  forests.  It  is  designed  for  the 
information  of  students  of  forestry,  owners  or  purchasers  of  timber- 
lands,  and  timber  operators.  The  subject  matter  so  treated  is  funda- 
mental to  the  purchase  or  exchange  of  forest  property  or  of  timber 
stumpage,  the  valuation  of  damages,  the  planning  of  logging  operations, 
and  the  management  of  forest  lands  for  the  production  of  timber  by 
growth. 

The  publication  is  intended  as  the  successor  of  Graves'  Forest  Men- 
suration, and  was  undertaken  at  the  request  of  the  author,  H.  S.  Graves, 
whose  original  text,  Forest  Mensuration,  appearing  in  1906,  set  a  stand- 
ard for  text-books  in  forestry  and  has  been  of  inestimable  value  to 
foresters  and  timberland  owners  in  America.  The  present  text  is  not  a 
revision  of  the  former  publication,  but  an  entirely  new  presentation, 
both  as  to  arrangement,  methods  of  treatment  and  much  of  the  subject 
matter.  The  author  has  in  some  instances  quoted  or  borrowed  portions 
of  the  former  text  and  is  indebted  to  it  for  many  of  the  more  fundamental 
conceptions  and  descriptions  of  processes  used  in  Forest  Mensuration. 

It  is  the  purpose  of  Part  I  to  bring  out  the  relations  of  the  cubic 
contents  of  logs,  and  their  measurement,  to  the  contents  as  expressed  in 
terms  of  products,  and  to  encourage  the  substitution  of  sound  units  of 
measure  and  methods  of  measurement  for  defective  standards  and 
methods  as  far  as  possible. 

The  application  of  these  standards  to  the  measurement  of  standing 
timber  is  the  subject  of  Part  II.  This  part  presents  a  complete  analysis 
of  the  art  of  timber  estimating  as  practiced  in  every  timber  region  of  the 
United  States,  the  methods  employed  by  skilled  timber  cruisers,  the 
principles  upon  which  these  methods  are  based,  the  relative  accuracy 
of  the  various  systems  used,  the  factors  and  averages  which  enter  into 
the  use  of  these  methods,  and  the  application  of  these  principles  and 
factors  in  practical  work  and  in  the  training  of  men  for  timber  cruising. 


vi  PREFACE 

The  object  sought  in  Part  III  is  to  systematize  the  principles  and 
problems  confronting  the  student  in  the  stud}'  of  tree  growth,  and  to  so 
correlate  these  problems  that  he  is  not  diverted  from  the  ultimate  object 
of  such^  studies,  which  is  the  determination  of  yields  per  acre,  by  details 
of  methods  having  to  do  with  the  measurement  of  growth  of  individual 
trees.  Research  and  field  studies  of  growth  per  acre  are  rendered  dif- 
ficult not  only  by  the  lack  of  an  accepted  unit  of  measure,  but  bj'  the 
great  variations  in  the  character  of  the  stands  comprising  our  virgin 
and  second  growth  forests,  yet  it  is  just  these  stands,  and  not  planta- 
tions, whose  growth  will  determine  our  yields  of  timber  for  the  next 
four  or  five  decades. 

Attention  is  called  to  the  substitution  of  the  International  j-inch 
kerf  log  rule  in  the  present  volume,  for  the  |-inch  kerf  rule  in 
Graves'  Mensuration.  It  is  hoped  that  this  rule  will  be  accepted  as  a 
scientific  standard  for  board  feet  since  it  is  adapted  to  conditions  of 
second  growth  and  is  conservative  in  values. 

Instead  of  attempting  to  include  tables  of  volume  or  yield,  a  table 
of  references  is  printed  to  such  tables  as  are  of  standard  quality  and 
which  are  in  possession  of  the  U.  S.  Forest  Service,  Washington,  D.  C. 

The  author  wishes  to  acknowledge  the  many  helpful  criticisms 
received  from  foresters  in  the  preparation  of  this  book. 


TABLE   OF  CONTENTS 


Part  I 

THE    MEASUREMENT    OF    FELLED    TIMBER    AND    ITS 
PRODUCTS 

CHAPTER  I 
INTRODUCTION  TO  FOREST  MENSURATION 

PAGE 

1.  Definition  and  Purpose 1 

2.  Relation  between  Lumbering  and  Timber  Estimating 2 

3.  Relation  between  Forestry  and  Growth  Measurements 2 

4.  Relation  between  Forest  Mensuration,  Stumpage  Values  and  the  Valuation 

of  Forest  Property 3 

6.  Relation  of  Mensuration  to  other  Forestry  Subjects 3 

6.  Absolute  versus  Relative  Accuracy  in  Mensuration 3 

7.  Forest  Survey 5 

CHAPTER  II 
SYSTEMS  AND  UNITS  OF  MEASUREMENT 

8.  Systems  of  Measurement  used  in  Forest  Mensuration 6 

9.  Piece  Measure 7 

10.  Cord  Measure 7 

11.  Cubic  Measure 8 

12.  Board  Measure 8 

13.  Log  Rules 8 

14.  Measurement  of  Standing  Timber  Postponed  till  after  Manufacture 8 

15.  Measurement  of  Standing  Timber  Postponed  till  after  Logging 9 

16.  Measurement  of  Standing  Timber  in  the  Tree 9 

17.  Need  of  Standardization  for  both  Commercial  and  Scientific  Measurements .  10 

18.  Forms  of  Products  into  which  the  Contents  of  Trees  are  Converted 11 

19.  The  Factor  of  Waste  in  Manufacture 13 

20.  Actual  versus  Superficial  Contents  of  Sawed  Lumber 13 

21.  Round-edged  Lumber 14 

22.  Products  made  from  Bolts  and  Billets 14 

CHAPTER  III 
THE  ME.^SUREMENT  OF  LOGS.     CUBIC  CONTENTS 

23.  Total  versus  Merchantable  Contents 16 

24.  Log  Lengths 16 

25.  Diameters  and  Areas  of  Cross  Sections 17 

vii 


viii  TABLE  OF  CONTENTS 

PAGE 

26.  The  Form  of  Logs 18 

27.  Formulae  for  Solid  Contents  of  Logs 19 

28.  Relative  Accuracy  of  the  Smalian  and  Huber  Formulae 21 

29.  The  Technique  of  Measuring  Logs 22 

30.  Girth  as  a  Substitute  for  Diameter  in  Log  Measurements 24 

CHAPTER  IV 
LOG  RULES  BASED  ON  CUBIC  CONTENTS 

31.  Comparison  of  Log  Rules  Based  on  Diameter  at  Middle  and  at  Small  End 

of  Log 26 

32.  Log  Rules  in  Use,  Based  on  Cubic  Volume 28 

33.  The  Blodgett  or  New  Hampshire  Cubic  Foot 30 

34.  Use  of  Cubic  Foot  in  Log  Scahng 31 

35.  Log  Rules  for  Cubic  Contents  of  Squared  Timbers 33 

36.  Log  Rules  Expressed  in  Board-feet  but  Based  Directly  upon  Cubic  Contents  34 

37.  Formula  for  Board-foot  Rules  Based  on  Cubic  Contents 35 

38.  Comparison  of  Scaled  Cubic  Contents  by  Different  Log  Rules 36 

39.  Relation  between  Cubic  Measure  and  True  Board-foot  Log  Rules 39 

CHAPTER  V 
THE  MEASUREMENT  OF  LOGS.     BOARD-FOOT  CONTENTS 

40.  Necessity  for  Board-foot  Log  Rules 40 

41.  Relation  of  Diameter  of  Log  to  per  cent  of  Utilization  in  Sawed  Lumber ...  40 

42.  Errors  in  Use  of  Cubic  Rules  for  Board-feet 42 

43.  Taper  as  a  Factor  in  Limiting  the  Scaling  Length  of  Logs  for  Board-foot 

Contents 43 

44.  The  Introduction  of  Taper  into  Log  Rules 44 

45.  Middle  Diameter  as  a  Basis  for  Board-foot  Contents 46 

46.  Definition  and  Basis  of  Over-run 46 

47.  Influences  Affecting  Over-rim.    The  Log  Rule  Itself 47 

48.  Influences  Affecting  Over-run.    Methods  of  Manufacture 47 

49.  Standardization  of  Variables  in  Construction  of  a  Log  Rule 49 

50.  The  Need  for  More  Accurate  Log  Rules 50 

51.  The  Waste  from  Slabs  and  Edgings 50 

52.  The  Waste  from  Crook  or  Sweep 51 

63.  The  Waste  from  Saw  Kerf 53 

54.  Total  Per  Cent  of  Waste  in  a  Log 55 

CHAPTER  VI 

THE  CONSTRUCTION  OF  LOG  RULES  FOR  BOARD-FOOT 
CONTENTS 

55.  Methods  Used  in  Constructing  Log  Rules  for  Board-feet 58 

56.  The  Construction  of  Rules  Based  on  Mathematical  Formulae 59 

57.  Comparison  of  Log  Rules  Based  on  Formulae 61 

58.  McKenzie  Log  Rule 63 

69.  International  Log  Rule  for  i"  Kerf,  Judson  F.  Clark,  1900 63 


TABLE  OF  CONTENTS 


PAGE 

60.  International  Log  Rule  for  i"  Kerf,  Judson  F.  Clark,  1917 64 

61.  British  Columbia  Log  Rule,  1902 64 

62.  Other   Formula   Rules,   Approximately  Accurate   Both  in   Principles   and 

Quantities 65 

63.  Tiemann  Log  Rule,  H.  D.  Tiemann,  1910 67 

64.  Formula  Rules  Inaccurately  Constructed.     Baxter  Log  Rule 67 

65.  Doyle  Log  Rule 68 

66.  Effect  of  Errors  in  Doyle  Rule  upon  Scaling  and  Over-run 70 

67.  The  Construction  of  Log  Rules  Based  on  Diagrams 72 

68.  Scribner  Log  Rule,  1846 73 

69.  Spaulding  Log  Rule,  1868 75 

70.  Maine  or  Holland  Rule,  1856 76 

71.  Canadian  Log  Rules 76 

72.  Hybrid  Log  Rules 76 

73-  General  Formula;  for  all  Log  Rules 77 

74.  The  Construction  of  Log  Rules  from  Mill  Tallies.     Graded  Log  Rules 78 

75.  The  Massachusetts  Log  Rule  for  Round-edged  Lumber 79 

76.  Conversion  of  Values  of  a  Standard  Rule  to  Apply  to  Different  Widths  of 

Saw  Kerf  and  Thicknesses  of  Lumber 

77.  Limitations  to  Conversion  of  Board-foot  Log  Rules 83 

78.  Choice  of  a  Board- foot  Log  Rule  for  a  Universal  Standard 84 

79.  Unused  and  Obsolete  Log  Rules 85 

CHAPTER  VII 
LOG  SCALING  FOR  BOARD    MEASURE 

80.  The  Log  Scale 88 

81.  The  Cylinder  as  the  Standard  of  Scaling 90 

82.  Deductions  from  Sound  Scale,  versus  Over-run 90 

83.  Scaling  Practice  Based  on  Measurement  of  Diameter  at  Small  End  of  Log  91 

84.  Scaling  Practice  Based  on  Measurement  of  Diameter  at  Middle  of  Log,  or 

CaUper  Scale 97 

85.  Scale  Records 98 

86.  The  Determination  of  What  Constitutes  a  Merchantable  Log 99 

87.  Grades  of  Lumber  and  Log  Grades 103 


CHAPTER  VIII 
THE  SCALING  OF  DEFECTIVE  LOGS 

88.  Deductions  from  Scale  for  Unsound  Defects 105 

89.  Methods  of  Making  Deductions 105 

90.  Effect  of  Minimum  Dimensions  of  Merchantable  Boards  upon  these  Deduc- 

tions    107 

91.  Interior  Defects ' 108 

92.  Exterior  Defects 113 

93.  Crook  or  Sweep 116 

94.  Check  Scaling 117 

95.  Scaling  from  the  Stump 118 

96.  The  Scaler 119 


X  TABLE  OF  CONTENTS 

CHAPTER  IX 
STACIvED  OR  CORD  MEASURE 

PAGE 

97.  Stacked  Measure  as  a  Substitute  for  Cubic  Measure 121 

98.  The  Standard  Cord  versus  Short  Cords  and  Long  Cords 121 

99.  Measurement  of  Stacked  Wood  Cut  for  Special  Purposes 122 

100.  Effect  of  Seasoning  on  Volume  of  Stacked  Wood 123 

101.  Methods  of  Measurement  of  Cordwood 123 

102.  Solid  Cubic  Contents  of  Stacked  Wood 124 

103.  Effect  of  Irregular  Piling  on  SoUd  Contents 124 

104.  Effect  of  Variation  in  Form  of  Sticks  on  Solid  Contents 125 

105.  Effect  of  Dimen.sions  of  Stick  on  Solid  Contents 126 

106.  The  Basis  for  Cordwood  Converting  Factors 127 

107.  Standard  Cordwood  Converting  Factors 128 

108.  Converting  Factors  for  Sticks  of  Different  Lengths 128 

109.  Converting  Factors  for  Sticks  of  Different  Diameters 129 

110.  The  Mea.surement  of  Sohd  Contents  of  Stacked  Cords.     Xylometers 132 

111.  Cordwood  Log  Rules.     The  Humphrey  Caliper  Rule 132 

112.  Discounting  for  Defect  in  Cord  Measure 133 

113.  The  Measurement  of  Bark 134 

114.  Factors  for  Converting  Stacked  Cords  to  Board  Feet 135 

115.  Weight  as  a  Measure  of  Cordwood 137 

Part  II 

THE    MEASUREMENT    OF    STANDING    TIMBER 

CHAPTER  X 

UNITS  OF  MEASUREMENT  FOR  STANDING  TIMBER 

116.  Board  Feet — Basis  of  AppUcation 139 

117.  The  Piece 140 

118.  Choice  of  Units  in  Estimating  Timber 140 

119.  The  Log  as  the  Unit  in  Estimating 140 

120.  Log  Run,  or  Average  Log  Method 143 

121.  The  Tree  as  a  Unit  in  Estimating.  Volume  Tables 144 

122.  Volume  Tables  Based  on  Standard  Taper  per  Log.     "Universal"  Volume 

Tables 144 

123.  Substitution  of  Mill  Factor  for  Log  Rules  in  Universal  Tables 146 

124.  Volume  Tables  Based  on  Actual  Volumes  of  Trees 147 

125.  The  Point  of  Measurement  of  Diameters  in  Volume  Tables 148 

126.  Bark  as  Affecting  Diameter  in  Volume  Tables 150 

127.  Classification  of  Trees  by  Diameter 151 

128.  Classification  of  Trees  by  Height 151 

129.  Diameter  Alone,  ver-sus  Diameter  and  Height,  as  Basis  of  Volume  Tables .  . .  152 

130.  Standard  versus  Local  Volume  Tables 153 

CHAPTER  XI 

THE  CONSTRUCTION  OF  STANDARD  VOLUME  TABLES 
FOR  TOTAL  CUBIC  CONTENTS 

131.  Steps  in  Construction  of  a  Standard  Volume  Table 154 

132.  Selection  of  Trees  for  Measurement 154 


TABLE  OF  CONTENTS  xi 

PAGE 

133.  The  Tree  Record 155 

134.  Measurements  of  the  Tree  Required  for  Classification 156 

135.  Measurement  Required  to  Obtain  the  Volume  of  the  Tree.  Systems  Used  158 

136.  Computation  of  Volume  of  the  Tree 161 

137.  Classification  and  Averaging  of  Tree  Volumes  According  to  Diameter  and 

Height  Classes 163 

138.  The  Graphic  Plotting  of  Data — Its  Advantages. 166 

139.  Application  of  Graphic  Method  in  Constructing  Volume  Tables 169 

140.  Harmonized  Curves  for  Standard  Volume  Tables,  Based  on  Diameter ....  169 

141.  Harmonized  Curves  Based  on  Height 170 

142.  Local  Volume  Tables,  Their  Construction  and  Use 174 

143.  The  Derivation  of  Local  Volume  Tables  from  Standard  Tables 175 

144.  Volume  Tables  for  Peeled  or  Solid  Wood  Contents 176 


CHAPTER  XII 

STANDARD  VOLUME  TABLES  FOR  MERCHANTABLE 
CUBIC  VOLUME  AND  CORDS 

145.  Purpose  and  Derivation  of  Tables  for  Cubic  Volume  of  Trees 177 

146.  Branchwood  or  Lapwood 177 

147.  Merchantable  Limit  in  Tops  and  at  D.B.H 177 

148.  Stump  Heights 178 

149.  Merchantable  versus  Used  Length 178 

150.  Waste,  Definition  and  Measurement 179 

151.  Defect  or  Cull 179 

152.  Conversion  of  Volume  Tables  for  Cubic  Feet  to  Cords 180 


CHAPTER  XIII 
VOLUME  TABLES  FOR  BOARD  FEET 

153.  The  Standard  or  Basis  for  Board-foot  Volume  Tables 182 

154.  Adoption  of  a  Standard  Log  Length 182 

155.  Top  Diameters,  Fixed  or  Variable  Limits 183 

156.  Defective  Trees,  Measurement 184 

157.  Total  versus  Merchantable  Heights  as  a  Basis  for  Tree  Classes 185 

158.  The  Coordination  of  Merchantable  Heights  with  Top  Diameters 185 

159.  Construction  of  Board-foot  Volume  Tables 188 

160.  Data  Which  Should  Accompany  a  Volume  Table 188 

161.  Checking  the  Accuracy  of  Volume  Tables 189 

CHAPTER  XIV 

VOLUME  TABLES  FOR  PIECE  PRODUCTS,  COMBINATION 
AND  GRADED  VOLUME  TABLES 

162.  Volume  Tables  for  Piece  Products 191 

163.  Volume  Tables  for  Railroad  Cross  Ties 191 

164.  Combination  Volume  Tables  for  Two  or  More  Products 193 

165.  Graded  Volume  Tables 193 


xii  TABLE  OF  CONTENTS 

CHAPTER  XV 
THE  FORM  OF  TREES  AND  TAPER  TABLES 

PAGE 

166.  Form  as  a  Third  Factor  Affecting  Volume 196 

167.  Taper  Tables,  Definition  and  Purpose ; 197 

168.  Methods  of  Constructing  Taper  Tables 197 

169.  Limitations  of  Taper  Tables 204 

CHAPTER  XVI 
FORM  CLASSES  AND  FORM  FACTORS 

170.  The  Need  for  Form  Classes  in  Volume  Tables 205 

171.  Form  Quotient  as  the  Basis  of  Form  Classes 206 

172.  Resistance  to  Wind  Pressure  as  the  Determining  Factor  of  Tree  Form. . . .  208 

173.  A  General  Formula  for  Tree  Form 209 

174.  Apphcability  of  Hoejer's  Formula  in  Determining  Tree  Forms 210 

175.  Form  Factors 211 

176.  The  Derivation  of  Standard  Breast  High  Form  Factors 213 

177.  Merchantable  Form  Factors 214 

178.  Form  Height 215 

179.  Form  Classes  and  Universal  Volume  Tables  as  Applied  to  Conditions  in 
America 215 

CHAPTER  XVII 

FRUSTUM  FORM  FACTORS  FOR  MERCHANTABLE 
CONTENTS  IN  BOARD  FEET 

180.  The  Principle  of  the  Frustum  Form  Factor 218 

181.  Basis  of  Determining  Dimensions  of  the  Frustum 219 

182.  Character  and  Utihty  of  Frustum  Form  Factors 219 

183.  Calculation  of  the  True  Frustum  Form  Factor 221 

184.  Calculation  of  the  Volume  of  Frustums.    Influence  of  Fixed  Versus  Variable 

Top  Diameters 221 

185.  Construction  of  the  Volume  Table  from  Frustum  Form  Factors.    A  Short 

Cut  Method 224 

186.  Other  Merchantable  Form  Factors  for  Board  Feet 225 

CHAPTER  XVIII 
THE  MEASUREMENT  OF  STANDING  TREES 

187.  The  Problem  of  Measuring  Standing  Timber  for  Volume 226 

188.  The  Measurement  of  Tree  Diameters.    Diameter  Classes.    Stand  Tables . .  227 

189.  Instruments  for  Measuring  Diameters.     Calipers,  Description  and  Method 

of  Use 227 

190.  The  Diameter  Tape 229 

191.  The  Biltmore  Stick 230 

192.  Ocular  Estimation  of  Tree  Dimensions 234 

193.  The  Measurement  of  Heights 235 

194.  Methods  Based  on  the  Similarity  of  Isosceles  Triangles 235 


TABLE  OF  CONTENTS 


PAGE 

195.  The  Principle  of  the  Klaussner  H>'psometer 236 

196.  Methods  Based  on  the  Similarity  of  Right  Triangles 238 

197.  Hypsometers  Based  on  the  Pendulum  or  Plumb-bob 239 

198.  The  Principle  of  the  Christen  Hypsometer 243 

199.  The  Technique  of  Measuring  Heights 245 

200.  The  Measurement  of  Upper  Diameters.    Dendrometers 247 

201.  The  Biltmore  Pachymeter 248 

202.  The  d'Aboville  Method  for  Determining  Form  Quotients 248 

203.  The  Jonson  Form  Point  Method  of  Determining  Form  Classes 249 

204.  Rules  of  Thumb  for  Estimating  the  Contents  of  Standing  Trees 251 

CHAPTER  XIX 

PRINCIPLES  UNDERLYING  THE  ESTIMATION  OF 
STANDING  TIMBER 

205.  Factors  Determining  the  Methods  used  in  Timber  Estimating 255 

206.  Direct  Ocular  Estimate  of  Total  Volume  m  Stand 256 

207.  Actual  Estimate  or  Measurement  of  the  Dimensions  of  Every  Tree  of 

Merchantable  Size 257 

208.  Estimating  a  Part  of  the  Timber  as  an  Average  of  the  Whole 257 

209.  The  Six  Classes  of  Averages  Employed  in  Timber  Estimating 258 

210.  The  Choice  of  a  System  for  Timber  Estimating,  with  Relation  to  Accuracy 

of  Results 261 

211.  Relation  betnveen  Size  of  Area  Units  and  Per  Cent  of  Area  to  be  Estimated  262 

212.  Degree  of  Uniformity  of  Stand  as  Affecting  Methods  Employed 265 

CHAPTER  XX 
METHODS  OF  TIMBER  ESTIMATING 

213.  The  Importance  of  Area  Determination  in  Timber  Estimating 267 

214.  The  Forest  Survey  as  Distinguished  from  Timber  Estimatmg 268 

215.  Timber  Appraisal  as  Distinguished  from  Forest  Survey 269 

216.  Forest  Surveying  as  a  Part  of  the  Forest  Survey 270 

217.  The  Cull  Factor,  or  Deductions  for  Defects 271 

218.  Total,  or  100  Per  Cent  Estimates 271 

219.  Estimates  Covering  a  Part  of  the  Total  Area.    The  Strip  Method 273 

220.  Factors  Determining  the  Width  of  Strips 274 

221.  Method  of  Running  Strip  Surveys.    Record  of  Timber 276 

222.  Tying  in  the  Strips.    The  Base  Line 281 

223.  Systems  of  Strip  Estimating  in  Use 282 

224.  Methods  Dependent  on  the  Use  of  Plots,  Systematically  Spaced 285 

CHAPTER  XXI 

METHODS   OF  IMPROVING   THE  ACCURACY   OF   TIMBER 
ESTIMATES 

225.  The  Use  of  Forest  Types  in  Estimating 288 

226.  Method  of  Separating  Areas  of  Different  Types 290 

227.  Site  Classes  and  Average  Heights  of  Timber 291 


xiv  TABLE  OF  CONTENTS 

PAGE 

228.  Methods  of  Estimating  which  Utilize  Types  and  Site  Classes.    Corrections 

for  Area 292 

229.  The  Use  of  Correction  Factors  for  Volume 293 

230.  Methods  Dependent  on  the  Use  of  Plots  Arbitrarily  Located 297 

231.  Estimating  the  Quahty  of  Standing  Timber 297 

232.  Method  of  Mill  Run  Applied  to  the  Stand 299 

233.  Method  of  Graded  Volume  Tables  AppUed  to  the  Tree 299 

234.  Method  of  Graded  Log  Rules  Applied  to  the  Log 299 

235.  Combination  Method  Based  on  Sample  Strips  and  Log  Tally 300 

236.  Limits  of  Accuracy  in  Timber  Estimating 301 

237.  The  Cost  of  Estimating  Timber _ 302 

238.  Methods  of  Training  Required  to  Produce  Efficient  Timber  Cruisers 303 

239.  Check  Estimating 308 

240.  Superficial  or  Extensive  Estimates 308 

241.  Estimating  by  Means  of  Felled  Sample  Trees 310 

242.  Method  of  Determining  the  Dimensions  of  a  Tree  Containing  the  Average 

Board-foot  Volume 311 

243.  The  Measurement  of  Permanent  Sample  Plots 312 

Part  III 
THE    GROWTH    OF    TIMBER 

CHAPTER  XXII 
PRINCIPLES  UNDERLYING  THE  STUDY  OF  GROWTH 

PAGE 

244.  Purpose  and  Character  of  Growth  Studies 315 

245.  Relation  between  Current  and  Mean  Annual  Growth 316 

246.  The  Character  of  Growth  Per  Cent 318 

247.  The  Law  of  Diminishing  Numbers  as  Affecting  the  Growth  of  Trees  and 

Stands 318 

248.  Yields,  Definition  and  Purpose  of  Study 320 

249.  Yield  Tables 321 

250.  The  Apphcation  of  Yield  Tables  in  Predicting  Yields 322 

251.  Prediction  of  Growth  by  Projecting  the  Past  Growth  of  Trees  into  the 

Future 323 

252.  The  Effect  of  Losses  versus  Thinnings  upon  Yields 324 

253.  The  Factor  of  Age  in  Even-aged  versus  Many-aged  Stands 325 

254.  The  Tree  or  Stem  Analysis  and  the  Limitations  of  its  Use 326 

255.  Relative  Utility  of  Different  Classes  of  Growth  Data,  and  Chart  of  Growth 

Studies 327 

CHAPTER  XXIII 
DETERMINING  THE  AGE  OF  STANDS 

256.  Determming  the  Age  of  Trees  from  Annual  Rings  on  the  Stump 335 

257.  Correction  for  Age  of  Seedling  below  Stump  Height. 336 

258.  Annual  Whorls  of  Branches  as  an  Indication  of  Age 337 

259.  Definition  of  Even-aged  versus  Many-aged  Stands 337 


TABLE  OF  CONTENTS  JCV 

PAGE 

260.  Average  Age,  Definition  and  Determination 337 

261.  Determining  the  Volume  and  Diameter  of  Average  Trees 338 

262.  Determining  the  Age  of  Average  Trees  and  of  the  Stand 339 

263.  Age  as  Affected  by  Suppression.    Economic  Age 341 

CHAPTER    XXIV 
GROWTH    OF   TREES    IN    DIAMETER 

264.  Purposes  of  Studying  Diameter  Growth 342 

265.  The  Basis  for  Determining  Diameter  Growth  of  Trees 342 

266.  The  Measurement  of  Diameter  Growth  on  Sections 342 

267.  The  Determination  of  Average  Diameter  Growth  from  the  Original  Data .   346 

268.  Correction  of  Basis  of  Diameter  Growth  on  Stump  to  Conform  to  Total 

Age  of  Tree 348 

269.  Correlation  of  Stump  Growi;h  with  D.B.H.  of  Tree 348 

270.  Factors  Influencing  the  Diameter  Growth  of  Trees  Growing  in  Stands.  .  .  .   351 

271.  Effect  of  Species  on  Diameter  Growth '. 351 

272.  Effect  of  Quahty  of  Site 352 

273.  Effect  of  Density  of  Stand 352 

274.  Effect  of  Crown  Class 353 

275.  Laws  of  Diameter  Growth  in  Even-aged  Stands,  Based  on  Age 354 

276.  Laws  of  Diameter  Growth  in  Many-aged  Stands,  Based  on  Diameter 357 

277.  Current  Periodic  Growth  Based  on  Diameter  Classes.     The  Increment 

Borer 358 

278.  Method  Based  on  Comparison  of  Growth  for  Diameter  Classes 360 

279.  ]\Iethod  Based  on  Projection  of  Growth  by  Diameter  Classes 361 

280.  Increased  Growth,  Method  of  Determination 363 

CHAPTER  XXV 
GROWTH  OF  TREES  IN  HEIGHT 

281.  Purpose  of  Study  of  Height  Growth 365 

282.  Influences  Affecting  Height  Growth 365 

283.  Relations  of  Height  Growth  and  Diameter  Growth 367 

284.  Measurement  of  Height  Growth 368 

285.  The  Substitution  of  Curves  of  Average  Height  Based  on  Diameter  for 

Actual  Measurement  of  Height  Growth.' 371 

CHAPTER  XXVI 
GROWTH  OF  TREES  IN  VOLUME 

286.  Relation  between  Volume  Growth,  Form  and  Diameter  Growth 374 

287.  Tree  Analysis,  its  Purpose  and  Application 374 

288.  Substitution  of  Volume  Tables  for  Tree  Analyses 375 

289.  Measurements  Required  for  Tree  Analyses 376 

290.  Computation  of  Volume  Growth  for  Single  Trees 377 

291.  Method  of  Substituting  Average  Growth  in  Form,  or  Tapers  for  Volume..  379 

292.  Substitution  of  Taper  Tables  for  Tree  Analyses 382 


xvi  TABLE  OF  CONTENTS 

CHAPTER  XXVII 
FACTORS  AFFECTING  THE  GROWTH  OF  STANDS 

PAGE 

293  Enumeration  of  Factors  Affecting  Growth  of  Stands 384 

294  Site  Factors  or  Quality  of  Site 384 

295  \'olume  Growth  a  Basis  for  Site  Quahties 385 

296  Height  Growth  a  Basis  for  Site  Quahties 386 

297.  ( )ther  Possible  Bases  for  Site  Qualities 387 

298  'I'ho  Form  of  Stands,  Even-aged  versus  Many-aged 388 

299  Annual  Increment  of  Many-aged  Stands 390 

300  'ilie  Effect  of  Treatment  on  Growth 391 

301  Density  of  Stocking  as  Affecting  Growth  and  Yields 392 

302.  Composition  of  Stands  as  to  Species 393 

CHAPTER  XXVIII 
NORMAL  YIELD  TABLES  FOR  EVEN-AGED  STANDS 

303.  Definition  and  Purpose  of  Yield  Tables 395 

304  Standards  for  Yield  Tables 395 

305  Construction  of  Yield  Tables,  Baur's  Method 396 

306.  Standard  for  "Normal"  Density  of  Stocking 397 

307.  Age  Classes 397 

308    Area  of  Plots 397 

309.  Measurements  Required  on  Each  Plot 398 

310    Construction  of  Yield  Table,  with  Site  Classes  Based  on  Height  Growth.  .  401 

311.  Rejection  of  Abnormal  Plots 404 

312.  Construction  of  Yield  Table,  with  Site  Classes  Based  Directly  on  Yields 

per  Acre 406 

313.  Yield  Tables  for  Stands  Grown  under  Management 407 

314.  Yield  Tables  for  Stands  of  Mixed  Species 408 

CHAPTER  XXIX 

THE  USE  OF  YIELD  TABLES  IN  THE  PREDICTION  OF 
GROWTH  IN  EVEN-AGED  STANDS,  WITH  APPLICA- 
TION TO   LARGE  AGE  GROUPS 

315.  Factors  Affecting  the  Probable  Accuracy  of  Yield  Predictions 412 

316.  Methods  of  Determining  Actual  or  Empirical  Density  of  Stocking 413 

317.  Application  of  Density  Factor,  in  Prediction  of  Growth  from  Yield  Tables  414 

318.  Separation  of  the  Factors  of  Volume,  Age  and  Area 416 

319.  Determination  of  Areas  from  Density  Factor 416 

320.  Ai)plication  to  Forest  having  a  Group  Form  of  Age  Classes 418 

321.  Determination  of  Volume  and  Area  for  Two  Age  Groups  on  Basis  of  Average 

Age 419 

322.  Application  of  Results  to  Forest  by  Use  of  Stand  Table  and  Per  Cent 421 

323 .  Determination  of  Volume  and  Area  for  Age  Groups  on  Basis  of  Diameter 

Groups • 422 

324.  The  Construction  of  Yield  Tables  Based  on  Crown  Space,  for  Many-aged 

Stands 422 

325.  Application  of  Method  to  Many-aged  Stands 425 

326.  Yield  Tables  for  Stands  Grown  under  Management 427 


TABLE  OF  CONTENTS  XVU 

CHAPTER  XXX 
THE  DETERMINATION  OF  GROWTH  PER  CENT 

PAGE 

327.  Definition  of  Growth  Per  Cent 429 

328.  Pressler's  Formula  for  Volume  Growth  Per  Cent 429 

329.  Pressler's  Formula,  Based  on  Relative  Diameter 430 

330.  Schneider 's  Formula  for  Standing  Trees 431 

331.  Use  of  Growth  Per  Cent  to  Predict  Growth  of  Stands 432 

332.  Use  of  Growth  Per  Cent  to  Determine  Growth  of  Stands  by  Comparison 

with  Measured  Plots 433 

333.  Use  of  Growth  Per  Cent  in  Forests  Composed  of  All  Age  Classes 434 

334.  Growth  Per  Cent  in  Quality  and  Value 435 

CHAPTER  XXXI 

METHODS  OF  MEASURING  AND  PREDICTING  THE   CUR- 
RENT OR  PERIODIC  GROWTH  OF  STANDS 

335.  Use  of  Yield  Tables,  in  Prediction  of  Current  Growth 436 

336.  Method  of  Prediction  Based  on  Growth  of  Trees,  with  Corrections  for 

Losses 436 

337.  Increased  Growth  of  Stands  after  Cutting 438 

338.  Reduced  Growth  of  Stands  after  Cutting 438 

339.  AppHcation  of  Yield  Tables  Based  on  Age,  to  Cut-over  Areas 441 

340.  Permanent  Sample  Plots  for  Measiu-ement  of  Current  Growth 443 

341.  Measurement  of  Increment  of  Immature  Stands  as  Part  of  the  Total 

Increment  of  a  Forest  or  Period 443 

342.  Comparative  Value  of  Current  Growth  versus  Yield  Tables  and  Mean 

Annual  Growth 445 

CHAPTER  XXXII 

COORDINATION  OF  FOREST  SURVEY  WITH  GROWTH 
DETERMINATION  FOR  THE  FOREST 

343.  Factors  Determining  Total  Growth  on  a  Large  Area 447 

344.  Data  Required  from  the  Forest  Survey 447 

345.  Site  Qualities,  Separation  in  Field 448 

346.  Relation  between  Volume  and  Age  of  Stands 449 

347.  Averaging  the  Site  QuaUty  for  the  Entire  Area 449 

348.  Growth  on  Areas  of  Immature  Timber 450 

349.  Effect  of  Separation  of  Areas  of  Immature  Timber  on  the  Density  Factor 

for  Mature  Stands 453 

350.  Stand  Table  by  Diameters  for  Poles  and  Saplings;  When  Required 454 

APPENDIX  A 
LUMBER  GRADES  AND  LOG  GRADES 

351.  Purpose  of  Log  Grades 455 

352.  Grades  of  Lumber 455 

353.  Basis  of  Lumber  Grades 455 


xviii  TABLE  OF  CONTENTS 

PAGE 

354.  Grades  for  Remanufactured  and  Finished  versus  Rough  Lumber 456 

355.  General  Factors  which  Serve  to  Distinguish  Lumber  Grades 456 

356.  Grouping  of  Grades  of  Rough  Lumber 457 

357.  Example  of  Grading  Rules 457 

358.  Relation  between  Grades  of  Lumber  and  Cull  in  Log  Scahng 458 

359.  Log  Grades,  Determination 459 

360.  Examples  of  Log  Grades 460 

361.  Mill-grade  or  Mill-scale  Studies 461 

362.  Method  of  Conducting  Mill-scale  Studies 462 

APPENDIX  B 
THE  MEASUREMENT  OF  PIECE  PRODUCTS 

363.  Basis  of  Measurement 466 

364.  Round  Products 466 

365.  Poles 467 

366.  Piling 470 

367.  Posts,  Large  Posts,  and  Small  Poles 471 

368.  Mine  Timbers 473 

369.  Cross  Ties 474 

370.  Inspection  and  Measurement  of  Piece  Products 477 

APPENDIX  C 

TABLES  USED  IN  FOREST  MENSURATION  (see  Index  of  Tables)  479 

APPENDIX  D 

BIBLIOGRAPHY 521 

INDEX 523 


TABLES 


44 

V 

48 

VI 

64 

VII 

66 

VIII 

Article         No.  Title  page 

32  I     Comparison  of  Results  Obtained  by  Scaling  the  Cubic  Con 

tents  of  Logs,  at  Small  End  and  at  Middle  of  Log 27 

38  II  Comparison  of  Per  Cents  of  Cubic  Contents  of  Cylinders 
Scaled  by  Various  Log  Rules,  for  Logs  18  Inches  in  Diam- 
eter at  Small  End,  with  2-inch  Total  Taper 37 

41  III     Relation  of  Cubic  and  Board-foot  Contents  of  16-foot  Logs 

with  a  Taper  of  1  inch  in  8  feet.  Based  on  Tiemann's  Log 
Rule  i^-inch  Saw  Kerf 41 

42  IV     Comparison  of  Blodgett  and  Tiemami  Log  Rules  for  Cer- 

tain Logs 42 

Effect  of  Different  Methods  of  Scaling  a  Log 45 

Gain  in  Output  Secured  bj^  Sawing  aroimd  Compared  with 

Slash  Sawing  in  Per  Cent  of  Latter  Output 48 

Distribution  of  Waste  between  Slabbing  and  Sawdust 56 

Thickness  of  Plank  to  be  Deducted  for  Slab  Waste  to  Coin- 
cide with  a  Collar  1.5  Inches  Thick.    Sawdust  Allowance 

20  Per  Cent 61 

5^  IX     Deductions  for  Slabbing  and  for  Saw  Kerf,  for.  12-inch  Logs, 

in  Ten  Log  Rules  Based  on  Formulae 62 

66  X    Over-run,  Doyle  Rule,  Texas 71 

XI     Over-run,  Doyle  Rule,  Ontario 71 

68  XII     Decimal  Values  below  12  Inches,  for  Scribner  Log  Rule 74 

76  XIII     Conversion  of  International  Rule  J-inch  Saw  Kerf  for  Other 

Widths  of  Kerf 81 

76  XIV     Conversion    of    Log    Rules  with    5 -inch  Saw  Kerf  and  No 

Shrinkage  Allowance  to  Other  Widths  of  Saw  Kerf 82 

XV     Per  Cent  of  Increase  in  Sawed  Lumber  Caused  by  Sawing 

Lumber  of  Different  Thicknesses 82 

XVI  Correction  in  Per  Cents  for  Contents  of  Logs  in  Superficial 
Board  Feet,  for  Lumber  Sawed  Less  than  1  Inch  in  Thick- 
ness   : 83 

83         XVII     Scaling  Practice,  or  "Scale"  in  Different  Logging  Regions.  .  .      94 
93       XVIII     Deductions  for  Crook  or  Sweep 116 

107  XIX     Solid  Contents  of  Stacked  Wood 127 

XX     Standard  Converting  Factors  for  Cordwood 129 

108  XXI     Influence  of  Length  of  Stick  upon  the  Solid  Cubic  Contents 

of  a  Cord 130 

XXII     Influence  of  Length  of  Stick  on  SoUd  Cubic  Contents  of  a 

Standard  Cord,  Balsam  Fir 130 

XXIII     Interdependence    of  the  Stick  Length  and   the   Volume   of 

Solid  Wood  per  Cord 131 

xix 


TABLES 


Article         No. 
109       XXIV 


112         XXV 


123       XXVI 
137     XXVII 


139  XXVIII 

140  XXIX 


141 


XXX 


142       XXXI 
152     XXXII 


168  XXXIII 


XXXIV 
183     XXXV 


184    XXXVI 


XXXVII 


191  XXXVIII 

XXXIX 

203 

XL 

220 

XLI 

224 

XLII 

XLIII 

228 

XLIV 

238 

XLV 

240 

XLVI 

246 

XLVII 

249 

XLVIII 

250 

XLIX 

257 


266 

269 


LI 
LII 


TITLE  PAGE 

Solid  Contents  of  a  Standard  Cord   Based  on    Diameter  of 

Stick.    Average  4-foot  Wood 131 

Measurement  of  4-foot  Round  Spruce  Pulpwood,  with  Cull 

Factors  Based  on  Solid  Cubic  Contents 134 

A  Portion  of  a  Volume  Table  Based  on  Mill  Factors 147 

Preliminary  Averages  for  Pitch  Pine.    Volume  Table  Based 

on  Diameter  and  Total  Height.   139  Trees.  . 165 

Comparison  of  Original  and  Harmonized  Average  Volumes.  .    171 
Volumes    Read   from    Curves   of  Volume  on  Diameter   for 

Different  Height  Classes 171 

Standard    Volume  Table   Read   from    Curves  of  Volume  on 

Height  for  Different  Diameter  Classes 174 

Local  Volume  Table,  Form 175 

Conversion  Factors  for  Second-growth  Hardwoods  by 
D.B.H.    Classes   with   Corresponding    Diameters   of     the 

Average  4-foot  Stick  in  the  Tree  or  in  the  Stack 181 

Form  or  Taper  for  White  Ash  Trees  of  Different  Diameters 
under   75  Years  of  Age,   Giving  Diameters  Inside  Bark  at 

Different  Heights  above  Ground 198 

Tapers  of  Loblolly  Pine,  Two  Trees 199 

True  Frustum  I'orm  Factors  for  Longleaf  Pine,  from  Frus- 
tums whose  Top  Diameter  Coincides  Exactly  with  the 
Average  Top    Diameters   of   Trees   of   Each    D.B.H.  and 

Height  Class 222 

Frustum  Form  Factors  for  555  Longleaf  Pines,  Coosa  Co., 
Alabama.     Based  on  Average  Top  Diameter  of  13.2  Inches 

for  Frustums 223 

Actual  Average  Top  Diameters  of  Merchantable  Lengths, 
Longleaf  Pine,  Coosa  Co.,  Ala.    Basis  555  Trees.    Average 

of  all  Top  Diameters,  13.2  Inches 224 

Errors  in  Using  Biltmore  Stick 232 

Figures  to  be  Used  in  Graduating  a  Biltmore  Stick 233 

Table  for  Determination  of  Form  Class  of  Trees  by  Means 

of  Position  of  Form  Point 250 

Relation  of  Width  and  Number  of  Strips  to  Area  Covered .  .   274 

Sizes  of  Circular  Plots 286 

Relation  between  Plots  and  Area  Covered 286 

Per  Cent  of  Total  Area  Required  in  Estimating 292 

Comparative  Estimates  of  a  Tract  of  40  Acres.  Board  Feet .    304 
Estimate  of  Taylor's  Creek  Logging  Unit,  Blooming  Grove 

Tract,  Pike  Co.,  Pa,,  1911 309 

Growth  of  Jack  Pine,  Minnesota 318 

Yield  Table  for  White  Pine 321 

Yield  Per  Acre  of    Spruce,  Cutting    to  Various  Diameter 

Limits 322 

Height  of    SeedUngs    at  Different  Ages,   Western   Yellow 

Pine,  Colfax  Co.,  New  Mexico 336 

Diameter  Growth  of  Five  Spruce  Stumps 345 

Stump  Tapers  Based  on  Stump  D.I.B.  for  Stumps  1   foot 
High 350 


TABLES 


XXI 


Article         No.  title  page 

LIII     Growth  of  Loblolly  Pine,  Old  Field,   in  D.B.H.   Based  on 

Age  of  Tree.    Urania,  La 350 

278  LIV     Current  Growth  of  Spruce,  Adirondacks  Region,  New  York .  360 

279  LV     Shortleaf  Pine,  Louisiana.  Growth  by  Diameter  Classes. . .  .  362 
LVI     Current  Growth,  Loblolly  Pine,  by  Diameters 363 

284  LVII     Height  Growth  of  Chestnut  Oak,  MUford,  Pike  Co.,  Pa 371 

288  LVIII     Growth  of  Chestnut  Oak  in  Cubic  Volume,  from  Diameter 

and  Height  Growth  and  Use  of  a  Standard  Volume  Table  376 

290  LIX     Stem  .Analysis  of  a  Tree 378 

296  LX     Standards  of  Site  Classification  Based  on  the  Height  of  Tree 

at  100  Years 387 

298  LXI     Average    Crown    Spread  of  Loblolly  Pine  in  the  Forest  at 

Vredenburgh,  Ala 389 

314  LXII     Normal  Yield  per  Acre  in  Cubic  Feet  and  Cords  of  Better 

Second-growth  Hardwood  Stands  in  Central  New  England  409 
LXIII     Percentage  of  the  Various  Species  in  Mixture  from  Table 

LXII  Classified  as  to  Type  and  Site  Class 410 

324  LXIV     Trees  per  Acre  Based  on  Crown  Space 425 

LXV     Yields    of   Cordwood,    for   Yellow   Poplar  in   Tennessee — 

Based  on  Crown  Space  and  Volumes  of  Trees  of  Given 

Ages 426 

337  LXVI     Adirondack  Spruce.  Average  Rate  of  Growth  in  Diameter 

on  the  Stump  of  1593  Trees  on  Cut-over  Land  at  Santa 

Clara,  New  York 440 

339         LXVII     Areas  Remaining  Stocked  on  Cut-over  Lands 443 

Appendix. 
365       LXVIII     Relation    between  Circumference    and  Diameter  for  White 

Cedar  Poles 467 

LXIX     Minimum    Dimensions    of  White    Cedar  Poles  in   Inches, 

Circumference,  Classes 468 

365  LXX     Minimum  Dimensions  of  Western  Red  Cedar  Poles  in  Inches  470 
LXXI     Minimum  Dimensions    of   Southern  Yellow  Pine  Poles   in 

Inches,  Circumference 471 

LXXII     Minimum  Circumference  of  Chestnut  Poles  in  Inches 472 

LXXIII     Minimum  Sweep  Poles,  Standard 472 

LXXIV     Minimum  Sweep  Poles,  Country 473 

366  LXXV     Dimensions  for  PiUng 473 

370       LXXVI     Board-foot   Converting  Factors  for  Various  Products,  U.  S. 

Forest  Service 478 

LXXVII     Cubic  Contents   of   Cylinders  and  Multiple  Table  of  Basal 

Areas 480 

LXXVIII     Areas  of   Circles  or  Table  of  Basal  Areas  for  Diameters  to 

Nearest  -jVinch 49O 

LXXIX     Tables    for    the  Conversion  of  the   Metric  to  the  English 

System,  and  Vice  Versa 492 

LXXX     The    International    Log    Rule    for  Saws    Cutting  a   J-inch 

Kerf 493 

LXXXI     Tables  for  Values  in   Schiffel's  Formula  for  Cubic  Volumes 

of  Entire  Stems 494 


xxu 


TABLES 


Article          No.  title                                                     page 

LXXXII     Breast-high  Form  Factors 497 

LXXXIII  Weights  per  Cord  of  Timber  of  \'arious  Species,  7-  to  8-inch 

Wood 498 

LXXXIV    Tiemann  Log  Rule  for  Saws  Cutting  a  ^-inch  Kerf 500 

LXXXV     Tiemann  Log  Rule  Reduced  to  Small  End  Diameters 502 

LXXXVI     Scribner  Decimal  C  Log  Rule 503 

LXXXVII     Index  to  Standard  Volume  Tables 505 

LXXXVni     Index  to  Yield  Tables 516 

LXXXIX     Index  to  Taper  Tables 519 


FOREST  MENSURATION 


PART  I 

THE  MEASUREMENT  OF  FELLED  TIMBER  AND  ITS 
PRODUCTS 


CHAPTER  I 
INTRODUCTION  TO  FOREST  MENSURATION 

1.  Definition  and  Purpose.  Forest  Mensuration  is  that  branch  of 
forestry  which  deals  with  the  determination  of  the  volume  of  the  wood 
material  contained  in  logs  or  portions  of  felled  trees,  in  standing  trees, 
in  stands  of  timber  and  in  forests,  expressed  in  terms  of  cubic  measure, 
board  measure,  or  any  other  unit.  It  also  determines  the  growth  and 
future  yields  of  trees,  stands,  and  forests  in  any  of  the  above  units  of 
volume.  The  measurement  of  standing  timber  is  termed  Timber 
Estimating  or  Timber  Cruising.  The  commercial  measurement  of  the 
contents  of  logs  is  called  Scaling. 

Forest  property  is  land  bearing  forest  trees  as  the  principal  vegeta- 
tion. The  trees  may  be  valued  for  their  appearance,  as  in  parks,  their 
protective  influences,  as  in  forests  at  headwaters  of  streams,  or  their 
wood,  as  in  all  forms  of  commercial  use,  including  by-products  such 
as  naval  stores  and  bark.  In  past  logging  operations  the  land  has  not 
always  been  regarded  as  true  forest  property,  capable  of  growing  other 
crops  of  trees;  but  unless  such  land  has  a  higher  economic  value  for 
agriculture,  grazing,  or  other  purposes  than  for  any  of  the  three  forest 
uses  above  mentioned,  it  is  as  truly  forest  property  as  the  timber. 
The  measurement  of  the  volume  and  growth  of  timber  is  an  indispen- 
sable factor  in  classifying  lands  for  their  highest  use,  whether  for  agri- 
culture or  forestry. 

Forest  Mensuration  makes  possible  the  systematic  management 
of  forest  property  by  ordinary  ])usiness  methods,  which  require,  first, 
a  knowledge  of  quantities  or  amount  of  material,  and  its  location  and 


2  INTRODUCTION  TO  FOREST  MENSURATION 

rate  of  production,'  and  second,  information  on  which  to  base  the  value 
of  the  property  for  the  purpose  of  sale,  exchange  or  the  appraisal  of 
damages. 

2.  Relation  between  Lumbering  and  Timber  Estimating.  The 
logging  of  timber  is  usually  conihictcd  as  a  Ijusiness  venture  entirely 
separate  from  the  growing  of  trees  or  management  of  forest  propertj^, 
but  whether  this  is  so,  or  the  forest  owner  cuts  and  logs  his  own  tim- 
ber, the  cost  of  the  logging  will  depend  in  a  great  measure  on  the  known 
quantity  of  timber  which  can  be  brought  out  over  a  given  route  and  by 
a  specific  method  of  logging.  The  greater  the  volume  of  standing 
timber,  the  greater  the  investment  which  is  justified  in  roads,  railroads, 
chutes,  or  flumes  to  cut  down  the  expense  of  hauling.  Overestimates 
cause  losses  through  excessive  investments;  underestimates  cause  losses 
through  not  investing  enough  money  in  these  transportation  systems. 
The  logger  cannot  wait  until  his  timber  is  cut  and  scaled  before  planning 
his  operation.  Accuracy  in  timber  estimating  is  therefore  an  under- 
lying factor  in  the  successful  conduct  of  the  business  of  lumbering. 

3.  Relation  between  Forestry  and  Growth  Measurements.  Lum- 
bering as  a  business  begins  at  the  stump,  w^hile  forest  production  may 
begin  with  the  seedling,  and  may  well  be  considered  as  a  separate  busi- 
ness enterprise.  The  growth  of  trees  is  the  basis  of  returns  on  this 
business,  no  matter  whether  these  returns  are  secured  on  the  stump,  or 
by  means  of  the  additional  operation  of  logging.  The  speculator  in 
standing  timber  hopes  to  realize  a  growth  in  unit  prices  such  as  was 
experienced  as  a  result  of  the  war.  But  the  business  of  forestr}^  depends 
for  its  profits  on  growth,  first,  in  volume,  and  second,  in  quality,  of  the 
product  by  reason  of  increased  sizes  and  improved  texture,  increase  in 
prices  being  merely  an  additional  guarantee  of  adequate  returns.  Since 
growth  determines  the  quantity  of  products  to  be  expected,  any  expen- 
diture in  planting  and  care  of  the  forest  can  be  undertaken  intelligently 
only  when  the  probable  rate  of  growth  per  acre  is  known.  The  study 
of  growth  is  therefore  a  necessary  part  of  the  business  of  forestry  and 
unless  growth  data  can  be   obtained,  there  is  no  possible  method  of 

1  A  business  is  an  undertaking  which  seeks  to  supply  a  pubhc  demand.  The 
most  common  form  of  business  is  that  which  produces  raw  materials  and  transforms 
them  into  finished  products  delivered  as  such  to  the  consumer.  Any  distmct  step 
in  this  process  may  and  often  does  constitute  a  separate  business.  To  accomplish 
the  purpose  of  its  existence,  a  business  deals  with  three  factors,  quantity,  location, 
and  time.  To  supply  forest  products  for  the  innumerable  demands  of  modern 
civilization,  a  well-conducted  business  ojieration  requires  full  knowledge  of  the 
quantity  of  raw  material  and  finished  products  with  which  it  deals,  their  location, 
and  the  time  or  periods  when  these  quantities  will  be  available.  Forest  Mensura- 
tion is  as  fundamental  to  forest  production  as  is  inventory  and  merchandise  account 
to  a  mercantile  business. 


RELATION  OF  MENSURATION  TO  FORESTRY  SUBJECTS  3 

determining  either  the  proper  investments  and  expenses,  or  the  probable 
returns  and  profits  from  such  an  enterprise. 

4.  Relation  between  Forest  Mensuration,  Stumpage  Values  and  the 
Valuation  of  Forest  Property.  In  determining  the  value  of  forest 
property  for  sale,  exchange,  or  the  appraisal  of  damages,  it  is  necessary- 
first  to  know  what  the  mature  standing  timber  is  worth  on  the  stump 
previous  to  cutting.  This  is  known  as  stumpage  value.  The  stumpage 
value  of  standing  timber  is  derived  from  the  value  of  the  finished  prod- 
ucts and  is  influenced  by  four  factors,  namely,  the  species  of  wood, 
its  quantity,  its  quality,  and  the  unit  price  of  the  product.  Forest 
mensuration  by  means  of  a  forest  survey  determines  as  accurately  as 
possible  the  first  three  factors.  By  determining  through  an  appraisal 
the  price  of  stumpage  for  the  different  kinds  and  qualities  of  timber 
found  on  the  area,  the  value  of  the  timber  may  be  found. 

The  value  of  young  timber  and  of  forest  soil  can  be  calculated  after 
the  possible  yields  at  given  ages  have  first  been  approximated  and  the 
stumpage  value  has  been  appraised  for  this  final  yield. 

5.  Relation  of  Mensuration  to  Other  Forestry  Subjects.  The  rela- 
tion of  Forest  Mensuration  to  other  subjects  in  forestry  is  shown  in 
Fig.  1.  In  the  threefold  division  of  forestry  indicated,  mensuration 
falls  in  the  mathematical  or  business  group,  but  is  included  in  the  phys- 
ical branch  of  that  group  which  deals  directly  with  the  forest. 

Mathematics  is  the  basis  of  Mensuration,  since  the  latter  subject 
deals  primarily  with  quantities.  But  as  both  timber  estimating  and 
growth  data  must  usually  be  expressed  on  terms  of  area  or  acreage, 
Mensuration  rests  directly  on  Surveying. 

Mensuration  in  turn  furnishes  the  quantitative  data  required  by 
the  science  of  Forest  Finance  as  a  basis  on  which  to  compute  the  cost  of 
production  and  the  probable  returns  from  forestry  and  to  indicate  the 
choice  of  methods  to  use  in  forest  production.  Although  it  falls  in  the 
business  group,  and  is  a  basic  subject  underlying  Forest  Management, 
Mensuration  is  a  statistical  science  similar  to  Forest  Finance.  Neither 
subject  constitutes  an  applied  science,  which  is  the  characteristic  of 
Forest  Management.  Mensuration  is  therefore  not  a  direct  subdivision 
of  Management,  but  a  distinct  subject  preparatory  to  Management. 

6.  Absolute  versus  Relative  Accuracy  in  Mensuration.  Forest 
Mensuration  attempts  to  secure  as  close  an  approach  to  mathematical 
accuracy  as  the  conditions  of  the  problem,  the  use  to  which  the  data  are 
put,  and  the  cost  of  the  work  will  permit.  In  scaling,  the  volumes  of 
logs  are  determined  before  sawing,  and  in  timber  estimating,  the  contents 
of  trees  and  stands  are  obtained  before  felling.  But  no  log  rule  will 
give  the  exact  quantity  of  lumber  which  will  be  sawed  from  a  given 
log,  and  no  tree  volume  table  can  predict  the  output  in  boards  from  a 


4  INTRODUCTION  TO  FOREST  MENSURATION 

given  tree,  since  these  results  will  vary  with  the  methods  and  conditions 
of  sawing  and  of  utilization. 


Forest  Physiography 
Dendrology 
Forest  Pk-ology 
Forest  Entomology 
Wood  Technology 

Silviculture 
Forest  Engineering 
Lumbering 
Wood  Using  Industriea 
Forest  Protection 

'?■  1 

So 

Geology 
Botany 
Zoology 
Mechanics 

y 

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1 

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=  1 

Forest 

Economics 
Forest 

History 

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S-3  s  =^  s 

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Again,  in  estimating  timber  it  is  seldom  possible  to  measure  every 
tree,  on  account  of  the  time  and  expense  involved.     For  this  reason, 


FOREST  SURVEY  5 

only  an  average  portion  of  the  stand  may  be  measured.  The  laws  of 
averages,  or  of  sampling  are  applied  to  solve  nearly  every  problem  in 
Forest  Mensuration,  in  order  to  bring  the  cost  of  the  field  work  within 
practical  limits. 

When  Mensuration  deals  with  the  growth  of  trees  and  stands,  and 
of  whole  forests,  its  purpose  is  to  predict  what  will  occur  in  the  future. 
It  bases  these  predictions  upon  the  results  which  have  occurred  in  the 
past,  under  conditions  judged  to  be  similar  to  those  which  will  affect 
these  future  stands.  The  laws  of  growth  of  trees,  and  especially,  of 
stands  composed  of  great  numbers  of  trees  competing  with  each  other 
for  existence  and  supremacy,  can  only  be  approximated  on  the  basis  of 
probabilities  and  averages.  The  results  of  living  forces  cannot  be 
predicted  with  mathematical  accuracy,  and  the  study  of  growth  par- 
takes of  the  nature  of  research  rather  than  of  routine  measurement  of 
definitely  determinable  quantities. 

Neither  Forest  Mensuration  nor  Forest  Surveying  produces  any 
physical  change  or  improvement  in  the  forest,  as  does  the  application  of 
silviculture,  protection,  and  lumbering.  The  achievements  of  forestry 
depend  upon  the  amount  and  character  of  the  actual  work  done  along 
these  latter  lines.  Misdirected  work,  done  at  the  wrong  time  or  place 
and  in  the  wrong  quantity,  or  by  too  expensive  a  method  when  com- 
pared with  results,  means  waste,  inefficiency,  and  ultimate  ruin  and 
bankruptcy  of  the  enterprise.  The  data  supplied  by  mensuration  and 
supplemented  by  forest  finance  are  the  balance  wheel  of  forest  industry. 
But  the  necessity  of  restricting  the  funds  expended  upon  the  mere  col- 
lection of  data  to  as  small  a  per  cent  as  possible  of  the  total  budget  of 
expenditures,  reserving  the  greater  portion  for  the  operations  which 
effect  actual  change  in  the  forest,  is  obvious  and  justifies  the  use  of  meth- 
ods based  on  averages  rather  than  extreme  mathematical  accuracy. 

7.  Forest  Survey.  Forest  Survey  is  the  general  term  applied 
to  the  project  of  gathering  all  the  quantitative  data  required  regarding 
a  specific  forest  property.  It  includes  a  survey  and  maps  of  the  area, 
thus  locating  the  property  and  its  subdivisions,  a  measurement  of  the 
volume  and  character  of  the  timber,  and  it  may  cover  other  resources 
such  as  land  classification,  waters,  forage,  game,  and  fish.  Forest 
Surveying  and  Forest  Mensuration  deal  with  the  principles  and  methods 
of  accomplishing  this  work.  The  Survey  itself  is  the  enterprise  or 
project  of  securing  the  data.  Accuracy  in  the  results  of  a  forest  survey 
is  judged,  not  on  an  absolute  standard,  but  in  relation  to  the  balance 
between  utility  of  the  results  and  the  cost  of  obtaining  them,  and  is 
therefore  always  a  relative  term. 


CHAPTER  II 
SYSTEMS  AND  UNITS  OF  MEASUREMENT 

8.  Systems     of     Measurement     Used     in     Forest     Mensuration. 

Throughout  the  United  States  and  Canada  the  Enghsh  system  of 
measure  is  used  in  all  practical  applications  of  Mensuration.  In  the 
Philippines  the  metric  system  is  the  standard.  (Appendix  C,  Table 
LXXIX.)  Efforts  to  substitute  the  metric  system  in  the  United  States 
for  the  units  established  by  custom  have  so  far  failed,  though  its  use 
was  sanctioned  bj^  Congress  in  1866.  Mensuration  is  applied  more 
generally  to  the  solution  of  practical  problems  such  as  timber  estimating 
than  to  purely  scientific  research,  and  for  the  former,  the  results  must 
be  expressed  in  the  customary  units  to  be  intelligible.  Scientific  forest 
measurements  have  also,  except  in  a  few  instances,  been  expressed  in 
English  units. 

In  measuring  distances  and  areas,  the  chain  of  66  feet,  or  4  rods, 
is  a  commonly  used  unit.  Five  chains  constitute  a  tally,  or  20  rods; 
and  16  tallies,  or  80  chains,  equal  1  mile.  One  tally  forms  the  side  of  a 
square  2^  acres  in  area.  Distances  are  commonly  measured  by  pacing, 
or  counting  the  number  of  paces,  the  average  length  of  the  individual 
pace  having  been  determined  by  previous  tests.  A  true  pace  is  the 
swing  of  one  foot,  or  twice  the  length  of  a  step.  In  counting,  the  pace 
rather  than  the  step  should  be  used,  since  it  reduces  the  count  by  half. 

The  acre,  containing  160  square  rods  or  43,560  square  feet,  is  the 
unit  of  area.  In  the  rectangular  system  of  survey  adopted  by  the 
United  States  the  following  definitions  apply: 

Township — a  tract  approximately  6  miles  square  containing 
36  sections. 

Section — a  rectangular  tract  containing  approximately  1  square 
mile  or  640  acres,  but  which  may  contain  more  or  less 
than  this  area  in  irregular  surveys. 

Quarter  Section — a  subdivision  of  a  section  containing  approxi- 
mately 160  acres. 

"  Forty  " — a  colloquial  term  describing  a  j^th  section  or  quarter 
of  a  quarter  section  containing  approximately  40  acres. 

Lot — a  tract  ordinarily  containing  not  less  than  20  or  more  than 
60  acres,   but  which   may   contain  less  area,   of  either 


PIECE  MEASURE  7 

rectangular  or  ii-regular  shape,  and  which  takes  the  place 
of  the  "  forty  "  in  irregular  surveys  or  bordering  lakes 
or  streams.^ 

In  measuring  trees,  the  foot  is  the  standard  for  height,  and  the 
inch,  divided  into  tenths  of  inches,  for  diameter.  Basal  area  is  the  cross- 
sectional  area  of  a  tree  or  stand,  in  square  feet,  measured  at  4|  feet  from 
the  ground.  This  is  obtained  from  area  of  circles  whose  diameters  equal 
those  of  the  trees  measured. 

9.  Piece  Measure.  Wood  products  which  are  used  in  the  round,  arid 
logs  or  bolts  which  are  barked,  shaped,  and  reduced  to  standard  dimen- 
sions where  felled,  are  usually  measured  and  sold  by  the  piece.  These 
pieces  are  graded  by  size  and  by  quality  into  accepted  pieces  and  culls, 
or  rejects,  whose  defects  render  them  unfit  for  the  special  purpose 
required.  The  standard  sizes  are  determined  by  specifications,  which 
also  prescribe  the  species  of  tree  and  the  required  quality  of  the  product. 
The  principal  products  purchased  on  this  basis  are  cross  ties,  poles, 
posts,  piles,  and  mine  timbers. 

Where  bolts  of  uniform  size  are  sawed  or  split  for  manufacture 
into  special  products,  they  may  be  counted  and  paid  for  by  the  piece. 
Their  average  volume  is  determined  beforehand.  When  the  number 
of  pieces  per  cord,  or  per  thousand  board  feet  is  agreed  on,  the  payment 
may  be  in  terms  of  these  latter  units. 

Linear  measure  is  sometimes  used  for  pieces  of  standard  width  and 
thickness  but  of  variable  length.  Such  products  are  sold  by  the  linear 
foot.     This  standard  is  widely  used  for  piling. 

10.  Cord  Measure.  When  the  pieces  into  which  trees  are  sawed  or 
split  are  of  lengths  shorter  than  ordinary  logs,  and  of  irregular  shape, 
the  expense  of  determining  separately  the  contents  of  each  piece  is 
avoided  by  stacking  them  in  regular  piles  or  cording  them  up,  and 
measuring  only  the  exterior  dimensions  of  the  stack  to  get  the  total 
stacked  cubic  space  occupied.  This  stacked  cubic  measure  does  not 
indicate  the  solid  contents,  which  may  vary  widely.  But  if  the  average 
per  cent  of  solid  contents  per  cubic  foot  of  stacked  measure  is  known  for 
sticks  of  given  sizes  and  character,  this  stacked  measurement  becomes 
a  practical  and  serviceable  standard,  though  not  well  suited  to  scientific 
investigations. 

The   cord   is   the   standard   generally   adopted   for   stacked   wood. 

1  References.  Manual  of  Surveying  Instruction  for  the  Sur^'ej'  of  the  Public 
Lands  of  the  United  States  and  Private  Land  Claims,  Commissioner  of  the  General 
Land  Office,  Washington,  D.  C,  Government  Printing  Office,   1902. 

Manual  for  Northern  Woodsmen,  Austin  Gary,  Part  I.  Section  VIII,  1918. 
Harvard  University  Press,  Cambridge,  Mass. 


8  SYSTEMS  AND  UNITS  OF  MEASUREMENT 

The  standard  cord  is  4  by  4  by  8  feet,  containing  128  cubic  feet.     There 
are,  however,  other  cord  units  in  use  (Chapter  IX). 

11.  Cubic  Measure.  The  cubic  volume  of  trees  and  logs  affords 
the  only  basis  of  accurate  and  permanent  scientific  records,  and  a  uni- 
form standard  of  measurement.  For  this  purpose  the  cubic  foot  should 
be  used  as  the  standard  unit. 

Where  cubic  volume  was  employed  by  lumbermen,  other  cubic 
units,  whose  contents  were  based  on  cylinders  of  given  sizes,  have  been 
adopted  arbitrarily.  These  units  possess  no  advantages  over  the  cubic 
foot  (Chapter  IV). 

In  most  regions,  the  desire  to  express  the  contents  of  logs  in  terms  of 
sawed  lumber  prevented  the  adoption  of  the  cubic  foot  as  the  standard 
of  measurement  for  logs. 

12.  Board  Measure.  Board  measure  may  be  defined  as  a  cubic 
standard  for  measuring  sawed  lumber.  A  board  foot  is  a  board  1  foot 
square  and  1  inch  thick.  Twelve  board  feet  of  sawed  lumber  equal  1 
cubic  foot.  The  board-foot  contents  of  sawed  lumber  is  found  by 
multiplying  the  product  of  the  width  and  thickness  in  inches  by  the 
length  in  feet  and  dividing  b}'  12. 

13.  Log  rules.  A  log  rule  is  a  table  giving  the  contents  of  logs  of 
different  diameters  and  lengths.  The  unit  of  volume  used  may  be 
based  on  cubic  measure,  or  board  feet.  The  latter  form  of  table  differs 
from  that  based  on  cubic  contents  since  it  indicates  onlj^  the  net  volume 
of  the  product  in  boards  which  result  from  sawing  the  log.  The  use  of 
such  log  rules  is  to  measure  the  contents  in  the  log  before  sawing,  as 
a  basis  of  sale  of  logs  or  for  other  purposes  requiring  such  measurement. 
Fixed  or  arbitrary  values  are  assigned  or  agreed  upon  for  logs  of  each 
diameter  and  length.  The  table  thus  becomes  a  standard  of  measure- 
ment based  upon  a  unit  of  volume. 

This  method  of  measuring  logs  has  consequently  led  to  the  develop- 
ment of  numerous  log  rules  whose  construction  is  discussed  in  Chapters 
IV,  V  and  VI.  These  rules  differ,  some  of  them  greatly,  for  logs  of 
the  same  dimensions. 

To  secure  the  universal  adoption  of  a  single  log  rule  which  is  at  once 
accurate  and  acceptable  is  probably  an  impossible  task,  and  several  of 
the  more  widely  used  ones  will  no  doubt  continue  as  standards. 

14.  Measurement  of  Standing  Timber,  Postponed  till  after  Manu- 
facture. This  lack  of  standardization  as  to  units  for  board-foot  contents 
of  logs  inevitably  reacts  upon  the  accuracy  and  consistency  of  measure- 
ments of  the  board-foot  contents  of  standing  timber.  The  contents 
of  a  given  stand  will  vsiry  widely  with  the  log  rule  used  in  estimating. 

The  custom  of  estimating  standing  timber  in  terms  of  the  product 
is  not  confined  to  measurement  by  board-foot  log  rules.     Hewn  ties, 


MEASUREMENT  OF  STANDING  TIMBER  IN  THE  TREE  9 

poles,  staves  and  other  piece  products  are  customarily  used  as  units  for 
timber  estimating,  when  the  timber  is  to  be  used  for  these  purposes. 

Thus  the  standard  commonly  sought  in  America  for  measuring  stand- 
ing timber  is  the  net  merchantable  volume,  which  results  from  deducting 
all  forms  of  waste  in  manufacture  from  the  total  contents  of  the  tree. 

There  is  but  one  accurate  method  of  measuring  this  net  contents, 
and  that  is  to  postpone  the  measurement  until  the  timber  is  logged 
and  manufactured  into  boards  or  other  products.  Since  a  purchaser  of 
standing  timber  is  always  conservative  wherever  a  doubt  exists,  it  is  to 
the  owner's  interest  to  sell  on  the  basis  of  actual  mill  cut  of  boards  or 
output  of  other  products,  whenever  this  is  possible.  This  basis  is 
often  used  in  regions  where  the  timber  is  cut  by  small  portable  mills, 
located  in  or  near  the  tract  and  where  small  amounts  are  purchased. 

15.  Measurement  of  Standing  Timber  Postponed  till  after  Logging. 
Where  the  logs  must  be  driven  down  streams  or  hauled  long  distances 
by  the  purchaser,  this  basis  becomes  impractical  both  l^ecause  of  the 
delay  in  settlement  of  account  and  the  difficulty  of  checking  the  output 
of  lumber.  The  timber  owner  is  thus  forced  to  substitute  a  log  scale  for 
a  mill  tally  of  lumber.  This  scale  is  always  based  on  some  log  rule  agreed 
upon  beforehand,  and  may  or  may  not  give  results  coinciding  with  the 
actual  sawed  output.  If  the  log  rule  is  known  to  be  inaccurate,  the 
excess  or  deficiency  of  manufactured  products  can  be  ascertained  only 
by  a  comparison  of  the  mill  tally  with  the  log  scale.  Such  comparisons 
will  give  an  idea  of  over-run  or  under-run  (§46).  The  owner  can  then 
adjust  the  price  in  subsequent  sales  of  logs  according  to  the  difference 
between  the  scaled  contents  of  his  logs  and  their  probable  output  in 
sawed  lumber. 

16.  Measurement  of  Standing  Timber  in  the  Tree.  But  even  the 
log  scale  is  inapplicable  when  standing  timber  is  purchased  in  large 
amounts  and  a  long  period  is  required  for  completion  of  logging.  The 
owner  desires  prompt  payment  even  if  based  on  a  less  accurate  measure- 
ment of  volume.  The  volume  of  the  standing  timber  must  be  measured 
as  well  as  possible,  and  since,  at  best,  only  the  diameter  of  the  trees 
together  with  a  few  heights  can  be  actually  determined  and  the  rest  of 
the  work  is  done  ocularly  or  by  guess,  the  result  is  only  a  rough  estimate. 
This  method  has  given  rise  to  the  term  Timber  Estimating.  The  prin- 
cipal sources  of  error  in  timber  estimating  lie  in  the  effort  to  arrive  at  the 
net  merchantable  contents  minus  waste,  in  the  use  of  inaccurate  and 
variable  standards  of  log  measure  for  this  purpose,  and  in  the  difficulty 
and  cost  of  determining  even  the  superficial  dimensions  of  standing  trees. 
This  leads  to  short-cut  methods,  approximations  and  guess  work  and 
calls  for  the  development  of  system  and  of  personal  skill.  One  improve- 
ment in  timber  estimating  widely  used  by  foresters  is  the  tree-volume 


10  SYSTEMS  AND  UNITS  OF  MEASUREMENT 

table,  which  gives  the  average  contents  of  entire  trees  of  different  dimen- 
sions, in  terms  of  standard  log  rules  or  other  units,  tlius  eliminating  a 
certain  amount  of  ocular  work. 

17.  Need  of  Standardization  for  Both  Commercial  and  Scientific 
Measurements.  The  justification  of  the  use  of  standards  which  give 
the  contents  of  standing  timber  in  terms  of  products,  rather  than 
actual  cubic  volume,  lies  in  the  fact  that  the  value  of  the  timber,  standing 
or  cut,  depends  upon  the  volume  and  quality  of  these  products  and  not 
upon  the  cubic  volume. 

Had  it  been  possible  to  secure  the  adoption  of  a  uniform  standard 
of  conversion  into  board  feet,  the  use  of  this  standard  would  be  more 
serviceable  than  the  apparently  simpler  cubic  standard.  But  in  prac- 
tice the  same  motives  which  here  gave  rise  to  standards  based  on  products 
have  led  the  French  to  adopt,  as  substitutes  for  cubic  measurement, 
rules  of  thumb  which  are  less  accurate  by  far  than  many  of  our  log 
rules.  ^ 

The  greatest  drawback  to  the  use  of  units  intended  to  measure 
the  product  directly  lies  not  in  their  character  but  in  their  inaccuracy 
and  in  the  multiplicity  of  standards.  It  is  easily  seen  that  volume 
tables  and  measurements  of  growth  which  are  based  on  some  widely 
used  commercial  log  rule  may  coincide  with  custom,  but  are  incapable 
of  use  or  comparison  with  other  log  rules  (§  77)  and  are  inaccurate  as 
a  scientific  basis  of  measuring  growth  or  volume.  This  fact  has  led  to 
endless  duplication  of  effort  and  has  been  the  chief  reason  for  the  lack 
of  real  progress  in  accumulating  standard  data  on  volume  and  growth 
of  American  trees. 

A  continuance  of  such  duplication  of  effort  will  hinder  the  progress 
of  forestry  in  America,  which  must  depend  in  a  large  part  upon  the 
accuracy  of  volume  and  growth  data  gathered  by  forest  measurements. 
While  the  local  value  of  data  based  on  log  rules  sanctioned  by  custom 
will  continue,  these  field  data  should  be  gathered  in  such  form  as  to  be 
of  permanent  value  independent  of  these  variable  local  standards. 

It  is  possible  to  convert  all  measurements  to  the  common  standard 
of  cubic  feet,  which  gives  a  basis  of  scientific  comparison  between  the 
volumes  of  different  trees  and  species,  and  a  permanent  basis  for  measure- 
ment of  growth  for  trees  and  stands.  It  is  also  possible  to  adopt,  for 
the  purposes  of  permanent  record,  a  log  rule  based  on  scientific  principles 
which  will  give  an  equally  reliable  comparison  of  the  contents  of  trees  in 
board  feet  and  the  growth  of  stands  expressed  in  this  unit  of  product. 

But  for  a  permanent  record  from  which  the  volumes  of  trees  may  be 
derived  in  any  unit  of  product,  standard  or  local,  the  average  form  of  the 

1  Mensuration  in  France,  Donald  Bruce,  Journal  of  Forectry,  Vol.  XVII,  1919, 
p.  686. 


FORMS  OF  PRODUCTS  11 

tree  is  required,  as  expressed  in  diameters  at  different  points  on  the 
stem.  Investigations  of  tree  form  are  therefore  at  the  root  of  all  per- 
manent progress  in  Mensuration  (Chapter  XVI). 

18.  Forms  of  Products  into  which  the  Contents  of  Trees  are  Converted.  The 
products  manufactured  from  trees  may  be  classed  according  to  the  following  group- 
ing: 

Group  I.     Manufactured  products  of  definite  form,  retaining  the  wood  structure 
and  requiring  waste  in  manufacture. 

A.  Manufactured  from  logs. 

1.  Lumber 

a.  For  construction. 

r.  Structural  timbers. 

2'.  Dimension. 

3'.  Boards. 

4'.  Remanufactured  or  planing  mill  products. 

5'.  Special  products. 

6'.  For  export. 
h.  For  remanufacture.     Square  edge  or  round  edge. 

1.'  For  mill  work,  furniture,  fixtures. 

2/  For  utensils  and  supplies. 

3.'  Boxes  and  containers. 

2.  Veneers. 

3.  Manufactured  direct  from  log  for  finished  articles. 

B.  Manufactured  from  bolts. 

Billets,  flitches,  squares,  blocks,  shingles,  spokes,  staves,  etc. 

C.  Manufactured   from   mill   refuse,    i.e.,    from   slabs,   trimmings   and 

edgings.     Shingles,  lath,  boxboards,  etc. 
Group  II.     Bulk  products  in  which  the  form  or  both  form  and  structure  are 
destroyed. 

1.  Excelsior. 

2.  Wood  pulp. 

a.  Mechanical. 
h.  Chemical. 

3.  Distillates. 

4.  Ex-tracts. 

5.  Fuel. 

a.  Charcoal, 
h.  Fuel  wood. 

6.  Bark. 

Group  in.     Piece  products  retaining  in  whole  or  in  part  the  original  form. 

1.  Round  products, 
Poles,  piling,  posts,  etc. 

2.  Shaped  products, 
Hewn  cross  ties. 

r.  Standard  ties. 
2'.  Mine  ties. 

Group  I.  In  converting  round  logs  into  lumber,  there  is  unavoidable  waste  in 
sawing  due  to  the  difference  in  shape  between  the  products  desired  and  the  log, 
and  to  the  saw  kerf.     The  per  cent  of  waste  depends  upon  the  dimensions  of  the 


12 


SYSTEMS  AND  UNITS  OF  MEASUREMENT 


smallest  board  which  is  merchantable,  and  upon  the  thickness  of  saw  used.  Further 
intensive  utilization  of  slabs  (pieces  slabbed  off  from  the  round  surface  of  logs  in 
sawing)  and  of  edgings  (pieces  cut  from  the  edges  of  boards  to  give  parallel  edges 
and  remove  bark),  by  manufacture  into  sawed  products  depends  upon  finding  a 
market  for  pieces  whose  size  is  small  enough  to  permit  of  their  manufacture  from 
these  otherwise  waste  products. 

The  waste  in  manufacturing  articles  direct  from  the  log  depends  on  the  shape 
of  the  manufactured  article  with  reference  to  the  bolts  from  which  it  is  made.  Unless 
profitable  use  can  be  found  for  the  portions  so  wasted,  or  unless  antiquated  methods 
and  machinery  are  in  use,  the  portions  of  a  tree  or  log  lost  in  manufacture  cannot 
be  regarded  as  wasted,  any  more  than  the  loss  in  bulk  of  a  rough  block  of  stone  in 
process  of  transformation  under  a  sculptor's  hand  is  considered  waste.  It  is  for 
this  group  that  log  rules  are  required. 


"Woods  Waste 
16M 


Mill  Waste 
•14.3s« 


Lumber 
39.l!« 


r 

^\^ 

•^ 

Tops 
Limbs 
Stumps 

5  ^ 

-^1 

Seasoned 

L^nplaned 

Lumber 

33.5^ 

'Careless  mfg. 
miscellaneous  2.55* 


5  TYPICAL  INDUSTRIES 
Rough  Lumber  100 jS 


Factory  Waste 

Finished  Product 

«l 

Planing  Mill  Products 

96^ 

■„  1 

Car  Construction 

89^ 

^     1 

Boxes 

m 

25:^ 

Furniture 

75^ 

2^i 

Vehicles 

755^ 

ill 

III 


Fig.  2. — The  percentage  of  utilization  of  the  volume  of  a  tree  when  manufactured 
into  lumber. 


Group  II.  To  this  group  belong  also  those  waste  products  from  Group  I  for 
which  use  as  bulk  materials  can  be  found.  The  characteristics  of  this  grou])  are 
that  the  entire  volume  of  the  log,  and  a  much  larger  per  cent  of  the  volume  of  the 
tree  is  utilized  than  in  Group  I.  Material  may  be  taken  to  very  small  diameters, 
since  size  is  not  a  requisite  of  utility  but  merely  a  convenience  in  handling.  For 
this  group,  cubic  volume  is  the  required  standard  of  measurement,  and  the  use  of 
stacked  cubic  measure  is  customary. 

Group  III.  Nearly  all  the  round  or  shaped  products  in  this  group  may  also  be 
obtained  from  larger  logs  by  sawing  as  poles,  ties,  fence  posts,  in  which  case  they 
can  be  measured  for  their  contents  in  sawed  lumber.  For  round  products,  as  poles, 
piles  or  posts,  or  for  hewn  products,  as  hewai  or  "  pole  "  ties,  the  niunber  of  pieces 
of  standard  sizes  and  shaj)es  is  the  simplest  method  of  measurement.  For  this 
group  the  important  factor  in  measurement  is  the  set  of  specifications  which  deter- 
mine the  grades  of  product.  The  waste  to  be  expected  in  manufacture  under  Group  I 
is  shown  in  Fig.  2. 


THE  FACTOR  OF  WASTE  IN  MANUFACTURE  13 

19.  The  Factor  of  Waste  in  Manufacture.     A  waste  product  is  one  for  which  a 

profitable  use  has  not  been  found.  It  is  not  sufficient  that  the  product  could  be  used 
for  some  purpose  if  it  could  be  transported  to  some  place  other  than  the  site  of  its 
first  appearance  as  waste.  The  value  of  the  product  must  be  such  as  to  bear  the 
cost  of  manufacture  and  transportation  plus  a  profit.  Unless  some  portion  of  a 
tree  yields  products  which  fulfill  these  conditions,  the  whole  tree  remains  unutilized 
to  finally  die  and  rot,  a  true  waste  product  of  nature.  In  inaccessible  places,  entire 
stands  go  to  waste. 

Waste  in  tops  and  limbs  represents  those  portions  of  the  tree  which  under  the 
existing  conditions  do  not  yield  profitable  products.  But  little  deliberate  or  inexcus- 
able waste  occurs  over  any  long  period  without  discovery  and  correction.  The 
per  cent  of  waste  for  unprofitable  portions  of  the  trees  is  often  as  high  as  50  per  cent 
for  staves  or  other  special  products  and  2.5  per  cent  or  over  for  lumber.  The  average 
of  16.6  per  cent  shown  in  Fig.  2  for  lumber  is  far  too  high  for  bulk  products  such 
as  pulp  wood  or  for  trees  with  small  limbs  and  boles  of  regular  form. 

Bark  is  atypical  example  of  a  "waste"  product.  As  fuel,  it  is  not  wasted.  When 
tannin  extract  or  cork  is  jnelded  it  is  carefully  gathered.  For  lumber,  it  is  entirely 
wasted,  except  as  incidental  fuel.  The  waste  in  sawdust,  slabs,  edgings  and  factory 
finishing,  when  reduced  to  the  lowest  possible  terms  by  good  machinery,  can  hardly 
be  regarded  as  avoidable  waste,  since  the  product  which  results  from  this  apparent 
waste  has  a  value  much  higher  and  a  utility  much  greater  than  before  the  "  lo.ss  " 
of  the  extra  bulk. 

When  this  sawdust  and  refuse  is  used  as  fuel  in  the  mill,  as  is  now  the  common 
practice,  it  replaces  coal,  thus  not  only  effecting  a  great  economy  but  performing  an 
important  public  function  in  saving  transportation  costs  on  coal.  The  only  real 
waste  in  manufacture  is  where  methods  are  used  which  unduly  increase  sawdust 
and  slab  waste  at  the  expense  of  finished  products.  Waste  caused  by  seasoning  of 
wood  is  not  avoidable,  and  increases  the  value  of  the  product  in  greater  ratio  than 
its  loss  in  bulk. 

The  per  cent  of  actual  avoidable  waste  in  utilization  of  the  tree  is  difficult  to 
determine  or  to  prove.  It  constitutes  the  per  cent  of  difference  between  what  is 
utilized  in  higher  forms,  and  what  cotild  be  utilized  under  the  same  economic  condi- 
tions, at  a  profit.  It  is  a  measure  of  the  efficiency  and  alertness  of  the  operator, 
and  will  seldom  exceed  from  5  to  10  per  cent  even  under  exceptionally  bad  conditions; 
while  under  good  management  this  avoidable  waste  is  probably  not  over  from  2  to 
5  per  cent. 

The  utilization  of  small-sized  pieces  and  bulk  products  not  only  reduces  the  per 
cent  of  waste  in  single  trees,  but  brings  entire  trees  of  smaller  dimensions  into  the 
merchantable  class,  thus  increasing  the  per  cent  of  volume  in  a  stand  of  timber 
which  is  merchantable,  and  k)wering  the  age  at  which  trees  can  be  marketed.  Since 
the  number  of  trees  per  acre  rapidly  diminishes  with  increasing  size,  close  utilization 
of  small  diameters  will  very  greatly  increase  the  per  cent  of  merchantable  volume 
in  young  stands  and  reduce  the  per  cent  of  waste  by  natural  losses  of  trees  before 
they  reach  the  larger  diameters. 

20.  Actual  versus  Superficial  Contents  of  Sawed  Lumber.  The  variation 
between  actual  cubic  contents  of  sawed  lumber,  and  the  superficial  contents  as 
expressed  in  board  measure,  must  not  be  overlooked  in  Forest  Mensuration.  Log- 
rules  for  board  feet  are  uniformly  based  on  the  sawing  of  boards  1  inch  thick.  Mill 
tallies  of  lumber  which  is  sawed  scant,  such  as  |-inch  boxboard  material,  will  con- 
sequently greatly  overrun  the  scale  of  the  logs,  in  so-called  superficial  feet,  which 
is  the  number  of  square  feet  of  surface  measure  regardless  of  thickness.     On  the 


14  SYSTEMS  AND  UNITS  OF  MEASUREMENT 

other  hand,  hardwoods  are  customarily  sawed  to  thicknesses  slightly  greater  than 
1  inch  to  allow  surfacing  down  to  full  inch  thickness,  and  this  practice  reduces  the 
superficial  yield  in  board  feet  as  compared  to  softwood  species  which  are  commonly 
sawed  scant.  Either  practice  causes  the  actual  output  measured  in  board  feet 
(§  12)  to  differ  from  the  scaled  contents  of  the  logs.  The  actual  dimensions  of  board 
which  are  accepted  as  inch  lumber  and  other  standard  thicknesses,  and  the  amount 
of  difference,  scanting  or  extra  thickness,  permitted,  is  standardized  by  trade  prac- 
tice for  each  region  and  species.  ^ 

These  differences  in  sawing  affect  the  over-run  of  sawed  limiber,  which  for  the 
same  log  rule  would  thus  be  greater  for  softwoods  than  for  hardwoods. 

21.  Round-edged  Lumber.  Most  lumber  is  square  edged  in  sawing.  Close 
utilization  by  the  box,  match,  sash  and  blind,  woodenware,  furniture  and  certain 
other  industries  has  led  to  the  sawing  of  logs  "  alive  "  or  through  and  through  into 
boards  from  which  the  waney  edges  are  not  removed  by  squaring.  These  boards, 
except  when  sawed  from  the  middle  of  the  log,  have  one  face  narrower  than  the  other 
and  owing  to  the  taper  of  the  log,  the  faces  are  not  of  uniform  width  throughout 
their  length.  As  the  lumber  in  such  boards  is  closely  utilized,  its  board-foot  contents 
is  computed  by  measuring  the  average  width  of  the  narrow  face.  The  thickness 
is  considered  on  the  same  basis  as  for  square-edged  lumber.  Lumber  of  this  char- 
acter is  usually  cut  by  portable  sawmills  and  sold  direct  to  factories.  The  scale 
at  the  factory  is  used  to  check  that  at  the  mill.  This  prevents  taking  advantage 
of  the  uncertainties  of  the  method.  The  logging  and  sawing  are  paid  for  on  the 
basis  of  the  mill  scale,  which  scale  usually  becomes  the  standard  for  measuring  the 
contents  of  the  standing  timber. 

Round-edged  lumber  will  yield  from  10  to  20  per  cent  more  scale  than  square- 
edged,  the  excess  being  greater,  the  smaller  the  logs  sawed.  For  plank  2  inches 
or  more  in  thickness,  a  loss  is  incurred  both  in  utilization  and  in  scaling  by  reason 
of  the  wane,  which  causes  an  excessive  difference  in  width  of  the  two  faces.  This 
loss  is  reduced  by  cutting  1-inch  boards  from  the  sides  of  the  log  (§  51). 

Closeness  of  utilization  of  the  tree  and  stand  is  increased  by  this  method  of  saw- 
ing. Tops  are  sometimes  taken  down  to  2  inches  and  never  to  greater  than  4  inches. 
Branches  which  crook  only  in  one  plane  are  used. 

22.  Products  Made  from  Bolts  and  Billets.  Bolts  are  sections  of  logs  still  in 
the  round,  and  less  than  8  feet  long,  i.e.,  too  short  to  be  conveniently  measured  as 
logs.  Billets  are  obtained  by  halving,  quartering,  or  otherwise  splitting  or  sawing 
bolts  lengthwise.  Bolts  may  be  split  into  billets,  each  of  which  is  intended  to  pro- 
duce one  finished  article,  such  as  a  wagon  spoke  or  stave.  These  are  measured  by 
count.  Billets  of  larger  size  may  also  be  split  from  bolts.  So-called  shingle  bolts 
are  billets  split  or  sawed  from  large  trees,  or  blocks  from  thick  slabs. 

Billets  are  also  obtained  by  sawing  bolts,  and  are  then  termed  flitches,  squares, 
slats,  or  blocks.  Squares  are  used  in  turning  out  round  articles,  such  as  shuttles, 
spools  and  bobbins.  On  account  of  their  regular  form,  squares  are  sold  by  count, 
or  by  bulk,  on  standards  agreed  on,  the  price  being  based  on  either  the  number  or 
the  board-foot  contents.  They  may  be  sold  by  stacked  cords.  Bolts,  and  split 
or  sawed  billets  of  irregular  form,  not  yet  manufactured  into  squares,  are  sold  by 
stacked  cubic  measure  except  in  the  case  of  bolts  over  12  inches  in  diameter  and  over 
4  feet  long,  which  may  be  scaled  by  a  log  rule.  The  width  of  the  stack  is  determined 
by  the  length  of  the  product  and  may  range  from  22  inches  to  5  feet  and  over.     In 

1  Lvmnber  and  its  Uses,  by  R.  S.  Kellogg,  1914,  Radford  Architectural  Company, 
Chicago,  Illinois. 


PRODUCTS  MADE  FROM  BOLTS  AND  BILLETS  L5 

this  case  a  cord  is  a  stack  4  by  8  feet  but  whose  width  is  that  of  the  given  product 
(§99). 

Different  customs  prevail  in  different  industries.  Shingle  bolts  (split  or  sawed 
billets)  are  sold  in  lengths  which  allow  three  cuts.  For  16-inch  shingles,  with  4 
inches  for  trimming,  the  piece  is  52  inches  long.  For  18-inch  shingles,  a  length  of 
58  inches  is  required.     The  cord  is  4  by  8  feet  by  the  indicated  width. 

Spoke  manufacturers  dealing  in  standard  30-inch  spoke  billets  compute  a 
cord  as  4  by  8  by  2^  feet,  or  80  cubic  feet.  Others  measure  the  cubic  contents, 
using  128  feet  for  a  cord.  In  the  stave  industry  a  cord  measuring  4  by  11  feet  by 
the  length  of  the  stave  bolts  is  quite  common.  For  36-inch  billets  this  gives  132 
cubic  stacked  feet,  but  the  rule  is  applied  to  billets  of  other  lengths. 

Billets  and  bolts  for  tool  handles  are  always  measured  by  the  rank,  in  cords 
measuring  4  by  8  feet  by  the  required  width. 

References 

Measuring  and  Marketing  Woodlot  Products,  Wilbur  R.  Mattoon   and  William  B. 

Barrows,  Farmers  Bulletin,  715,  U.  S.  Forest  Service,  1916. 
Wood  Using  Industries  of  New  York,  John  G.  Harris,  U.  S.  Forest  Service,  New 

York  State  College  of  Forestry,  Series  XIV,  No.  2,  1917. 


CHAPTER  III 
THE   MEASUREMENT   OF  LOGS.     CUBIC   CONTENTS 

23.  Total  versus  Merchantable  Contents.  Logs  are  measured  to 
determine  their  total  cubic  contents  with  or  without  bark,  or  they 
are  scaled  for  merchantable  contents  only.  The  total  cubic  con- 
tents is  required  in  scientific  studies  of  volume  and  growth  and  for 
such  commercial  purposes  as  make  use  of  the  entire  volume  of  the  log. 
The  cubic  contents  is  found  by  measuring  the  length  and  the  diameter 
at  one  or  more  cross  sections  and  computing  the  volume  of  the  log  as  a 
whole,  or  by  sections,  from  these  measurements.  Where  the  thickness 
of  bark  is  measured,  the  difference  in  volume  of  the  log  measured  out- 
side and  inside  the  bark  gives  the  volmne  of  bark. 

24.  Log  Lengths.  Softwood  or  coniferous  logs  are  usually  cut  into 
even  lengths,  or  nmltiples  of  2  feet,  and  may  be  any  length  from  8  feet 
to  over  60  feet,  being  limited  only  by  the  height  and  upper  merchant- 
able diameter  of  the  tree,  the  length  of  material  demanded  for  manu- 
facture, or  the  convenience  of  transporting  long  versus  short  logs. 
Logs,  especially  hardwoods,  are  sometimes  cut  to  odd  lengths  or  multi- 
ples of  1  foot.  The  standard  commercial  lengths  for  softwood  logs 
vary  from  10  to  22  feet,  and  average  16  feet.  In  hardwoods,  log  lengths 
average  somewhat  shorter,  since  utilization  of  shorter  lengths  is  more 
common.  Log  lengths  are  marked  off  on  the  felled  tree  by  notching 
with  an  axe.  It  is  customaiy  to  use  a  wooden  measuring  stick  8  feet 
long,  and  divided  into  2-foot  lengths.^ 

For  exact  measurement  of  length,  the  steel  tape,  graduated  to  feet, 
and  tenths  instead  of  inches,  is  used.  The  log  length  is  measured  along 
the  surface,  which  is  assumed  to  equal  the  length  of  the  axis.  For 
commercial  uses,  an  excess  length  of  from  2  to  6  inches  is  required  as  a 
margin  for  trimming.  For  total  cubic  contents  the  logs  or  sections  are 
measured  to  their  actual  lengths. 

1  The  accidental  chopping  off  of  the  top  of  the  measuring  stick  sometimes  results 
in  short  measurements.  In  some  regions,  notably  in  Southern  pine,  careless  measure- 
ment of  log  lengths  resulting  in  excess  trimming  allowance  and  odd  lengths  causes  a 
waste  in  woods  and  mill,  in  trimming  to  standard  sizes,  of  from  3  to  5  per  cent  of  the 
total  cut.  This  statement  is  based  on  careful  measurements  covering  14  years' 
experience  in  six  states  with  eight  different  companies. 

16      ' 


DIAMETERS  AND  AREAS  OF  CROSS  SECTIONS  17 

25.  Diameters  and  Areas  of  Cross  sections.  Cross  sectional  areas 
are  assumed  to  be  circular  in  form,  and  were  this  assumption  correct 
the  measurement  of  any  average  diameter  would  give  the  cross  section. 

If  B  =  "basal"  area,  or  area  of  circle, 

D  =  Diameter  of  circle, 

7r=  Ratio,  or  3.1416. 
Then 

i?=—- =  .78547)2. 
4 

But  practically  every  cross  section  departs  slightly  from  a  true 
circle,  and  a  large  proportion  are  very  eccentric,  some  showing  a  dif- 
ference of  several  inches  between  their  longest  and  shortest  diameters, 
and  having  an  eUiptical  or  oval  form.i 

No  attempt  is  ever  made  to  compute  the  actual  cross  sectional  area 
of  such  eccentric  sections.  Instead,  two  diameter  measurements  are 
taken  at  right  angles  and  the  average  of  these  is  assumed  to  be  the 
average  diameter.  A  circle  with  corresponding  diameter  is  assumed  to 
have  the  same  cross  sectional  area  as  that  of  the  actual  section.  Usually 
the  longest  diameter  is  taken,  and  one  at  right  angles  to  it,  through  the 
geometric  center  of  the  section.^ 

Abnormal  cross  sections  are  occasionally  encountered  in  which  the  average 
diameter  of  the  section  and  its  area  are  either  too  large  or  too  small  to  give  the  volume 
accurately  owing  to  some  distortion  in  form  of  the  log  as  a  whole  or  of  the  portion 

1  The  area  of  an  ellipse  is 

when  D  and  (/  represent  the  long  and  short  axes. 

D+d 
The  area  of  a  circle  whose  diameter  is  calculated  as ■  is 

2 

jrjD^dY 
4(2)     ■ 
Then 

Tr{D-{-dY     irPd     TT  (D-dY 
4f2)  4~"4       (2)     ' 

which  is  equal  to  the  area  of  a  circle  whose  diameter  equals  one-half  the  difference 
between  D  and  d.  This  correction  which  is  always  minus,  is  ignored  in  measuring 
cross-sections. 

^  In  determining  the  average  diameter,  no  attention  is  paid  to  the  growth  rings 
or  the  position  of  the  pith  or  growth  center  of  the  section.  In  eccentric  cross  sections 
the  pith  is  always  found  some  distance  to  one  side  of  the  geometric  center,  which  is 
the  point  through  which  the  diameter  measurement  must  fall. 


18  THE  MEASUREMENT  OF  LOGS.     CUBIC  CONTENTS 

measured.  Abnormally  large  sections  are  found  at  forks  or  at  the  base  of  limbs  or 
are  caused  by  swellings.  Stumps  cut  low  give  a  section  averaging  much  too  large 
to  indicate  the  true  volume  of  the  log,  due  to  the  rapid  flare  of  the  butt. 

Abnormally  large  diameters  at  the  top  end  of  logs  should  be  measured  by  reduc- 
ing the  diameter  to  what  the  log  would  have  if  it  held  its  regular  form.  Where 
flaring  butts  are  measured,  the  errors  incurred  may  be  serious.  It  is  preferable  to 
adopt  a  method  which  does  not  require  this  butt  measurement,  or  else  to  subdivide 
the  log  by  caliper  measurements  into  shorter  sections.  Abnormal  cross  sections 
caused  by  limb  swellings,  or  knots,  should  be  measured,  if  possible,  by  taking  the 
diameters  at  equal  distances  above  and  below  the  swelling.  When  logs  are  cut  to 
small  diameters  in  the  top,  the  log  may  taper  rapidly  in  the  last  few  feet,  and  the 
disproportionally  small  diameter  at  the  top  will  reduce  the  computed  volume  of  the 
log  as  a  whole.  This  problem  may  be  solved  by  measuring  the  tapering  portion 
separately  as  a  short  piece.  In  commercial  scaling  of  logs  which  have  abnormal 
diameters,  the  scaler  should  apply  a  measurement  which  in  his  judgment  will  give 
the  correct  contents  of  the  log. 

In  ordinary  scaling,  the  diameter  of  logs  is  expressed  in  the  nearest 
inch  with  fractions  entirely  dropped  or  rounded  off  (§83).  For  accu- 
rate volume  measurements,  each  diameter  is  secured  to  the  nearest 
tenth  of  an  inch,  for  which  purpose  the  rule  or  cahpers  used  must  be 
graduated  to  tenths.  In  commercial  practice,  thickness  of  bark  is  never 
included  in  measuring  the  diameter  of  a  log  except  when  the  bark  is  to 
be  utilized,  as  for  fuel  or  tannin,^  in  which  case  the  diameter  is  measured 
outside  the  bark. 

When  the  diameter  of  the  log  is  taken  in  the  middle,  the  thickness 
of  bark  must  be  ascertained  and  deducted.  For  accurate  volume 
measurements,  thickness  of  bark  on  one  side  may  be  determined  by 
notching  and  measuring  to  the  nearest  tenth  of  an  inch.  Double  this 
thickness  when  deducted  gives  diameter  inside  bark.  Or  the  bark  may 
be  stripped  from  opposite  faces  in  order  to  apply  the  calipers  directly  to 
the  wood.  This  latter  method  is  laborious  and  is  seldom  used  even 
in  scientific  volume  determination. 

26.  The  Form  of  Logs.  Logs  diminish  in  diameter  from  butt  to 
top,  corresponding  to  the  form  and  growth  of  trees.  This  difference 
or  loss  in  diameter  at  successive  distances  from  the  butt,  is  termed  taper. 
The  taper  of  logs  gives  them  their  characteristic  forms.  On  account 
of  this  taper,  logs  are  never  truly  cylindrical  no  matter  how  closely 
they  may  approach  the  cylinder  in  form. 

The  geometrical  forms  to  which  logs  can  be  compared  must  there- 
fore be  circular  in  cross  section  and  tapering.  The  forms  suitable  for 
this  purpose  are  the  paraboloid,  cone,  and  neiloid. 

'  Exceptions  to  this  practice  may  be  found  in  some  regions,  in  scaling,  when  the 
log  rule  in  use  gives  a  large  over-run  which  is  offset  by  including  width  of  one  bark 
(§83). 


FORMULAE  FOR  SOLID  CONTENTS  OF  LOGS  19 

These  three  soUds  form  a  series  of  successively  diminishing  per- 
centages of  the  volume  of  a  cylinder  of  equal  basal  area  and  height.^ 
Each  tapers  to  zero  at  the  tip.  But  logs  are  cut  with  two  parallel 
faces  at  the  two  ends.  The  corresponding  solids  are  the  truncated 
forms  of  these  bodies,  termed  frustums,  as  shown  in  Fig.  3. 


Fig.  3. — Forms  of  the  cylinder,  paraboloid,  cone  and  neiloid,  and  truncated  forms 
or  frustums  of  the  last  three  solids. 


27.  Formulae  for  Solid  Contents  of  Logs.     The  comparative  vol- 
umes of  these  four  solids  are  stated  by  formulae  below;  when 


B  =  Area  of  base,  square  feet, 

6^  =  Area  of  cross-section,  at  |  height, 

6  =  Area  of  top, 

/i  =  Height  or  length,  in  feet. 


1  Each  of  these  solids  is  formed  by  the  revolution  of  a  curve  about  a  central  axis. 

A  true  Appolonian  paraboloid  is  derived  from  that  form  of  a  conic  section  (a 
symmetrical  curve  formed  by  the  intersection  of  a  plane  with  a  cone)  in  which  the 
plane  is  parallel  with  the  side  of  the  cone.  For  the  conoid  formed  by  the  revolution 
of  this  curve  about  its  axis,  the  ratio  between  a  cross  section  taken  at  right  angles 
with  the  axis  at  any  point,  and  the  height  above  this  point  to  the  apex,  is  constant 

for  all  points  on  the  axis.     This  gives  a  volume  equal  to  — .      Logs  which  taper 

regularly  will  have  straight  sides,  and  resemble  a  truncated  cone.  Logs  whose  taper 
is  most  rapid  near  the  butt,  diminishing  towards  the  top,  will  have  concave  sides  and 
resemble  a  truncated  neiloid.  The  form  and  volume  of  such  logs  will  usually  fall 
somewhere  between  a  neiloid  and  a  cone.  Most  logs  taper  more  rapidly  at  the  top 
than  at  the  butt  and  will  have  convex  sides,  and  resemble  in  form  a  truncated  para- 
boloid— ^their  volume  usually  falls  between  that  of  a  paraboloid  and  a  cone.  Where 
most  of  the  taper  occurs  close  to  the  top,  the  log  may  exceed  the  paraboloid  in  volume, 
falling  between  it  and  the  volume  of  the  cylinder. 


20 


THE  MEASUREMENT  OF  LOGS.     CUBIC  CONTENTS 


Form 


Volume  of 
perfect  solid 


^'olume  of  FriLstum 


Cylinder 
Paraboloid 


Cone 
Neiloid 


Bh 
Bh 
2 

Bh 

3 
Bh 

4 


(B+h), 


Bh 


or     (B+h)-.     Srnalian's  Formula 


b^h.     H liber's  Formula 

(B+b+Vsly)^ 

3 

{B+ib^+b)-.     Newton's  Formula 


Newton's  formula  will  also  give  the  volume  of  the  cone,  paraboloid 
and  cvlinder. 


The  per  cent  of  the  volume  of  the  cylinder  which  is  contained  in  the  other  three 
forms,  when  of  equal  diameter  at  base  and  equal  height,  is 

Paraboloid 50  per  cent 

Cone 33^  per  cent 

Neiloid 25  per  cent 

But  each  of  these  three  solids  decreases  in  cross  section  from  base  to  tip,  while  that 
of  a  cylinder  remains  the  same.  The  frustum  of  a  cylinder  is  always  a  cylinder, 
while  the  frustum  of  a  paraboloid,  cone  or  neiloid  with  equal  basal  area  tends  to 
more  nearly  resemble  a  cyUnder  as  the  area  of  its  top  section  approaches  that  of 
its  base,  which  results  when  the  relative  height  of  the  frustum  is  shortened.  The 
per  cent  of  the  cubic  contents  of  a  cylinder  of  equul  base  and  height,  which  is  con- 
tained in  these  fru.stums  increases  in  the  same  manner,  and  the  possible  limits  of 
variation  in  form  and  volume  between  the  cylinder  and  each  of  the  other  three 
frastums  correspondingly  dimini-shes. 

E.g.,  when  the  height  of  the  frustum  is  one-fourth  that  of  the  perfect  soUd,  the 
per  cent  of  cylindrical  volume  is,  for 

Frustum  of  paraboloid 87  per  cent 

Frustum  of  cone 77  per  cent 

Frustum  of  neiloid Gl  per  cent 

When  the  height  is  one-eighth  of  a  perfect  solid,  these  per  cents  are: 

Frustum  of  paraboloid 94  per  cent 

Frustum  of  cone 88  per  cent 

Fru.stum  of  neiloid 77.5  per  cent 

A  rapidly  tapering  log  forms  a  truncated  section  of  a  relatively  shorter  completed 
paraboloid  or  cone  than  a  log  with  gradual  taper.  The  greater  the  height  of  a  com- 
plete paraboloid  with  a  given  basal  area,  the  less  it  will  taper  for  a  given  length,  as 
16  feet.  \ATiether  the  taper  is  rapid  or  gradual,  a  log  may  exactly  resemble  the 
frustum  of  a  paraboloid,  cone,  or  neiloid. 


RELATIVE  ACCURACY  OF  SMALIAN  AND  HUBER  FORMULAE      21 

Provided  it  has  the  true  form  of  one  of  these  solids,  its  volume  can  be  exactly 
determined  by  employing  the  corresponding  formula.  But  the  true  form  of  the 
log  may  fall  anywhere  between  the  fixed  points  or  forms  in  the  series,  which  are 
marked  successively  by  paraboloid,  cone  and  neiloid,  and  in  this  case  the  volume 
even  when  calculated  by  the  formula  which  corresponds  most  nearly  to  its  urue 
form,  will  still  be  in  error  by  the  amount  of  this  divergence.  This  error  may  be 
excessive  for  long  logs. 

But  by  taking  advantage  of  the  effect  of  reducing  the  proportional  height  of  the 
frustum,  the  probable  error  from  this  source  may  be  reduced  to  any  desired  limit  of 
accuracy.  This  is  done  simply  by  shortening  the  length  of  the  logs,  or  by  dividing 
each  log  into  several  shorter  sections,  measured  separately.  It  is  then  no  longer 
necessary  to  employ  two  or  more  forms  arbitrarily  according  to  the  variations  in 
the  form  of  the  logs,  but  a  single  standard  geometric  form  may  be  chosen,  which 
most  nearly  resembles  the  average  form  of  logs,  and  the  same  formula;  applied  to  all 
logs  measured. 

The  paraboloid  comes  nearest  to  answering  this  requirement,  and  for  this  reason 
the  Smalian  formula  and  the  Huber  formula  have  been  generally  adopted  for  both 
scientific  and  practical  measurements  of  cubic  volume  of  logs,  to  the  exclusion  of 
the  formula;  for  cone  and  neiloid. 

28.  Relative  Accuracy  of  the  Smalian  and  the  Huber  Formulae. 

Logs  having  the  form  of  a  truncated  paraboloid  are  measured  with 
absolute  accuracy  regardless  of  their  taper  by  either  Ruber's  or  Smalian's 
formula.  But  if  the  form  of  the  log  is  more  convex  and  lies  between 
that  of  the  paraboloid  and  the  cylinder,  the  Smalian  formula,  measur- 
ing the  two  ends,  gives  too  small  a  result,  while  the  Huber  formula  will 
give  too  large  a  volume.  Nearly  all  logs  lie  between  the  frustum 
of  a  paraboloid  and  the  frustum  of  a  cone  in  form,  having  slightly 
convex  sides,  but  not  the  full  form  of  the  paraboloid,  so  the  end  area 
formula  (Smalian's)  shows  an  excess,  while  the  middle  area  measurement 
(Huber's)  gives  too  small  a  result.  In  either  of  the  above  cases, 
the  error  by  Huber's  formula  Is  one-half  that  of  Smalian's  and  opposite 
in  character. 

Newton's  or  Prismoidal  Forviula.  To  check  the  accuracy  of  measure- 
ments made  on  sections  of  given  length  and  to  determine  the  maximum 
length  of  section  which  will  secure  the  desired  degree  of  accuracy,  the 
prismoidal  formula  may  be  applied.  This  formula  is  correct  for  cylinder, 
paraboloid,  cone  or  neiloid,  and  consequently  for  logs  of  regular  form 
whose  volume  lies  within  these  extremes.  It  will  not  measure  accu- 
rately eccentric  or  distorted  forms  resembling  none  of  the  above  solids. 
The  formula  requires  the  measurement  of  both  ends  and  the  middle 
section,  and  is  known  as  Newton's  formula. 

When  the  form  of  logs  resembles  more  closety  the  cylinder,  cone  or 


22  THE  MEASUREMENT  OF  LOGS.     CUBIC  CONTENTS 

neiloid  than  the  paraboloid,  the  errors  in  the  use  of  the  Huber  or  the 
Smahan  formula  may  easily  be  checked  bj^  the  above  formula.^ 

29.  The  Technic  of  Measuring  Logs.  By  either  of  the  two  para- 
boloidal  formulae,  Huber's  or  Smalian's,  the  area  of  a  single  average 
cross -section  is  obtained  which,  multiplied  by  the  length  of  log,  gives 
the  cubic  contents.  By  the  Smalian  method,  this  area  is  the  average 
of  two  cross-sections,  while  by  the  Huber  method  it  is  obtained  directly. 
The  volume  of  the  frustum,  or  log,  is  thus  equal  to  that  of  a  cylinder 
of  equal  height,  with  a  base  equal  in  diameter  to  the  average  cross- 
section. 

Diameters  Measured  at  Ends  of  Log.  Diameter  inside  the  bark  is 
usually  required,  and  is  best  obtained  at  the  exposed  ends  of  the  log. 
But  if  only  the  small  end  is  measured,  the  corresponding  cylinder 
does  not  give  the  cubic  contents  of  the  log  on  account  of  neglect  of  its 
taper  (§26).  Although  almost  universally  practiced  in  scaling  for 
board  feet,  this  single  measurement  is  never  used  to  scale  cubic  contents. 
The  choice  lies,  therefore,  between  the  single  measurement  at  middle 
of  log,  or  the  averaging  of  two  end  areas. 

The  volumes  of  cylinders  vary  directly  as  their  basal  areas,  or  as  D^,  and  not  as 
their  diameters.  Hence  an  accurate  procedure  would  require  first,  measurement 
of  each  diameter;  second,  determination  of  each  corresponding  area;  third,  averag- 
ing these  areas;  fourth,  computing  the  corresponding  diameter.  The  volume  of  a 
cylinder  of  this  diameter  and  length  is  required.  Such  a  procedure  is  practical  only 
in  scientific  studies;  in  scaling,  the  two  end-diameters  are  averaged  directly.  The 
assumption  is  that, 

*  The  following  formula?  are  cited  by  Guttenberg,  in  Lorey's  Handbuch  der 
Forstwissenschaft,  3d  Ed.,  Chapter  XII,  1913. 

Breymann,  V  =-{B+b+3b^+bl). 

8 

Hossfeld,  V  =  -(Sb\+b). 

4 

Simoney,  V  =  -(2{b^i+bl)-b^). 

While  the  substitution  of  the  Hossfeld  formula?  for  that  of  Smalian  on  butt  logs 
would  give  far  more  accurate  results,  and  would  be  closer  than  the  Huber  formula, 
the  point  one-third  from  butt  is  not  ordinarily  measured  in  the  field  and  is  trouble- 
some to  ascertain.  Hence  this  formula  is  impractical.  The  same  objection  applies 
to  Breymann's.  Simonej^'s  formula  has  no  advantage  over  either  Huber's  or 
Smalian's,  since  by  using  the  small  lengths,  one-fourth  log,  the  latter  formuljB  will 
secure  results  within  1  per  cent  of  the  true  volume  for  the  standard  16-feet  length. 


THE  TECHNIC  OF  MEASURING  LOGS  23 

This  gives  a  slightly  smaller  volume  than  by  the  correct  method.  The  error  increases 
as  the  square  of  the  difference  between  the  top  and  the  bottom  diameters. • 

This  error,  expressed  in  per  cent  of  total  contents,  falls  below  1  per  cent  for  logs 
not  over  16  feet  long  with  a  taper  of  2  inches  or  less.  It  also  tends  to  offset  the  plus 
error  caused  by  the  use  of  the  Smalian  method  as  a  whole  ( §  28) .  The  error  increases 
with  length  of  log  scaled  as  one  piece. 

A  far  more  serious  source  of  error  by  this  method  is  that  due  to  the  flare  of  butt 
logs.  Due  to  the  excessively  large  cross-section  thus  obtained  at  the  butt,  this 
error  may  give  an  excess  cubic  volume  for  the  log  of  from  10  to  20  per  cent.  Chiefly 
for  this  reason,  the  end  area  method  is  confined  in  practice  to  scientific  studies  of 
volume,  in  which  the  length  of  the  sections  can  be  regulated  to  reduce  this  error, 
and  time  is  not  the  determining  factor.  For  such  studies,  the  computation  of  average 
basal  areas  is  no  drawback.  The  volumes  of  the  lengths  into  which  the  log  is  to  be 
divided  are  more  conveniently  computed  by  the  Smalian  formula  than  by  the  Huber 
formula,  which  requires  the  middle  diameter  of  each  short  section.  Smalian 's 
mean  end  formula  is  therefore  universally  adopted  in  these  studies, 

Diameter  Measured  at  Middle  of  Log.  Since  it  is  impossible  to 
measure  the  diameter  at  the  middle  of  a  log  unless  the  log  is  exposed, 
logs  cannot  be  scaled  by  this  method  if  they  lie  in  large  roUways  or 
piled  one  on  another.  The  scaling  for  cubic  contents  therefore  requires 
a  time  and  place  for  the  work  where  each  log  is  exposed  for  its  entire 
length  and  is  less  convenient  than  scaling  for  board  feet  (§  83). 

By  measuring  the  middle  diameter,  the  error  due  to  flaring  butts 
is  avoided.  But  this  practice  requires,  in  addition  to  total  length, 
the  determination  of  this  middle  point.  The  use  of  calipers  is  required, 
since  it  is  impossible  to  obtain  consistent  accuracy  by  placing  a  scale 
stick  across  a  log  and  judging  the  diameter;  the  error  thus  incurred 
is  always  minus.     This  method  is  therefore  termed  a  caliper  scale. 

In  applying  a  caliper  scale,  the  double  width  of  bark  is  subtracted 
either  by  taking  off  a  fixed  average  thickness  or  by  adjusting  the  calipers 

'  The  error  in  use  of  mean  diameters  is  shown  as  follows: 
Volume  of  truncated  cone  may  be  expressed  as, 

V  =  ^^h(D^-+Dd+d^). 

Volume  of  cylinder  having  a  basal  area  equal  to  the  mean  diameter  of  the  log  is, 

4         2 
Then, 

-  h(D^+Dd+d'-)  — h^ ^~h- -. 

12  4         2  12         2 

The  minus  error  thus  shown  is  equivalent  to  the  volume  of  a  cone  having  a  basal 
area  equal  to  the  difference  between  the  mean  end  diameters  of  the  log.  For  the 
paraboloid,  this  error  equals  the  contents  of  a  cylinder  with  a  basal  area  equal  to 
that  of  the  above  cone.     The  error  thus  increases  with  the  total  taper  of  the  log. 


24  THE  MEASUREMENT  OF  LOGS.     CUBIC  CONTENTS 

to  read  that  much  less  in  diameter  for  all  logs  alike.  For  more  accurate 
scaling  the  width  of  bark  is  deducted  separately  for  each  log. 

The  caliper  scale  is  the  more  accurate  of  the  two  methods  for 
commercial  use.  The  volumes  by  this  formula,  in  average  logs,  are 
slightly  below  the  actual  contents. ^ 

Where  the  length  of  a  log  exceeds  that  which  can  be  accurately 
measured  as  one  log  by  the  above  methods,  the  practice  is  to  consider 
it  as  composed  of  two  or  more  shorter  sections.  By  Smalian's  method, 
the  intermediate  points  measured  are  taken  as  the  ends  of  these  sec- 
tions. By  Ruber's  method,  the  middle  point  of  each  section  is  found. 
In  either  case,  calipers  should  be  used.  The  length  of  section  which 
can  be  measured  without  subdivision  depends  primarily  on  the  rapidity 
of  taper.  Logs  or  sections  whose  total  taper  does  not  exceed  2  inches 
may  be  scaled  or  measured  as  one  piece  regardless  of  length.  In  com- 
mercial scaling  logs  less  than  18  feet  long  are  seldom  subdivided.  In 
scientific  studies  8  feet  is  usually  the  maximum  length  between  measurp- 
ments  of  diameter,  and  4  feet  is  often  required  for  the  first  or  butt 
sections. 

30.  Girth  as  a  Substitute  for  Diameter  in  Log  Measurements. 
The  circumference  of  the  circle,  corresponding  to  the  girth  of  the  log, 
may  be  used  to  determine  the  area  of  the  cross-section.-  In  this  case, 
if  G  =  girth,  and  B  =  Basal  or  end  area, 

5  =  ^=.0796^2 

47r 

A  tape  is  used  in  which  the  results  are  read  directly  in  inches  of 
diameter,  each  inch  being  equal  to  3.1416  inches  on  the  tape.  A  pin 
in  the  end  of  the  tape  enables  one  man  to  encircle  the  log. 

The  ratio  between  diameter  and  circumference,  tt,  holds  good  only 
for  the  circle.  The  more  eccentric  the  cross-section,  the  greater  this 
ratio  Vjecomes,  and  the  smaller  the  actual  area  in  proportion  to  girth. 
Hence,  Avhatever  error  occurs  by  this  method  tends  to  give  a  cross- 
sectional  area  greater  than  the  actual  area.^ 

^  Tests  of  4398  spruce  and  fir  logs  measured  in  lengths  up  to  40  feet  by  this  method 
in  Maine  indicated  that  the  scale  required  a  correction  factor  of  1.049  or  4.9  per  cent 
over-run.     The  Measurement  of  Logs,  Halbert  S.  Robinson,  Bangor,  Me.,  1909. 

-  Girth  measurements  are  commonly  used  in  India,  and  in  commercial  measure 
ment  of  imported  logs  in  England.  In  the  United  States,  the  girth  of  large  logs  is 
sometimes  taken,  when  more  convenient  than  the  measurement  of  diameter,  but 

(7 

the  result  is  reduced  to  diameter  by  the  formula  D=— =  ..3183G. 

TT 

3  Mensuration  of  Timber  and  Timber  Crops,  P.  J.  Carter,  Office  of  Supt.  of 
Gov't.  Printing,  Calcutta,  1893,  p.  2. 


GIRTH  AS  A  SUBSTITUTE  FOR  DIAMETER  25 

One  advantage  of  girth  measurements  over  diameter  is  that  two 
measurements  taken  at  the  same  point  give  consistent  results,  while 
in  determining  the  average  diameter  of  large  and  ii'regular  or  eccentric 
logs,  considerable  differences  ma}^  occur  in  two  separate  measurements. 
Owing  to  the  difficulty  of  measuring  the  girth  of  a  log  at  its  middle 
point,  the  mean  of  the  two  ends  may  be  taken.  This  incurs  an  error 
identical  with  that  by  the  mean  diameter  method  (§29).  This  error 
is  offset  by  the  tendency  of  girth  measurement  to  over-run. 

The  volume  of  the  cylinder  whose  basal  area  is  obtained  from  girth 
may  be  found  by  the  method  of  the  Fifth  Girth  in  which 


(f)^ 


2h- 


G  is  here  expressed  in  feet.     If  measured  in  inches,  divide  the  result 
by  144.     Another  method,  known  as  the  Quarter  Girth,  is  expressed  as 

-)h^m. 

In  this  formula  G  is  expressed  in  inches.^ 

1  The  Fifth  Girth  method  will  give  a  result  which  is  only  approximately  correct. 


therefore, 


and 


^D\       ,        ,,  .       /7rD\ 

h   should  equal     (  —  1  2h, 

4  V  5   ' 


-    should  equal     (  -      X2, 
4  V.5/ 

.7854  should  equal  .6283=  X2, 

.7854  should  equal  .7895, 

an  error  of  less  than  1  per  cent. 

The  Quarter  Girth  formula  is  of  no  particular  value  as  it  is  merely  a  means  of 
correcthig  a  commercial  standard  (§35  Hoppus  or  Quarter  Girth  Log  Rule)  to 
obtain  the  full  volume  of  the  cylinder. 


CHAPTER  IV 
LOG  RULES  BASED  ON  CUBIC  CONTENTS 

31.  Comparison  of  Log  Rules  Based  on  Diameter  at  Middle  and 
at  Small  End  of  Log.  Log  rules  giving  the  contents  of  logs  in  cubic 
feet  should  be  based  on  the  diameter  inside  bark  at  middle  of  log.  If, 
instead,  the  diameter  is  measured  at  the  small  end  of  the  log,  the  indi- 
cated contents  falls  short  of  the  true  cubic  volume  (§29). 

But  the  measurement  of  diameters  at  the  small  end  of  logs  rather 
than  at  the  middle  point  is  so  great  a  convenience  in  log  scaling  (§  83) 
that  efforts  have  been  made  to  find  a  converting  factor,  or  ratio,  by 
which  the  true  contents  of  logs  may  be  correlated  with  diameters  at 
the  small  end,  and  expressed  directly  in  a  log  rule  based  on  these  diam- 
eters. Since  the  true  contents  is  assumed  to  be  equal  to  the  cylinder 
whose  diameter  is  that  of  the  log  at  its  middle  point,  the  ratio  or  factor 
desired  is  the  multiple  required  for  converting  the  volume  of  the  smaller 
cylinder  whose  diameter  is  measured  at  the  small  end  of  the  log  into 
the  true  cubic  volume  of  the  log  taken  as  equaling  this  large  cylinder. 
This  ratio  is  influenced  by  three  factors — namely,  rate  of  taper,  length, 
and  diameter  of  the  log. 

A  log  rule,  if  based  on  the  same  conversion  factor  for  logs  of  all  sizes  and  tapers, 
will  give  correct  volumes  only  for  a  log  of  a  given  diameter,  length  and  taper  and 
will  be  in  error  for  logs  of  all  other  dimensions. 

A  log  rule  based  on  separate  conversion  factors  for  logs  of  each  diameter  but 
making  no  further  distinction  for  different  lengths  or  tapers  will  give  correct  volumes 
only  for  logs  of  a  specific  length  and  rate  of  taper  in  each  diameter  class,  and  will 
be  in  error  for  all  other  lengths  and  tapers. 

A  log  rule  based  on  separate  conversion  factors  for  each  different  diameter  and 
length,  can  be  applied  accurately  to  obtain  the  average  scale  of  logs  of  all  diameters 
and  lengths  only  in  case  the  average  taper  of  the  logs  scaled  agrees  with  that  of  the 
logs  measured  in  determining  the  factor  used,  and  is  in  error  when  the  average 
taper  of  the  logs  scaled  is  greater  or  less  than  this. 

While  these  conditions  apply  to  log  rules  based  on  measurement  at  the  small  end 
of  log,  a  log  rule  based  on  measurement  at  middle  of  log  is  correct  for  all  the  above 
conditions,  incurring  only  the  errors  due  to  divergence  in  shape  of  log  from  that  of 
a  paraboloid. 

The  ratio  of  volumes,  and  the  loss  in  scaling  legs  by  a  rule  based  on  the  cylinder 
measured  at  small  end,  are  illustrated  in  Table  I.  The  figures  in  the  last  column 
represent  the  loss  in  scale  expressed  in  per  cent  of  the  volume  scaled,  e.g.,  a  16-foot 
log  6  inches  at  the  small  end  with  2-inch  taper  contains  36  per  cent  greater  volume 
than  shown  by  the  scale. 

26 


COMPARISON  OF  LOG  RULES  BASED  ON  DIAMETER 


27 


a 

:^ 

m 

% 
a 

1 

33 

Over-run. 
Per  cent 

(MCOrt^-*!^ 

Oi-ffOlMt^ 

COt-hC0<M  t- 

i>co(MOtj* 

^1:;;^°^^ 

^^?5^2 

J:^?5^S 

gj:?^^ 

Proportion 

of  total 

contents 

scaled. 

Per  cent 

-*<Ml>iM  t^ 

C0«O^C0O5 

COlOrHCOOl 

OCOOiOOi 

t^  00  GO  Oi  05 

lOlxOOOOX 

IOI>00«  00 

^J§^?2f: 

a 

8 
.^   ■ 

.P 

a 

CD  00  CO  GO  CO 

i>.»o  aii>^ 

t^  IC  05t^  —1 

oi>o>o^ 

O  TtH  Ot^CD 

^^2^2 

coo  GOrf  Ol 

^^s?^?^ 

6 

^2g5^??' 

SSS^S 

:§SS?2g 

i::S§^g 

^(M  CO-*  lO 

•*05C0t-;^ 

<Mt)<«0  000 

^  05  t>.OTjH 
r-H  .-H  (M  CO-* 

a 

1 

5 
o 

Middle. 
Cubic  feet 

§5i2§SS 

^?5SS§S 

gssi^ 

^S^Sg 

^S;3SS8 

^:^§Sg 

"^i^^ss 

^^^§§ 

Small 
end. 

Cubic  feet 

>-<  lO  (N  <N  "O 

?52gs§ 

Sis^^s 

§52SS§ 

^S^§i°2 

^^ssg 

^SS§?2 

=°c5§8g 

Diameter 

at 

middle 

of 

log. 

Inches 

^22^J^ 

GO"*  O  COC^ 
^  C^  (M  CO 

*:^§^?? 

22g^S^ 

Diameter 

at 
small 
end. 

Inches 

CO<N  CZ)  '^  O 
^^-NCO 

CO  C<)  CC  '^  o 

^E22^g 

^^2^g 

Total 
taper. 

Inches 

C-] 

^ 

* 

00 

Taper 

per 
16-foot 
length. 

Inches 

(M 

(M 

•^ 

•* 

£3 

1 

O 

CO 

2 

?? 

28  LOG  RULES  BASED  ON  CUBIC  CONTENTS 

Table  I  indicates  that  the  per  cent  of  error  resulting  from  assuming  that  the  total 
contents  of  a  log  is  equal  to  that  of  the  cylinder  measured  at  the  small  end  decreases 
with  increased  diameter,  increases  with  the  total  nunihcr  of  inches  of  taper  in  the 
log  but  for  logs  with  a  given  diameter  and  the  same  nunihcr  of  inches  of  total  taper, 
the  per  cent  of  error  is  the  same  regardless  of  the  rate  of  taper  or  length  of  log,  and  is 
determined  by  the  difference  in  volume  of  the  cylinders  based  respectively  on  diameter 
at  small  end  and  middle  of  log. 

32.  Log  Rules  in  Use,  Based  on  Cubic  Volume.  There  are  two 
classes  of  log  rules  in  use,  based  on  cubic  volume.  The  first  class  gives 
the  actual  or  total  cubic  contents  of  the  log.  The  second  class  gives 
the  volume  of  sawed  lumber  expressed  in  board  feet,  but  these  rules 
are  based  upon  the  use  of  a  fixed  ratio  of  conversion  from  cubic  volume 
and  not  upon  the  volume  of  sawed  lumber  which  can  actually  be  obtained 
from  logs  of  different  sizes  (§  39). 

Cubic  measure  was  early  adopted  in  log  measurements,  but  owing 
to  the  fact  that  logs  are  roughly  cylindrical  in  shape,  the  custom  grew 
up  of  using  the  contents  of  a  cylinder  of  standard  dimensions  instead 
of  the  simpler  standard"  of  the  cubic  foot.  There  is  no  advantage  in 
this  substitution  of  new  arbitrary  cubic  standards  for  the  cubic  foot.^ 

The  principle  used  in  the  application  of  such  a  standard  is  that  the 
volumes  of  cylinders  of  different  sizes  will  vary  as  the  square  of  the 
diameter  multiplied  by  the  length.  The  contents  of  all  logs  can  then 
be  expressed  in  a  log  rule  in  terms  of  the  number  of  standards  they 
contain. 

The  Adirondack  Standard,  or  Market.  In  the  Adirondack  region 
of  New  York  several  such  standards  have  been  used  but  the  only  one 
of  importance  is  the  19-inch  or  Glens  Falls  Standard,  termed  also  the 
Market.^     This  is  a  cylinder  19  inches  in  diameter  and  13  feet  long, 

1  The  cubic  meter  is  the  standard  of  volume  used  in  the  Philippine  Islands. 
Logs  less  than  8  meters  (26  j  feet)  long  are  measured  as  a  cy Under  whose  diameter 
is  the  small  end.  The  average  diameter  in  centimeters  is  taken,  the  end  area  is 
obtained  from  tables  and  multiplied  by  the  length  of  the  log  in  meters  to  give  the 
volume  in  cubic  meters.  For  logs  over  8  meters  in  length,  the  diameter  at  the  middle 
is  taken,  or  if  this  is  impractical,  the  average  of  the  diameters  of  the  two  ends  is  used. 

2  It  is  assumed  that  one  market  equals  200  board  feet  which  is  65.1  per  cent  of 
its  cubic  contents  regarding  the  log  as  a  cylinder  measured  at  the  small  end  of  log 
and  neglecting  taper.     This  gives  7.8  board  feet  per  cubic  foot. 

Tests  of  actual  output  in  board  feet  per  market,  sawed  from  600  logs  of  each  sepa- 
rate diameter,  gave  the  results  as  shown  in  table  on  opposite  page. 

The  saws  used  were  a  band  and  a  band  resaw,  both  cutting  ^-inch  kerf.  The 
lumber  was  60  per  cent  1-inch,  the  rest  l|-inch  and  2-inch  thicknesses.  These 
ratios  are  therefore  higher  than  for  inch  lumber  sawed  with  |-inch  kerf.  The  ratio 
is  still  further  increased  by  the  fact  that  the  cubic  contents  measured  does  not  include 
the  entire  log  but  only  the  cylinder  measured  at  small  end  while  the  sawed  output 
is  from  the  entire  log.     H.  L.  Churchill,  Finch,  Pruyn  Co.,  Glens  Falls,  N.  Y. 

Twenty-two-inch    Standard,      A    different   unit    is    in    use    to    a    slight    extent 


LOG  RULES  IN  USE,  BASED  ON  CUBIC  VOLUME 


29 


equivalent  to  25.6  cubic  feet.  In  application  the  log  is  measured  at 
the  small  end  and  its  contents  are  taken  as  that  of  the  corresponding 
small  cylinder.     The  taper  is  disregarded. 

When     Z)  =  diameter  of  standard  log  in  feet  or  in  inches; 
L  =  length  of  standard  log  in  feet. 

The  volume  of  the  standard  is  .7854  D^L. 

Let  d  and  /  equal  the  diameter  and  length  of  any  other  log,  whose 
volume  will  be  .7854  cPl. 

The  volume  of  any  log  is  found  in  terms  of  standard  units  by  the 
formula, 

.7854dH       dH 
.78o4D^L~DH.' 


V  = 


The  market  is  still  a  common  standard  of  log  measure  on  the 
Hudson  River  watershed  in  the  Adirondack  region. 

Its  neglect  of  the  taper  makes  the  Adirondack  standard  unsuitable 
for  measurement  of  pulp  wood,  but  were  it  applied  at  middle  of  log 

on  the  Saranac  river  drainage  in  New  York,  termed  the  Twenty-Two-Inch  Standard. 
The  standard  log  is  here  22  inches  at  small  end,  and  12  feet  long,  containing  3L68 
cubic  feet.  It  is  assumed  that  one  standard  equals  250  board  feet  which  equals 
65.8  per  cent  of  the  cubic  contents  of  the  small  cylinder.  There  have  been  still  other 
log  standards,  which  are  now  obsolete. 


Diameter  at 

Board  feet 

Board  feet 

Diameter  at 

Board  feet 

Board  feet 

small  end 

per 

per 

small  end 

per 

per 

inside  bark. 

market 

cubic  foot 

inside  bark. 

market 

cubic  foot 

Inches 

Inches 

5 

135 

5.3 

13 

228 

8.9 

6 

1.55 

6.0 

14 

236 

9.2 

7 

168 

6.6 

15 

243 

9.5 

8 

179 

7.0 

16 

248 

9.7 

9 

190 

7.4 

17 

252 

9.8 

10 

200 

7.8 

18 

255 

9.9 

11 

210 

8.2 

19 

257 

10.0 

12 

219 

8.5 

20 

259 

10.1 

In  principle  and  practice,  these  standards  coincide  closely  with  the  use  of  the 
cubic  meter,  the  only  difference  being  in  the  size  or  cubic  contents  of  the  unit.  The 
difference  in  shape,  or  use  of  a  cylinder  instead  of  a  cubic  foot,  is  of  no  significance. 
Since  the  cubic  meter  contains  35.3156  cubic  feet,  the  market  is  a  smaller  standard. 
The  cubic  volumes  are  convertible  from  one  of  these  standards  to  another  by  using 

25  6 
the  proper  ratios;   markets  to  cubic  meters  ---—  =  .725;  markets  to  cubic  feet  25.6 

do.  31 


30  LOG  RULES  BASED  ON  CUBIC  CONTENTS 

it  would  give  accurate  contents.  This  standard,  in  common  with  all 
other  cubic  rules,  is  unsuited  to  the  mcasiuement  of  the  Ixjard  f(!ot  con- 
tents of  logs. 

33.  The  Blodgett  or  New  Hampshire  Cubic  Foot.  A  cylindrical 
unit  has  been  adopted  as  the  legal  standard  of  the  state  of  New  Hamp- 
shire. The  statute  reads,  "  All  round  timber  shall  be  measured  accord- 
ing to  the  following  rule.  A  stick  of  timber  16  inches  in  diameter  and 
12  inches  in  length  shall  constitute  1  cubic  foot;  and  in  the  same  ratio 
for  any  other  size  and  quantity."  This  arbitrary  cubic  foot  contains 
1.396  or  approximately  1.4  cubic  feet. 

The  contents  of  logs  is  computed  in  Blodgett  feet  by  the  formula, 

This  log  rule  is  based  on  the  middle  diameter,  and  is  therefore  more 
accurate  in  application  than  the  Adirondack  standards.  The  diameter 
is  measured  by  calipers  and  double  width  of  bark  is  deducted  (§84). 

This  rule  is  a  rough  attempt  to  use  the  cubic  foot,  with  an  allowance  for  waste 
in  squaring  round  logs.  But  the  per  cent  of  waste  by  the  rule  is  28.4  per  cent  of  the 
cylinder,  utilizing  71.6  per  cent,  while  the  area  of  an  inscribed  square  is  63.6  per 
cent  of  the  circle  with  .36.4  per  cent  waste.  The  "squared"  stick  1  foot  long  would 
therefore  have  considerable  wane.  The  Blodgett  Rule  was  an  attempt  to  secure  a 
standard  which  could  be  converted  into  board  feet.  The  statute  fixed  the  converting 
factor  as, 

100  Blodgett  feet  =  1000  board  feet,  or  a  ratio  of  1  :  10 

But  in  scaling  practice  it  was  concluded  that  this  ratio  was  unsatisfactory,  and 
gave  too  large  a  scale  in  board  feet.     So  it  was  arbitrarily  set  in  practice  at 

115  Blodgett  feet  =  1000  board  feet,  or  a  ratio  of  1  :  ,S.7, 

when  the  rule  was  applied,  as  intended,  to  the  middle  diameter  inside  bark.  Though 
the  scale  in  Blodgelt  feet  in  either  case  was  the  same,  the  converted  residt  gave  for 
the  ratio  of  1  :  10,  .59.7  per  cent  of  the  contents  of  the  log  in  board  feet,  and  for  the 
ratio  1  :  8.7,  51.9  per  cent.     Since  12  board  feet  =  l  cubic  foot, 


and 


Likewise, 


and 


—  =83g  per  cent  of  1  cubic  foot, 


.831 

^  =  .597. 

1.396 


8.7 

—  =  72 . 5  per  cent, 
12 


1.396 


USE  OF  CUBIC  FOOT  IN  LOG  SCALING 


31 


In  order  to  permit  measurement  of  diameter  at  the  small  end  of  log  instead  of 
the  middle  (§31),  a  further  modification  of  the  rule  more  radical  in  its  character 
was  now  made.  The  loss  in  cubic  contents  by  measuring  the  small  cylinder  was 
offset  by  arbitrarily  increasing  the  ratio  of  board  feet  to  each  Blodgett  foot.  This 
new  ratio  was  set  for  logs  of  all  sizes  at 

106  Blodgett  feet  =  1000  board  feet. 


.781 


When  compared  with  the  cubic  contents  of  the  small  cylinder  this  makes  the  ratio 
1  :  9.44.  For  the  ratio  of  1  :  9.44  the  per  cent  of  the  small  cylinder  scaled  as  boards 
is  56.2  per  cent.  But  for  the  true  cubic  contents  of  the  log  the  ratio  would  vary 
with  length  and  taper  of  log  (§  31) . 

9.44 
12 


■  781 
1 . 396 ' 


=  56.2  per  cent. 


From  Table  I,  §  31,  the  following  comparisons  can  be  made  between  the  volume 
thus  expressed  and  the  true  volume.     Taking  16-foot  logs  with  2-inch  taper. 


Diameter 
of 
log. 

Inches 

Per  cent  of  total  con- 
tents of  log  in  small 
cylinder 

Per  cent  of  total  con- 
tents scaled  as  boards 
by  above  ratio  of 
56.2  per  cent. 
Per  cent 

6 
12 
18 
24 
30 

73.4 
85.2 
89.7 
92.2 
93.7 

41.2 
47.8 
50.4 
51.8 
52.6 

The  attempt  to  convert  this  rule  to  apply  at  small  end  gives  values  which  agree 

with  the  current  ratio  of  115  Blodgett  feet  to  1000  board  feet  in  16-foot  only  when 

these  logs  are  24  inches  in  diameter  and  with  2-inch  total  taper,  while  for  6-inch  logs, 

41.2 
tapering  2  inches  the  scale  is or  79 . 3  per  cent,  incurring  a  loss  of  20 . 7  per  cent 

of  the  true  cubic  scale  measured  at  the  middle  point. 

Thus  the  change  in  point  of  measurement  destroys  the  consistency  of  this  log 
rule  for  cubic  contents,  while  the  conversion  to  board  feet  introduces  still  another 
error,  discussed  in  §  42.  The  rule  should  either  be  used  for  Blodgett  feet  only,  as  a 
cubic  measure,  and  apphed  only  at  middle  diameter,  or  if  the  end  diameter  is  used, 
the  conversion  factor  should  have  been  separately  computed  for  logs  of  different 
diameters  and  lengths  on  basis  of  an  average  taper. 

34.  Use  of  Cubic  Foot  in  Log  Scaling.  The  cubic  foot  has  been 
substituted  for  the  Blodgett  foot  as  the  basis  for  measuring  logs,  by 
the  U.  S.  Forest  Service  on  the  National  Forests  in  Maine  and  New 
Hampshire. 


32 


LOG  RULES  BASED  ON  CUBIC  CONTENTS 


A  caliper  with  a  long  arm  to  the  end  of  which  is  attached  a  measuring  wheel,  is 
vised.  The  wheel  consists  of  ten  spokes,  each  tipped  with  a  spike,  and  all  painted 
black  except  one,  which  is  yellow.  The  tips  of  the  .spokes  are  6  inches  apart.  The 
yellow  .spoke  is  weifjhted.  When  the  wheel  is  run  along  a  log,  each  revolution  as 
counted  by  the  yellow  spoke  measures  5  feet,  and  the  remaining  spokes  permit  the 
length  of  log  to  be  measured  to  the  nearest  6  inches.  The  measuring  wheel  is  run 
the  length  of  the  log,  and  then  brought  back  to  the  center,  at  which  point  the  caliper 
measurement  is  taken.  Allowance  for  bark  is  made  by  moving  the  caliper  jaw 
inward  by  a  distance  in  inches  equal  to  the  estimated  double  width  of  bark  on  each 
log  separately. 

The  diameter  in  inches  is  stamped  on  one  edge  of  the  arm,  and  around  the  base 
of  the  arm  are  placed  standard  lengths  running  from  8  to  34  feet.  Opposite  each 
length,  and  below  each  diameter,  on  the  arm,  is  stamped  the  cubic  volume  of  a  log 
of  these  dimensions.  The  lengths  are  also  stamped  on  the  movable  arm.  When 
the  log  is  calipered,  the  scaler  reads  the  volume  which  lies  opposite  the  proper  length, 


Fig.  4. 


-Caliper  scale  for  measuring  logs  in  middle,  outside  bark,  with 
determining  length  of  log. 


;heel  for 


the  diameter  being  indicated  by  the  position  of  the  movable  arm  after  calipering  the 
log  and  taking  off  the  bark  correction.  Defects  are  then  deducted  from  the  gross 
volume,  either  by  measuring  the  defective  portion  or  by  ocular  estimate  of  the  volume 
of  the  defect.     J.  J.  Fritz,  Gorham,  N.  H.,  1921. 

Note.  In  1909  a  commission  of  investigation  recommended  to  the  Maine 
Legislature  the  adoption  of  the  cubic  foot  as  the  statute  rule  of  Maine.  This  was 
not  done.  One  lumber  company,  Hollingsworth  &  Whitney,  Waterville,  Maine, 
has  since  1904  used  a  cubic  foot  standard,  measuring  the  middle  diameter  with  cali- 
pers, outside  bark.  The  rule  then  allows  \2h  per  cent  deduction  for  volume  of  bark, 
and  gives  the  net  cubic  contents  of  sohd  wood.  The  per  cent  of  volume  of  bark  is 
not  constant  but  varies  with  the  size  of  tree  and  its  age  and  exposure.  The  arbitrary 
figure  chosen  simply  represented  the  approximate  average  volume  for  the  species 
and  region  in  question,  namely,  spruce  and  balsam  in  Maine. 

A  converting  factor  for  this  rule  has  been  suggested,  of  185  cubic  feet  to  1000 
feet  B.  M.  This  gives  5.4  board  feet  per  cubic  foot,  or  45  per  cent  of  the  cubic  con- 
tents when  measured  at  the  middle.  Reduced  to  diameter  at  small  end,  for  a  taper 
of  1  inch  in  8  feet,  logs  18  inches  in  diameter  would  give  50  per  cent  of  the  small 


LOG  RULES  FOR  CUBIC  CONTENTS  OF  SQUARED  TIMBERS       33 

cylinder  in  board  feet.  This  suggested  ratio  is  therefore  lower  than  those  adopted 
for  the  New  Hampshire  and  most  other  converted  cubic  log  rules. 

Note.  Weight  as  a  Bads  for  Measuring  Cubic  Contents.  Actual  weight  of  logs 
is  seldom  used  as  a  basis  of  measurement,  as  the  variation  in  moisture  contents 
caused  by  seasoning  prevents  standardization  even  for  a  given  species.  A  few 
valuable  timbers  are  imported  by  weight.     The  long  ton  of  2240  pounds  is  used. 

The  ton  as  ordinarily  used  in  measuring  timber  is  a  cubic  measure  equivalent  to 
either  40  or  to  50  cubic  feet  and  is  usually  applied  to  squared  timbers.  The  unit  of 
50  cubic  feet  is  also  termed  a  "load"  and  is  used  in  measuring  teak. 

Red  cedar  logs  are  sometimes  purchased  by  weight,  on  account  of  their  extreme 
irregularity  and  the  difficulty  of  measuring  them. 

35.  Log  Rules  for  Cubic  Contents  of  Squared  Timbers.  A  definite 
departure  from  the  use  of  total  cubic  contents  is  found  in  log  rules 
giving  the  cubic  contents  of  the  squared  timbers  which  may  be  hewn 
or  sawed  from  round  logs.  The  waste  constitutes  the  portion  hewn 
or  slabbed  off.  A  square  inscribed  in  a  circle  occupies  63.6  per  cent 
of  its  area.  Rules  based  on  this  principle  would  give  a  waste  factor 
of  36.4  per  cent  of  the  cylinder  scaled. 

Inscribed  Square  Rule.  The  width  of  a  square  inscribed  in  a  24-inch 
circle  is  17  inches.^  The  width  of  any  other  inscribed  square  is  seven- 
teen twenty-fourths  of  the  diameter  of  the  log.  The  cubic  contents 
of  the  log  is  that  of  the  square  so  determined,  measured  at  the  small 
end  of  log. 

The  width  of  a  square  inscribed  in  a  17-inch  circle  is  12  inches,  each 
foot  of  log  containing  1  cubic  foot  of  squared  timber.     The  cubic  con- 

tents  of  any  log  is  t^^/.    By  either  of  these  rules  of  thumb,  the  so-called 

Inscribed  Square  Rule  is  obtained.  The  latter  method  is  termed  the 
Seventeen- Inch  Rule.  The  rule  gives  63.4  per  cent  of  the  cubic  contents 
of  the  small  cylinder,  and  proportionately  less  of  the  entire  log  depend- 
ing on  taper,  length  and  diameter  (§31). 

Big  Sandij  Cube  Rule.  Synonyms:  Cube  Rule,  Goble  Rule.  This 
Cube  Rule,  used  on  the  Ohio  River,  assumes  that  it  requires  a  log  18 
inches  in  diameter  at  small  end  to  give  a  timber  1  foot  square.  This 
rule  scales  56.6  per  cent  of  the  small  cylinder.  The  volume  of  logs  of 
other  sizes  is  found  by  the  formula, 

^      18^ 

This  rule  is  sometimes  expressed  in  board  feet  by  multiplying  the 
cubic  contents  by  12. 

1  The  side  of  the  inscribed  square  is  found  by  squaring  the  diameter  of  the  log, 
dividing  by  2  and  extracting  the  square  ropt, 


34  LOG  RULES  BASED  ON  CUBIC  CONTENTS 

Two-thirds  Rule.  By  this  rule,  the  diameter  of  the  log  is  reduced 
one-third,  the  remainder  squared,  and  multiplied  by  the  length  of  the 
log.  As  diameters  are  in  inches  the  formula  is  y=  (|Z))- L-^144. 
This  is  a  caliper  rule  applied  to  the  middle  area,  and  gives  56.5  per 
cent  of  the  full  cubic  contents  of  the  log.  It  is  sometimes  erroneously 
applied  to  the  small  end. 

Quarter  Girth  or  Hoppus  Rule.  This  rule  depends  upon  the  direct 
use  of  the  girth,  rather  than  diameter.     The  average  girth  is  taken 

in  inches  at  middle  point,  or  by  averaging  both  ends.     Then  T'=  (  y)  L. 

This  formula  gives  78.5  per  cent  of  the  actual  total  cubic  contents  of 
the  log.  It  is  a  commonly  used  standard  for  measuring  round  logs  in 
England  and  India.  To  express  the  contents  in  cubio  feet  the  result 
is  divided  by  144. 

36.  Log  Rules  Expressed  in  Board  Feet  but  Eased  Directly  upon 
Cubic  Contents.  The  Blodgett  or  New  Hampshire  rule  is  not  the  only 
log  rule  based  on  cubic  contents,  which  attempted  to  express  the  results 
in  terms  of  board  feet.  Any  cubic  rule  can  be  converted  into  board- 
foot  form,  in  theory,  by  the  use  of  a  ratio  similar  to  those  used  for  the 
Blodgett  Rule.  The  ratio  for  board-foot  contents  of  one  cubic  foot  is  12. 
Twelve  1-inch  boards  cannot  be  sawed  from  1  cubic  foot,  but  a  squared 
timber  12  by  12  inches  contains  12  board  feet  per  linear  foot.  For  con- 
verting the  entire  log  directly  into  board-foot  contents  of  squared 
timbers,  it  is  evident  that  the  ratio  will  be  less  than  12  board  feet  per 
cubic  foot,  due  to  waste  in  squaring  the  log,  while  the  conversion  into 
contents  in  inch  lumber  requires  a  still  lower  ratio. 

The  characteristic  of  all  converted  rules  is  that  a  fixed  multiple 
or  converting  factor  is  used,  regardless  of  the  diameter  or  taper  of 
the  log.  The  rules  differ  only  in  the  converting  factor  used,  and  in 
the  method  of  measuring  the  log,  whether  at  middle,  or  end. 

Constantine  Log  Rule.  This  rule  is  merely  the  expression  of  the  cubic 
contents  of  a  log  regarded  as  a  cylinder,  in  terms  of  board  feet,  by 
multiplying  the  cubic  contents  by  12.  The  diameter  is  measured  at 
the  small  end  of  log.     The  formula  is 

■■      '^   L. 


4X144 


The  rule  is  used  to  measure  the  contents  of  logs  used  for  veneers. 

Cuban  One-fifth  Rule.  This  Rule  is  based  on  the  square  of  one- 
fifth  of  the  girth  taken  in  middle  of  log.  The  formula  when  G  is  in 
inches  is 


FORMULA  FOR  BOARD-FOOT  RULES  35 

The  rule  gives  just  50  per  cent  of  the  total  cubic  contents  of  logs 
in  board  feet.  This  is  equivalent  to  6  board  feet  per  cubic  foot.  This 
rule  is  extensively  used  for  imported  hardwood  logs.  The  contents 
of  logs  in  cubic  feet  is  found  by  dividing  bv  144  instead  of  12. 

In  practice,  fractional  inches  resulting  from  the  fifth  girth  are  dropped  as  follows, 
e.g., 

Girth,  .50,  51  or  .52  inches  Square,  10  b}^  10  inches 

53,  54  inches  11  by  10  inches 

55,  56,  57  inches  11  by  11  inches 

58,  59  inches  12  by  11  inches,  etc. 

Square  of  Two-thirds  Rule.  Synonyms:  St.  Louis  Hardwood, 
Two-Thirds,  Tennessee  River,  Lehigh,  Miner.  This  rule  is  derived  from 
the  Two-thirds  Rule  bj^  multiplying  the  cubic  scale  by  12.  The  rule 
is  used  for  hardwood  logs  in  the  Middle  States,  and  for  pine  to  some 
extent  in  the  South  Atlantic  States,  and  is  frequently  erroneously 
applied  to  the  small-end  diameter  of  the  log. 

Cumberland  River  Rule.  Synonyms:  Evansville,  Third  and  Fifth. 
This  rule  resembles  the  Square  of  Two-Thirds  Rule,  in  that  one-third 
of  the  diameter  is  deducted  and  the  remainder  squared.  But  it  differs,  in 
that  one-fifth  of  the  volume  of  the  squared  stick  is  then  subtracted  for 
saw  kerf,  and  the  remainder  converted  into  board  feet.  The  rule  is 
alwaj^s  applied  to  the  small  end  of  the  log  except  for  long  logs,  when 
the  diameter  at  middle  point  is  taken.  This  rule  is  used  on  the  Missis- 
sippi Valley  and  its  tributaries,  for  hardwood  logs. 

Square  of  Three-fourths  Rule.  Synonyms:  Portland,  Noble  & 
Cooley,  Cook,  Crooked  River,  Lumberman's.  In  this  rule,  one-fourth 
is  deducted  from  the  diameter  at  small  end,  and  the  squared  timber 
expressed  in  board  feet.  The  rule  was  formerly  used  in  New  England 
but  is  now  obsolete. 

Vermont  Rule.  This  rule  is  derived  from  the  Inscribed  Square 
Rule  by  multiplying  the  values  by  12.  It  is  the  legal  standard  of  the 
State  of  Vermont.  The  contents  of  a  12-foot  log  may  be  calculated  by 
a  rule  of  thumb,  by  multiplying  the  average  diameter  of  the  top  of  the 
log  inside  bark,  in  inches,  by  half  such  diameter  in  inches.  The  rule  is 
not  extensively  used  even  in  Vermont,  being  supplanted  by  others, 
notably  the  New  Hampshire  or  Blodgett  Rule. 

37.  Formula  for  Board-foot  Rules  Based  on  Cubic  Contents. 
Any  board-foot  log  rule  the  values  for  which  are  obtained  by  deducting 
the  same  per  cent  from  the  cubic  contents  of  logs  of  all  sizes,  may  be 
expressed  by  the  formula 

Board  feet  =  (1-C)^X^ XL, 
'4        144 


36  LOG  RULES  BASED  ON  CUBIC  CONTENTS 

in  which        C  =  total  per  cent  of  waste  deducted  from  the  c^'linder, 
1  — C  =  per  cent  of  cubic  contents  utilized, 

— r-7    reduces  I)'-  from  inches  to  square  feet,  and 
144  * 

12    converts  cubic  feet  to  Ixjard  measure. 
The  fornuila,  sim])lified,  becomes 

Board  feet  =  (1-C)^L. 
4o 

But  the  important  distinction  remains,  that  some  of  these  log  rules 
are  meant  to  apply  to  the  middle  diameter  and  others  to  the  small  end, 
and  while  the  per  cent  subtracted  from  the  cylinder  meaaured  is  uniform 
for  the  rule,  the  per  cent  actually  subtracted  fromfthe  log  is  uniform  onl}- 
for  those  rules  using  middle  diameter,  and  varies  over  a  wide  range  for 
rules  based  on  diameter  at  small  end  of  log. 

Note.  Obsolete  Rules.  The  following  log  rules,  obsolete  or  unused,  are  based 
on  the  above  formula  and  principles:  Saco  River  (Maine),  Derby  (Mass.),  Partridge 
(Mass.),  Stillvvell's  Vade  Mecum  (Ga.),  Ake  (Pa.),  Orange  River  or  Ochultree 
(Texas).  A  new  rule,  the  Calcasieu  (La.),  deserves  the  same  fate.  The  Tatarian 
rule  (Wis.),  which  is  based  on  this  principle,  gives  approximately  correct  board- 
foot  contents  for  a  log  of  a  given  size.     It  has  never  been  adopted  in  practice. 

38.  Comparison  of  Scaled  Cubic  Contents  by  Different  Log  Rules. 

In  Table  II  is  shown  the  comparative  volumes,  in  per  cent  of  total  cubic 
contents,  which  are  scaled  b}'  different  log  rules  based  upon  cubic 
volume.  These  per  cents  represent  the  converting  factor  used  to  obtain 
the  values  given  in  the  rule  from  the  volumes  of  cylinders. 

Note.  The  values  in  this  table  were  obtained  by  applying  the  ratio  between 
the  volume  of  two  cylinders  16  feet  long,  18  inches  and  19  inches  in  diameter  respect- 
ively.    This  ratio  is  28.27  :  31.50.     Log  rules  based  on  cylinder  at  small  end  then 

28  27 
scale  but  — - —  or  89.7  per  cent  of  their  volume,  to  which  the  reduction  per  cent  for 
31.50  ^ 

waste  is  applied;  e.g.,  the  Vermont  rule  wastes  36.6  per  cent  by  the  inscribed  square 

method.     Then,  based  on  the  small  end,  the  per  cent  scaled  is  63.4,  but  based  on 

middle  diameter  for  the  above  size,  it  is  89.7X63.4  =  56.9  per  cent.     The  table  gives 

a  correct  comparison  of  the  different  log  rules  which  are  constructed  by  using  a 

fixed  per  cent  of  cubic  volume.     The  per  cents  given  for  the  rule  under  the  first 

column,  based  on  the  point  at  which  the  rule  is  applied,  are  consistent  for  all  logs. 

But  the  equivalent  per  cents  obtained  by  converting  the  scaled  contents  into  terms 

of  the  cylinder  based  on  the  other  diameter — as  middle,  for  logs  measured  at  the  end 

and  vice  versa,  will  vary  as  the  relative  contents  of  these  two  cylinders  varies   (§  31). 

This  will  not  change  the  rank  or  order  in  which  the  rules  fall.     The  rules  are  tabulated 

in  order  of  the  relative  per  cent  of  total  contents  which  they  scale. 

There  is  no  common  standard  for  measuring  the  cubic  contents  of  squared  timbers. 

The  Quarter  Girth  method  gives  the  tallest  measurements,  while  the  others  more 

closely  approximate  the  net  contents  as  given  by  board-foot  rules. 


COMPARISON  OF  SCALED  CUBIC  CONTENTS 


37 


TABLE  II 

Comparison  of  Per  Cents  of  Cubic  Contents  of  Cylinders  Scaled  by  Various 
Log  Rules,  for  Logs  18  Inches  in  Diameter  at  Small  End,  with  2-inch 
Total  Taper 

Cylindrical  contents  measured  inside  bark 


Log  rule 


Cubic  Standards 
Market  or  Glens  Falls  standard 

22-inch  standard 

Blodgett  or  New  Hampshire. .  . 

Cubic  foot — Maine 

Cubic  meter— Philippines: 

Short  logs 

Long  logs 


Basis  of  measure- 
ment of  cylin- 
der, in  applica- 
tion of  rule 


Cubic  Log  Rules  for  Squared 
Timbers 

Quarter  girth  or  Hoppus 

Inscribed  square 

Two-thirds 

Cube  rule,  or  Big  Sandy 


Log  Rules  Expressed  in  Board 

Feet  but  Based  on  Cubic 

Contents 

Constantine 100 

Tatarian 84 . 0 

Saco  River 72  ^  4 

Derby |     72  . 1 

Square  of  Three- Fourths j     71.7 

Partridge '     08. 8 

Blodgett,  converted,  ratio  lOO' 

tolOOOft.  B.M !    

I 


at 
small 

end. 

Per 
cent 


100 
100 


100 


63.4 


50 . 6 


at 
middle 


Per 
cent 


100 
100 


100 


Per  cent  of  scale 
if  measured  at 
other  point 


at 
middle 


56.5 


59.7 


89.7 
89.7 


at 
small 
end 


56,9 


50.8 


89.7 
75.4 
65.0 
64.7 
64.3 
61.8 


111.4 
111.4 


78.5      87.5 

I 


62.9 


Per  cent  deducted 
from  contents  of 
cylinder  to  ob- 
tain contents 
given  in  rule — 
For  rules  applied 


at 
small 
end 


0 

0 
11.4^ 
11.4^ 

0 

11.4^ 


12.5 
36.6 
37.1 
43.4 


0 

16.0 
27.6 
27.9 

28.3 
31.2 


33.5 


at 
middle 


10.3 
10.3 

0 

0 

10.3 
0 


21.5 
43.1 
43.4 
49.2 


10.3 
24.6 
35.0 
35.3 
35.7 
38.2 

40.3 


38  LOG  RULES  BASED  ON  CUBIC  CONTENTS 

TABLE  11— Continued 


Log  rule 


i  I 

Basis  of  measure-;  Per  cent  of  scale!  Per  cent  deducted 
ment  of  cylin-1    if  measured  at     from '  contents  of 


der,  in  applica- 
tion of  rule 


at 
small 

end. 

Per 
cent 


at 
middle 


Per 

cent 


other  point 


at 
middle 


at 
small 
end 


cylinder  to  ob- 
tain contents 
given  in  rule — 
For  rules  applied 


at       j       at 
small    '  middle 
end 


Log  Rules. — Continued 
22-inch     standard,   converted 

ratio  1  to  250  ft.  B.M 

Market,   or   19-inch  standard 

converted,  ratio  1  to  200  ft 

B.M 

Vermont , 

Vade  Mecum  (Stillwell's) 

Square  of  Two-thirds 

Ake 

French's  (Los  Angeles) 

Calcasieu 

Blodgett,  converted,  ratio  n5 

to  1000  ft.  B.M 

Blodgett,  converted,  ratio   106 

to  100  ft.  B.M 

Cuban  One-Fifth 

Orange  River 

Maine    cubic    rule,    converted 

185  cu.  ft.  per  1000  ft.  B.M.  . 

Cumberland  River 

Delaware  or  Eastern  Shore.  .  . 


65.6 


65.1 
63.4 
63.2 


62.4 


57, 


56.2 
50.9 


45.2 
42.4 


56.5 
52.2 

51.9 

50.1 

45.0 


58. 9 


58.4 
56.9 
56.7  I 


!     62.9 


56.0 
51.9 

50.4 
45.7 


40.6 
38.1 


I     58.2 


57. 


55.9 


50.1 


34.4 


34.9 
36.6 
36.8 
37.1 
37.6 
41.8 
42.2 

42.2 

43.8 
44.1 
49.1 

49.9 
54.8 
57.6 


41.1 


41.6 
43.1 
43.3 
43.5 
44.0 
47.8 
48.1 

48.1 

49.6 
49.9 
54.3 

55.0 
59.4 
61.9 


Of  the  cubic  log  rules  expressed  in  board  feet,  the  Constantine  is  frankly  a  cubic 
rule,  converted  from  the  cubic  foot,  but  based  on  the  small  end  of  log.  The  rest 
are  suitable  neither  for  cubic  contents  nor  for  board  feet,  since  they  do  not  express 
the  former  nor  do  they  measure  the  latter  correctly  (^Chapter  \). 

These  rules  are  all  convertible  into  cubic  units  or  from  one  to  the  other,  when 
based  on  cylinders  measured  at  the  same  point. 

wD- 

The  formula.  Board  feet  =  (l— C) L,  can  be  used  to  obtain  the  values  for  any 

48 

of  these  rules,  by  sub.stituting  for  C  the  per  cent  given  in  the  last  two  colunuis  of 
Table  II,  e.g. 


RELATION  BETWEEN  CUBIC  MEASURE  39 

To  derive  the  Inscribed  Square  rule,  the  cubic  contents  of  cyHnders  from  Table  II 
are  multipHed  by  1  —36.6,  or  63.4  per  cent. 

To  convert  the  Inscribed  Square  rule  into  terms  of  the  Cumberland  River  rule; 

since  1  —54.8  =  45.2  per  cent,  the  volumes  of  the  two  rules  are  as  45.2  to  63.4.     The 

45.2 
Cumberland  River  rule  gives  -^ —  of  the  Inscribed  Square  rule,  or  71.3  per  cent. 
63.4 

But  the  Hoppus  Rule  cannot  be  converted  into  terms  of  either  of  the  above  rules, 

since  it  is  measured  at  the  middle  point,  unless  a  log  of  a  given  diameter  and  average 

taper  is  assumed. 

39.  Relation  between  Cubic  Measure  and  True  Board-foot  Log 
Rules.  The  conversion  of  these  log  rules  from  cubic  to  board  feet  is 
based  on  the  erroneous  assumption  that  logs  of  all  dimensions  when 
sawed  into  lumber  will  yield  the  same  ratio  of  board-foot  contents  to 
cubic  contents.  In  practice,  the  larger  the  log,  the  greater  will  be  the 
ratio  or  per  cent  of  its  contents  which  makes  lumber  and  the  less  the 
per  cent  wasted.  For  this  reason  it  is  not  possible  to  use  the  same 
standard  for  scaling  both  the  cubic-  and  board-foot  contents  of  logs, 
no  matter  what  converting  factor  is  chosen. 

Cubic  rules,  converted  to  board-foot  contents  by  a  fixed  ratio,  tend 
to  scale  small  logs  too  high  and  large  logs  too  low,  as  compared  to  the 
actual  sawed  contents.  The  common  mistake  of  the  authors  of  these 
rules  is  to  assume  that  once  the  sawed  contents  of  a  log  of  given  diameter 
and  length  is  found,  the  ratio  obtained  will  apply  unchanged  to  logs  of 
all  other  sizes.  These  rules  have  therefore  fallen  into  disrepute  in  the 
scaling  of  board  feet,  because  of  their  inconsistencies  for  this  purpose. 

For  products  such  as  pulpwood,  which  utilizes  the  entire  contents 
of  the  log,  these  so-called  board-foot  rules  give  consistent  results  for 
logs  of  all  sizes,  but  do  not  possess  any  advantage  over  the  direct  use 
of  the  cubic  standard  upon  which  they  are  based.  On  the  other  hand, 
if  log  rules  are  intended  for  the  measurement  of  the  actual  output  of 
1-inch  lumber,  they  must  be  based  on  other  principles  (§  54). 

The  two  quantities  of  measurement,  cubic  volume,  and  squared 
board  feet  obtainable,  are  incommensurable  unless  the  diameter  and 
also  the  taper  of  each  log  is  known.  The  lump  sum  of  a  lot  of  logs 
measured  in  cubic  volume  therefore,  cannot  be  converted  into  board-foot 
measure  except  by  readjusting  each  individual  value  by  the  diameter 
of  each  individual  log.  The  use  of  these  hybrid  rules  should  be  discon- 
tinued in  favor  of  cubic  standards  on  the  one  hand,  and  board-foot  log 
rules  based  on  correct  principles  on  the  other. 


CHAPTER  V 
THE  MEASUREMENT  OF  LOGS— BOARD-FOOT  CONTENTS 

40.  Necessity  for  Board-foot  Log  Rules.  In  other  lines  of  industry 
it  is  not  customary  to  measure  raw  materials  in  terms  of  the  quantity  of 
finished  product  contained  therein.  The  volume  or  weight  of  the  raw 
product  is  the  basis  of  sale.  On  this  basis  logs  would  be  sold  for  their 
cubic  contents. 

But  the  purchaser  of  raw  material  must  know  approximately  the 
quantity  of  finished  product  he  can  obtain  from  it  before  he  can  estimate 
its  value.  If  the  product  is  to  be  lumber,  the  possible  yield  of  boards 
of  certain  qualities  and  grades  determines  for  him  the  value  of  the  logs. 

If  it  had  been  found  by  experience  that  all  logs  regardless  of  size 
would  yield  the  same  per  cent  of  their  contents  in  lumber,  if  sawed  by  the 
same  methods,  the  cubic  standard  might  have  been  universally  accepted, 
as  it  was  in  the  Adu'ondack  region.  But  when  it  developed  that  there 
was  no  consistent  ratio  of  cubic  to  board  feet  the  onlj'-  alternative  was 
to  measure  the  product  directly  as  boards. 

That  the  board-foot  log  rule  was  needed  is  shown  bj^  the  fact  that  such 
rules  were  originated  independently  in  practically  eveiy  lumbering 
region.  The  contents  of  the  log  in  sawed  1-inch  boards  was  placed  on 
the  scale  stick,  separate^  for  each  inch-class  and  each  standard  length. 
These  board-foot  rules  soon  became  practically  the  universal  standard 
of  log  measure,  and  are  only  recently  being  superseded  where  the  logs 
are  used  for  other  purposes  than  lumber;  they  will  continue  to  be  a 
generally  accepted  commercial  standard  of  log  measure  for  the  lumber 
industiy  as  a  whole,  until  such  time  as  the  original  stands  of  timber  of 
the  countrj^  give  way  to  smaller  second-growth  and  closer  utilization 
and  probably  as  long  as  a  large  percentage  of  logs  are  sawed  into  luml)or. 

41,  Relation  of  Diameter  of  Log  to  Per  Cent  of  Utilization  in  Sawed 
Lumber.  The  sawed  output  from  logs  in  board  feet  shows  an  increasing 
per  cent  of  utilization  with  increasing  diameter  of  the  logs.  This  result 
may  be  expressed  by  the  ratio  of  board  feet  produced  from  each  cubic 
foot  of  total  volume.     This  tendency  is  illustrated  in  Table  III. 

The  per  cent  of  utilization  in  this  table  is  based  on  the  total  cubic 
contents  of  the  log  as  measured  by  Huber's  formula  at  middle  diameter 
inside  bark.  But  practically  all  log  rules  for  board  feet  base  the  con- 
tents upon  the  cylinder  whose  diameter  is  taken  at  the  small  end,  in 

40 


RELATION  OF  DIAMETER  OF  LOG 


41 


which  case  the  volume  of  the  log  lying  outside  the  cylinder  is  neglected. 
On  this  basis,  the  apparent  per  cent  of  utilization  would  be  con- 
siderably increased  over  the  figures  given  in  the  table.^ 

TABLE  III 


Relation  of  Cubic  and  Board-foot  Contents  of  16-foot  Logs  with  a  Taper 
OF  1  Inch  in  8  Feet,  Based  on  Tiemann's  Log  Rule,  j^-inch  Saw  Kerf. 
(§63) 


Diameter 
inside  bark  at 
middle  of  log. 

Cubic 

contents. 

Sawed 

contents, 

Tiemann 

Log  Rule. 

Ratio 
feet  B.M.  to 
1  cubic  foot 

Volume 
utilized 

Inches 

Cubic  feet 

Feet  B.M. 

Per  cent 

3 

0.79 

1 

1  27 

10.5 

4 

1.40 

4 

2.85 

23.8 

5 

2.18 

9 

4.13 

34.4 

6 

3.14 

15 

4.77 

39.5 

7 

4.28 

23 

5.37 

44.8 

8 

5.59 

32 

5.71 

47.7 

9 

7.07 

43 

6.08 

50.7 

10 

8.73 

55 

6.30 

52.5 

11 

10.56 

69 

6.53 

54.4 

12 

12.57 

84 

6.68 

55.7 

13 

14.75 

101 

6.85 

57.0 

14 

17.10 

119 

6.96 

57.9 

15 

19.63 

139 

7.08 

59.0 

16 

22.34 

160 

7.16 

59.7 

17 

25.22 

183 

7.26 

60.5 

18 

28.27 

207 

7.32 

61.0 

19 

31.50 

233 

7.39 

61.6 

25 

54,54 

419 

7.68 

64.0 

31 

83.86 

659 

7.86 

65.5 

37 

119.47 

954 

7.99 

66.5 

43 

161.36 

1301 

8.06 

67.2 

49 

209.52 

1703 

8.13 

67.7 

55 

263.98 

2159 

8.18 

68.2 

61 

324.96 

2669 

8.22 

68.5 

1  For  a  16-foot  log  12  inches  at  middle,  with  2-inch  taper,  and  scaling  diameter 
at  end  of  11  inches,  the  cubic  contents  are  10.56  cubic  feet,  the  ratio  of  board  feet 
to  cubic  feet  is  7.95,  and  the  apparent  per  cent  of  utilization  is  66|  per  cent  as  against 
an  actual  55.7  per  cent  when  the  entire  volume  including  taper  is  taken  as  the  basis. 
For  logs  with  considerable  taper,  which  permits  more  lumber  to  be  cut  from  the  slabs 
lying  outside  the  cylinder,  the  apparent  per  cent  of  utilization  would  be  still  greater, 
while  the  actual  per  cent  utilized  would  in  reality  be  lower  for  such  rapidly  tapering 
logs  than  for  more  cylindrical  forms. 


42       THE  MEASUREMENT  OF  LOGS— BOARD-FOOT  CONTENTS 

It  is  practically  impossible  to  secure  closer  utilization  than  70  per 
cent  of  actual  total  cubic  contents  of  logs  in  the  form  of  sawed  inch 
lumber  exclusive  of  the  utilization  of  slabs,  edgings  and  sawdust  when 
circular  saws  whose  kerf  is  j  inch  or  more  are  used.  By  using  band 
saws  which  cut  a  |-inch  kerf  and  by  producing  a  large  per  cent  of  timbers 
and  boards  thicker  than  1  inch,  thus  reducing  the  waste  from  saw  kerf, 
the  utilization  may  rise  as  high  as  80  per  cent  for  the  larger  logs. 

42.  Errors  in  Use  of  Cubic  Rules  for  Board  Feet.  By  comparing  the 
per  cent  of  possible  utilization  in  Table  III  (§  41)  with  the  per  cents 
given  for  cubic  log  rules  in  Table  II  (§  38)  the  character  and  relative 
accuracy  of  these  log  rules  can  be  judged.  For  the  Blodgett  Rule,  with 
a  ratio  of  115  units  to  1000  board  feet  measured  at  middle  diameter, 
the  ratio  or  per  cent  scaled  is  51.9  for  all  classes  and  sizes  of  logs.  By 
comparison  with  Tiemann's  Rule  this  rule  is  shown  to  be  correct  for 
logs  between  9  and  10  inches  in  diameter,  but  over-scales  smaller  logs, 
and  under-scales  larger  logs.  The  original  Blodgett  ratio  of  100  :  1000 
gives  a  per  cent  of  59.7.  This  is  correct  for  16-inch  logs,  too  high  for 
all  logs  of  smaller  diameter  and  too  low  for  larger  logs. 

AMien  the  point  of  measurement  is  shifted  to  the  small  end  of  log,  the 
diameter  measurement  is  correspondingly  reduced.  ^Vhen  the  scale  of 
board-foot  contents  thus  determined  is  compared  with  this  smaller 
cylinder,  the  per  cent  of  utilization  can  be  expressed  for  such  log  rules 
and  applies  uniformly  to  logs  of  all  sizes,  but  only  to  the  small  cylinder 
thus  measured  (§  81). 

A  comparison  of  the  Blodgett  Rule  applied  at  the  small  end  of  log, 
with  the  Tiemann  rule  applied  at  the  middle  of  log,  is  shown  below.  The 
per  cents  will  apply  to  logs  of  all  lengths  whose  total  taper  is  but  2  inches. 


TABLE  IV 
CoMPAHisox  OF  Blodgett  and  Tiemann  Log  Rules  for  Certain  Logs 


Diam- 

^., 1    Per  cent  of 

Per  cent  of 

Per  cent  of 

Per  cent  of 

Error 

eter 

taper. 

small  cylinder 

total  log 

total  log 

total  log 

in 

log. 

scaled  by 

in  small 

scaled  by 

scaled  by 

Blodgett 

Inches 

Inches 

Blodgett  Rule 

cylinder 

Blodgett  Rule 

Tiemann  Rule 

Rule 

6 

2 

56.2 

73.4 

41.2 

44.8 

-  2.6 

12 

2 

.56.2 

85.2 

47.9 

57.0 

-  9.1 

18 

2 

56.2 

89.7 

50.4 

61.6 

-11.2 

24 

2 

56.2 

92.2 

51.8 

64.0 

-12.2 

30 

2 

56.2 

93.7 

52.6 

65.5 

-12.9 

Cubic  rules,  as  a  class,  when  converted  to  read  in  terms  of  board  feet, 
thus  tend  to  over-scale  small  logs  and  under-scale  large  logs,  whether 


SCALING  LENGTH  OF  LOGS  FOR  BOARD-FOOT  CONTENTS         43 

they  are  applied  at  the  middle  point,  or  at  the  small  end.  Of  the  two 
methods  the  small  end  gives  the  most  consistent  results  in  hoard  measure, 
since  both  the  actual  per  cent  utilized  and  the  per  cent  of  total  con- 
tents scaled  decrease  with  diameter  of  log.  But  the  decrease  in  scaled 
contents  is  always  at  a  lesser  rate  than  that  of  actual  sawed  contents, 
hence  the  tendency  to  over-scale  small  logs  remains  though  the  size  of 
the  error  is  reduced. 

43.  Taper  as  a  Factor  in  Limiting  the  Scaling  Length  of  Logs  for 
Board-foot  Contents.  Since  board-foot  contents  of  logs  is  equal  to 
cubic  contents  minus  waste  in  sawing,  the  character  and  amount  of  this 
waste  determines  the  net  scale  of  the  log.  This  waste  consists  of  saw- 
dust, slabs  and  edgings.  As  lumber  is  commonly  manufactured  with 
parallel  edges,  in  even  widths,  the  custom  of  sawing  boards  whose 
length  equals  that  of  the  log  and  rejecting  all  shorter  pieces  would  cause 
a  waste  not  only  of  the  slabs  sawed  from  the  cross  section  at  the  small 
end  but  of  the  entire  taper  of  the  log,  which  would  be  discarded  as 
edgings  and  slabs.  When  board-foot  rules  were  first  brought  into  use 
close  utilization  of  short  lengths  and  of  wedge-shaped  pieces  was  not 
practiced,  and  this  total  waste  actually  occurred.  Under  these  con- 
ditions the  correct  point  of  diameter  measurement  was  not  the  middle, 
but  the  small  end  of  the  log.  Owing  to  their  early  origin,  the  com- 
mercial board-foot  log  rules  now  in  use  are  nearly  all  based  on  measure- 
ment at  the  latter  point. 

This  waste,  as  measured  in  cubic  volume,  increases  rapidly  with 
increasing  length  of  log.  The  shorter  the  logs  cut  from  a  given  tree, 
the  less  will  be  the  apparent  waste  from  taper.  Long  logs,  the  scaled 
contents  of  which  are  based  on  cylinders  measured  at  their  small  end, 
would  give  an  entirely  different  and  much  smaller  scale  than  if  the  same 
logs  were  cut  instead  into  two  or  more  shorter  sections  and  sawed  into 
correspondingly  shorter  lumber.  Instead  of  scaling  one  log  of  a  given 
top  diameter  sometimes  extending  the  entire  length  of  the  bole,  we  would 
then  have  to  scale  a  series  of  shorter  logs,  each  of  which  has  a  top  diam- 
eter larger  than  the  preceding  one  by  the  amount  of  the  taper  between 
the  points  measured.  The  sum  of  volumes  of  these  short  logs  would 
always  exceed  that  of  the  single  log  measured  at  small  end.  These  long 
logs  are  usually  cut  into  two  or  more  sections  at  the  mill.  For  these 
reasons,  logs,  if  their  length  exceeds  a  definite  maximum  are  scaled 
as  the  sum  of  two  or  more  shorter  logs,  by  taking  caliper  measurements 
at  arbitrary  points  of  division;  e.g.,  a  26-foot  log  scaled  as  two  pieces 
would  be  measured  at  its  small  end,  and  at  a  point  12  feet  from  the  end, 
thus  scaling  as  a  12-foot  and  a  14-foot  log.  The  scaling  diameter  of  the 
larger  or  butt  section  exceeds  that  of  the  top  end  by  the  amount  of  the 
taper  between  the  points  measured.     Each  section  is  thus  scaled  as  a 


44       THE  MEASUREMENT  OF  LOGS— BOARD-FOOT  CONTENTS 

cylinder,  and  measured  at  its  upper  or  small  diameter,  and  the  sum  of 
volumes  of  these  cylinders  gives  the  scale  of  the  long  log. 

The  shorter  these  scaling  lengths  are  made,  the  larger  the  total  scale 
of  the  log,  but  the  maximum  scaling  length  must  not  be  shorter  than  the 
average  length  of  the  lumber  sawed.  In  log  rules,  figures  for  lengths 
up  to  40  feet  may  be  given,  and  scaling  practice  often  corresponds,  but 
in  selling  logs  the  U.  S.  Forest  Service  limits  the  scaling  length  to  16 
feet,  which  is  a  standard  commonly  accepted  by  timber  owners. 

44.  The  Introduction  of  Taper  into  Log  Rules.  With  the  increase 
in  utilization,  much  of  the  lumber  formerly  wasted  in  slabs  is  now  secured 
as  short  lengths.  All  log  rules  in  commercial  use  ignore  this  product 
and  treat  the  logs  as  if  cylindrical,  up  to  the  maximum  scaling  length. 
To  overcome  this  drawback  and  include  the  products  from  slabs  or  taper 
without  requiring  the  measurement  of  logs  in  separate  very  short  sec- 
tions, the  International  log  rule  was  constructed, ^  based  on  the  principle 


Taper,  2  inches  in  16  feet.      Vertical  scale  exaggerated. 

Fig.  5. — Short  versus  long  sections  in  measuring  log  contents  and  in  constructing 
a  log  rule. 


of  buUding  up  the  scaled  volume  of  a  log  from  shorter  cylindrical  sec- 
tions. These  short  cylinders  are  4  feet  long  and  each  successive  cylinder 
is  increased  by  |-inch  in  diameter.  The  scaled  contents  of  each  short 
section  is  determined,  and  the  sum  of  these  sections  gives  the  scale  of 
the  log  as  given  in  the  log  rule.  The  soundness  of  this  method  depends 
upon  demonstrating  that  the  average  taper  of  most  logs  is  not  less 
than  that  used  in  the  rule,  namely,  2  inches  in  16  feet.  This  holds  good 
for  most  Northern  and  Western  species,  but  for  vSouthern  pines  the  taper 
does  not  always  equal  this  figure.  To  guard  against  excessive  error 
from  tapers  differing  from  the  rate  used  in  the  rule,  the  maxmium 
scaling  length  is  hmited  to  20  feet. 

If  the  log  in  Fig.  5  is  regarded  as  a  64-foot  log,  scaled  in  four  16-foot  lengths  by 
any  commercial  log  rule,  the  scaling  diameters  are  taken  at  ^,  .6,  C  and  D.  The 
gain  in  scale  is  caused  by  inclusion  of  the  shaded  portions. 

1  The  Measurement  of  Saw  Logs,  Judson  F.  Clark,  Forestry  Quarterly,  Vol.  IV, 
1906,  p.  79. 


THE  INTRODUCTION  OF  TAPER  INTO  LOG  RULES 


45 


Regarded  as  a  64-foot  log  scaled  by  middle  diameter  the  scaUng  diameter  is  C, 
and  the  log  content  is  that  of  a  cylinder  64  feet  long  and  of  size  indicated  by  C  C. 

Regarded  as  a  64-foot  log  scaled  by  end  diameter,  the  scaling  diameter  is  A 
and  the  log  content  is  that  of  a  cylinder  64  feet  long  and  of  size  indicated  by  ^  A'. 

Regarded  as  a  16-foot  log  scaled  at  small  end,  and  not  in  middle,  the  loss  in 
scale  is  indicated  by  the  shaded  portions.  This  loss  is  common  to  all  commercial 
log  scales  based  on  small  end  of  log. 

But  if  the  contents  of  the  16-foot  log  as  given  in  the  scale  when  measm-ed  at  A 
is  built  up  by  measuring  the  log  as  four  4-foot  cylinders  whose  scaling  diameters 
are  A,  B,  C  and  D,  this  loss  from  taper  common  to  all  the  commercial  log  rules, 
except  when  apphed  at  middle  diameter,  is  avoided  and  practically  full  scale  secured. 

A  comparison  of  the  results  of  these  three  methods  of  treating  taper  is  brought 
out  in  Table  V. 

TABLE  V 
Effect  of  Different  Methods  of  Scaling  a  Log 


Length 
of 
log. 

Diameter 
inside  bark. 

Scaling 

diameter 

rounded  off. 

Scaled  as 

one  log  based 

on  small 

diameter. 

Scaled  as 

16-foot  logs 

each  regarded 

as  a  cylinder. 

Scaled  as 
16-foot  logs 

allowing 
1-inch  taper 
every  4  feet. 

Feet 

Inches 

Inches 

Board  feet 

Board  feet 

Board  feet 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

0 

24.5 

.... 

16 

20.6 

21.0 

328 

328 

355 

32 

19.6 

20.0 

590 

623 

675 

48 

17.3 

17.0 

618 

829 

900 

64 

14.0 

14.0 

531 

962 

1050 

The  final  column  in  each  of  the  above  examples  is  the  contents  of  a  log  4  feet 
long  as  scaled  by  the  International  log  rule.  The  difference  in  scale  by  the  other 
methods  is  due  entirely  to  the  length  of  section  scaled  as  one  piece.  In  column  4, 
this  cylinder,  with  top  diameter  indicated,  extends  the  full  length  of  the  log.  In 
column  5,  a  new  diameter  measurement  is  made  every  16  feet,  but  the  cylinder  of 
this  diameter  is  16  feet  long.  In  column  6,  the  diameter  is  taken  at  16-foot  intervals, 
but  the  cylinder  from  which  this  16-foot  log  is  scaled  is  built  up  from  four  cylinders 
each  4  feet  long,  and  each  |-inch  greater  in  diameter  than  the  one  preceding  it. 

If  the  average  taper  of  logs  is  ^-inch  for  4  feet,  and  pieces  4  feet  long  are  mer- 
chantable, then  the  scale  in  column  6  is  correct.  Based  on  this  conclusion  the  loss 
in  scale  through  neglect  of  taper  is  as  follows: 


Length  of 

Scaled  as  one 

Scaled  as  16-foot 

log. 

log. 

logs. 

Feet 

Per  cent  loss 

Per  cent  loss 

16 

8 

8 

32 

13 

8 

48 

31 

8 

64           1 

51 

8 

Thus  the  loss  in  scale  is  proportional  to  the  length  and  total  taper  of  the  log. 


46       THE  MEASUREMENT  OF  LOGS— BOARD-FOOT  CONTENTS 

45.  Middle  Diameter  as  a  Basis  for  Board-foot  Contents.  In  some 
regions  no  attempt  is  made  to  divide  long  logs  in  scaling.  While  short 
logs  are  scaled  at  the  end,  logs  over  a  given  length  are  measured  once  at 
the  middle  and  the  scale  applied  to  the  entire  log.  In  cypress  this 
measurement  is  sometimes  taken  at  a  point  distant  from  the  small  end 
by  one-third  of  the  total  length.  This  practice  of  substituting  middle 
for  end  diameters  on  long  logs  and  scaling  the  log  as  one  long  cylinder 
whose  diameter  is  thus  obtained  assumes  that  the  loss  in  sawing  the 
smaller  top  section  will  be  offset  by  gain  from  taper  in  the  butt  portion. 
The  total  scale  by  this  method  exceeds  that  obtained  by  scaling  the  log 
as  the  sum  of  separate  cylinders. 

In  theory  this  measurement  of  logs  for  board-foot  contents  at  the  middle  diameter 
should  possess  the  same  advantage  over  measurement  at  the  small  end  as  for  cubic 
contents.  But  for  the  former  purpose,  the  factor  of  waste  exercises  a  definite  influ- 
ence on  the  method  of  scaling  adopted,  where  for  cubic  contents  it  does  not. 

With  very  close  utilization  of  short  lengths,  it  may  be  assumed  that  the  sawed 
output  of  two  logs  of  the  same  middle  diameter,  one  of  which  tapers  rapidly,  the 
other  gradually,  would  be  nearly  equal,  since  what  is  lost  at  the  small  end  of  the 
rapidly  tapering  log  would  be  saved  at  the  larger  end.  That  this  is  approximately 
true  is  the  premise  on  which  Tiemann  based  his  board-foot  log  rule  (§  63)  on  middle 
diameter. 

If,  on  the  other  hand,  the  minimum  length  of  board  corresponds  with  the  ordinary 
length  of  log  sawed,  the  log  with  rapid  taper  loses  a  far  greater  percent  than  that 
with  small  taper,  and  two  logs  whose  diameters  at  their  small  end  are  the  same 
would  give  equal  sawed  contents  regardless  of  differences  in  taper.  Since  the  latter 
condition  held  when  the  log  rules  in  common  use  were  invented,  this  fact,  and  not 
the  difficulty  of  scaling  logs  at  the  middle  point,  explains  the  general  adoption  of 
the  custom  of  basing  the  contents  upon  the  diameter  at  the  small  end. 

46.  Definition  and  Basis  of  Over-run.  The  purpose  of  all  log  rules 
is  to  furnish  a  standard  of  measurement  for  logs,  fair  alike  to  buyer  and 
seller.  For  board-foot  log  rules  this  is  best  accomplished  when  the 
rule  measures  accurately  the  amount  of  lumber  that  may  be  sawed  from 
straight,  sound  logs.  It  was  the  intention  and  the  claim  that  each  of  the 
fifty  or  more  log  rules  extant  should  perform  this  service  under  the  con- 
ditions for  which  it  was  made;  j^et  in  spite  of  this  fact,  the  contents  of 
sound  logs  of  the  same  dimensions,  as  measured  by  different  rules,  may 
diiTer  more  than  100  per  cent. 

While  some  rules  based  on  incorrect  premises  never  were  accurate,  most  of  the 
rules  as  checked  by  actual  mill  tests  were  probably  satisfactory  when  first  employed. 
But  these  rules  were  not  changed  to  keep  pace  with  the  closer  utilization  brought 
about  by  the  improvements  in  machinery,  methods  and  markets.  Although  obso- 
lete as  a  mea.sure  of  actual  product,  they  have  been  retained  through  custom.  It  is 
difficult  to  supplant  or  alter  a  commonly  accepted  standard  of  measure,  even  if 
grossly  inconsistent  and  inaccurate. 

Antiquated  log  rules  thus  cease  to  perform  the  true  function  for  which  they 


INFLUENCES  AFFECTING  OVER-RUN  47 

were  intended,  of  measuring  in  the  log  the  possible  output  of  lumber.  The  sawed 
product  tends  to  over-nm  the  scale  of  contents  shown  by  the  log  rule. 

An  excess  of  sawed  over  scaled  contents  of  logs  is  termed  the  over-run. 
The  over-run  is  always  stated  as  a  per  cent  of  the  log  scale.  The  log 
rule,  whether  accurate  or  defective,  is  accepted  as  the  fixed  standard, 
giving  the  same  contents  for  all  straight  and  sound  logs  of  the  same 
dimensions.  Over-run,  on  the  contrary,  will  vary  with  several  factors. 
A  knowledge  of  the  average  per  cent  of  over-run  which  may  be  expected 
over  the  scale  enables  both  buyer  and  seller  of  logs  to  gage  their  value 
more  accurately.  As  value  is  dependent  on  the  price  of  lumber,  the 
dealer  in  logs  must  know  whether  for  every  1000  board  feet  of  lumber 
scaled  by  the  log  rule,  there  will  be  obtained  say  1250  board  feet  of 
sawed  lumber,  or  only  the  1000  board  feet  scaled,  for  in  the  former 
case  the  logs  are  worth  25  per  cent  more  per  1000  board  feet  of  scaled 
contents  than  in  the  latter. 

47.  Influences  Affecting  Over-run.  The  Log  Rule  Itself.  Two  log 
rules  giving  different  scaled  contents  for  logs  of  the  same  sizes  will  yield 
correspondingly  different  per  cents  of  over-run.  Each  rule  is  arbitrarily 
assumed  to  represent  a  standard  of  100  per  cent,  the  over-run  being 
computed  in  terms  of  the  rule  employed. 

For  instance,  a  given  quantity  of  logs  when  scaled  by  the  Doyle  rule  may  measure 
67,000,  and  saw  out  100,000  board  feet.  Instead  of  stating  that  the  log  scale  gives 
67  per  cent  of  the  actual  product,  with  an  "over-run"  of  33  per  cent,  the  scale  is 
taken  as  the  standard  or  100  per  cent,  and  the  correct  over-run  in  this  case  is  49  per 
cent.  When  scaled  by  the  Scribner  rule,  these  same  logs  may  give  85,000  board 
feet.  In  this  case  the  over-nm  will  be  17.6  per  cent  since  15,000  board  feet  is 
17.6  per  cent  of  85,000  board  feet  scaled  in  the  log. 

Since  the  quantity  of  sound  lumber  contained  in  logs  can  be  measured  with 
only  approximate  accuracy,  due  to  hidden  defects  and  other  factors,  the  buyer 
demands  a  certain  margin  of  safety.  A  reasonable  over-run  of  from  5  to  10  per 
cent  is  usually  expected.  With  a  properly  constructed  log  rule,  the  over-run  should 
be  about  the  same  for  large  as  for  small  logs.  The  worst  defect  which  a  log  rule 
can  possess  is  inconsistency  in  scale  between  logs  of  different  sizes  (§39).  Slight 
irregularities  in  scale  of  individual  diameter  classes  may  average  out  in  the  general 
run  of  logs.  But  when  the  per  cent  of  board-foot  contents  scaled  by  a  log  rule 
increases  or  decreases  in  proportion  to  size  of  log,  there  Ls  no  way  of  adjusting  it. 
The  over-run  will  then  vary  with  the  average  size  of  the  logs  scaled.  Such  a  rule 
can  never  give  permanent  satisfaction  to  both  the  buyer  and  the  seller  of  logs. 

48.  Influences    Affecting    Over-run.     Methods    of    Manufacture. 

With  a  fixed  standard  set  by  a  log  rule,  the  greater  the  economy  of  man- 
ufacture, the  greater  will  be  the  over-run.  Any  factor  which  reduces 
the  waste  in  manufacture  increases  the  output.  The  waste  in  straight, 
sound  logs  consists  of  slabs,  edgings,  trimmings  and  sawdust.  In  addi- 
tion, there  may  be  a  loss  or  gain  in  the  scale  of  lumber  due  to  fractional 
thicknesses  not  measured  in  board  feet  (§20). 


48       THE  MEASUREMENT  OF  LOGS— BOARD-FOOT  CONTENTS 

Saw  Kerf.  The  fewer  the  number  of  saw  cuts  required,  the  less  the 
waste.  Lumber  sawed  and  measured  to  standard  thicknesses  greater 
than  1  inch  therefore  increases  the  total  output  in  board  feet.  A  dimin- 
ished thickness  of  the  saw  has  a  similar  influence.  Log  rules,  correct 
when  adapted  to  a  j-inch  saw  kerf,  give  an  over-run  of  more  than  10 
per  cent  when  a  |-inch  saw  kerf  is  cut.  The  use  of  circular  saws  cutting 
a  3^-inch  kerf  partially  accounts  for  the  small  scaled  contents  given 
by  some  of  the  old  log  rules. 

Slabs.  Waste  in  slabs  is  reduced  by  sawing  narrow  and  thin  boards 
and  short  lengths.  The  short  lengths  serve  to  fully  utilize  the  taper  in 
long  logs,  increasing  the  over-run  on  this  class  of  material.  The  method 
of  sawing  a  log  also  affects  the  per  cent  of  utilization  of  slabs.  Slash 
sawing,  or  sawing  alive,  as  practiced  for  round-edged  boards  (§  21) 
would  result  in  waste  where  the  boards  are  to  be  used  in  their  full  length, 
and  trimmed  to  square  parallel  edges.  By  this  method,  short  boards 
would  be  secured  from  but  two  sides  of  the  log.  The  usual  custom  in 
manufacturing  lumber  of  standard  lengths  is  to  turn  and  square  the  log, 
slabbing  all  four  sides. 

The  gain  in  sawed  product,  by  sawing  around,  in  comparison  with  slash  sawing, 
for  square-edged  boards,  was  shown  to  equal  the  following  per  cents,  as  determined 
by  H.  D.  Tiemann. 

TABLE  VI 

Gain  in  Output  Secured  by  Sawing  Around,  Compared  with  Slash  Sawing, 
IN  Per  Cent  of  Latter  Output 


Diameter 
of  log. 

Length  10  feet. 

Length  20  feet. 

Inches 

Per  cent  saved 

Per  cent  saved 

6 

15 

22 

7 

14 

18 

8 

13 

15 

9 

12 

13 

10 

11 

11 

11 

9 

10 

12 

6 

7 

13 

4 

6 

Above  13  inches  the  difference  is  less  perceptible.  Where  round-edged  boards 
are  fully  utilized  and  not  reduced  to  square  parallel  edges,  not  only  does  sawing 
around  give  place  to  slash  sawing,  but  the  per  cent  of  utilization  is  much  greater 
than  by  either  method  of  sawing  for  square-edged  lumber,  due  to  the  shorter  lengths 
utilized  in  working  up  the  round-edged  lumber  in  the  factory. 


STANDARDIZATION  OF  VARIABLES  IN  LOG  RULE  49 

Full  and  Scant  Thicknesses  of  Boards.  Boards  not  cut  to  exact 
dimensions,  if  cut  full  lose  the  excess  when  measured,  and  if  too  scant 
are  either  rejected,  or  reduced  in  grade.  If  cut  scant  but  within  pre- 
scribed hmits,  they  are  scaled  by  superficial  measure,  and  increase  the 
over-run  (§20). 

In  either  case  the  sawyer  to  secure  full  scale  of  lumber  must  pro- 
duce boards  measuring  within  ^-inch  of  the  required  thickness.  This 
is  impossible  without  good  machinery.  In  local  custom  mills,  much 
lumber  is  manufactured  in  uneven  thicknesses  causing  a  loss  in  scale 
and  reducing  the  over-run. 

49.  Standardization  of  Variables  in  Construction  of  a  Log  Rule. 
The  over-run  in  sawing  logs  will  depend  for  a  given  log  rule  upon  thick- 
ness of  saw  kerf,  average  dimensions  of  lumber,  closeness  of  utilization 
of  slabs  and  of  taper,  and  the  exactness  of  manufactured  dimensions. 
All  four  of  these  factors  are  variables. 

For  a  given  mill,  the  saw  kerf  alone  is  constant  and  even  then  the  waste  will  vary 
if  two  or  more  saws  of  different  kerfs  are  used.  The  other  factors  are  variable. 
For  different  mills,  one  or  more  conditions  are  certain  to  differ  radically,  giving  a 
corresponding  increase  or  decrease  in  over-rmi.  Standardization  of  output  and 
methods,  possible  in  mills  of  the  same  class  serving  the  same  markets,  may  secure  a 
similar  degree  of  slab  utilization  and  of  efficiency  in  sawing  to  exact  dimensions, 
but  this  still  leaves  the  fourth  variable,  differences  in  thickness  of  lumber  sawed,  to 
affect  the  over-run. 

Where  the  sawed  output  is  in  thicknesses  less  than  1  inch,  and  expressed  in 
superficial  feet,  the  product  is  not  comparable  with  1-inch  lumber  and  must  be 
reduced  to  terms  of  1-inch  boards  for  a  true  comparison  with  the  log  scale. 

Arbitrary  Standards.  The  essentials  of  any  standard  of  measure 
are  fixed  qualities  and  common  acceptance.  Even  a  poor  or  faulty 
standard  which  is  universally  used  would  be  better  than  a  number  of 
different  rules,  or  a  rule  which  may  be  changed  to  suit  conditions  or 
the  preference  of  the  user.  These  four  variables  must  therefore  be 
arbitrarily  fixed  in  adopting  values  for  a  standard  or  common  log  rule, 
and  in  the  case  of  most  rules  which  have  found  wide  use  this  was  done. 
The  thickness  of  lumber  was  fixed  at  1  inch,  permitting  an  over-run 
whenever  thicker  dimensions  are  sawed.  The  width  of  saw  kerf  adopted 
by  the  rule  was  that  used  at  the  time  and  place  of  constructing  the 
rule,  and  was  usually  i-inch  or  larger.  Local  custom  determined  the 
width  of  the  narrowest  1-inch  board  sawed  and  this  fixed  the  amount 
of  waste  allowed  for  slabbing  and  edging.  Taper  was  disregarded. 
Boards  were  usually  measured  only  to  the  nearest  full  inch  of  width 
and  fractional  inches  disregarded.  Skill  in  manufacture  was  considered 
by  checking  the  results  of  the  rule  with  the  actual  sawed  output,  by 
means  of  mill  tallies. 


50        THE  MEASUREMENT  OF  LOGS— BOARD-FOOT  CONTENTS 

Variable  Standards.  As  contrasted  with  these  fixed  standard  rules, 
comes  the  suggestion  '  for  a  log  rule  in  which  average  thickness  of  lumber, 
saw  kerf  and  degree  of  utilization  of  slabs  and  taper  shall  be  represented 
by  variable  quantities,  and  adjusted  by  each  mill  owner  to  suit  the 
conditions  of  manufacture  prevailing  at  the  time  or  for  the  past  few 
months.  Such  a  rule,  when  adjusted,  would  eliminate  over-run  as 
long  as  the  variables  in  manufacture  on  which  it  was  computed  remained 
unchanged.  But  as  a  standard  of  measurement  it  could  never  have 
any  general  or  legal  status  unless  its  values  were  fixed,  when  it  would 
at  once  be  open  to  the  same  objections  which  by  its  flexibility  it  sought 
to  avoid. 

50.  The  Need  for  More  Accurate  Log  Rules.  The  great  question 
with  log  rules  is  whether  conditions  have  changed  so  permanently  that 
new  rules  adjusted  to  these  factors  should  replace  those  now  in  use. 
The  j-inch  circular  saw  is  still  retained  in  small  custom  mills,  and  there 
is  a  tendency,  in  regions  that  have  been  cut  over  by  big  operators,  to 
revert  to  these  primitive  methods.  The  operator  of  a  band  saw  mill 
is  probably  entitled  to  the  over-run  resulting  from  the  use  of  thinner 
saws  and  closer  utilization.  A  log  rule  made  to  scale  closely  the  out- 
put of  such  up-to-date  plants  would  exceed  the  product  of  the  small 
mill.  Provided  the  rule  is  consistent,  a  conservative  log  rule  which 
will  give  an  over-run  varying  in  per  cent  with  closeness  of  utilization 
is  probably  better  for  commercial  uses  than  one  which  aims  at  securing 
the  maximum  product  from  modern  mills. 

Log  rules  based  on  correct  mathematical  principles  are  the  only 
rules  from  which  consistent  and  satisfactory  results  can  be  expected, 
and  this  is  a  far  more  important  factor  than  the  elimination  of  over- 
run. If,  in  addition,  such  log  rules  conform  to  the  present  conditions 
of  manufacture,  they  have  a  use  in  scientific  measurements  of  logs  and 
standing  timber,  as  a  basis  for  estimates  of  volume  and  growth  expressed 
in  the  board-foot  unit.  This  use  of  such  a  rule  would  justify  its  exist- 
ence, entirely  aside  from  the  question  of  its  possible  universal  adoption 
as  a  legal  standard  of  log  measure. 

51.  The  Waste  from  Slabs  and  Edgings.  The  total  waste  in  sawing 
straight  sound  logs  is  the  sum  of  the  two  factors,  sawdust,  and  slabs 
plus  edgings.  For  lumber  of  a  given  thickness,  such  as  1-inch  boards, 
the  portion  of  the  cross  section  of  the  log  wasted  in  slabs  and  edgings 
may  be  shown  graphically  by  plotting  on  diagrams,  allowing  the  proper 
space  between  each  board  for  saw  kerf.  From  these  diagrams  it  is 
possible  to  compute  the  area  of  this  waste,  in  square  inches,  and  the 
thickness  of  a  ring  or  collar  which  will  have  the  same  area  and  thus 
represent  the  waste  from  slabbing  and  edging. 

1  H.  E.  McKenzie,  Bui.  5,  California  State  Board  of  Forestry,  1915. 


THE  WASTE  FROM  CROOK  OR  SWEEP 


51 


When  this  is  done  for  logs  of  all  sizes  it  is  found  that  except  for  the 
smaller  logs  the  width  of  these  collars  is  practically  the  same  regardless 
of  diameter.  This  law  does  not  hold  for  small  logs,  because  the  width 
of  the  minimum  boards  remains  the  same  for  all  logs  and  as  the  diameter 
of  the  log  approaches  this  minimum  width  of  board,  the  proportional 
waste  in  slabs  and  edgings  rapidly  increases  until  utilization  becomes 
zero  and  waste  100  per  cent  for  a  diameter  of  log  just  too  small  to  saw 
out  the  smallest  board  or  piece  that  is  merchantable. 

The  waste  in  slabbing  and  edging  varies,  for  any  log,  with  the  aver- 
age thickness  of  the  lumber  sawed.  Logs  sawed  entirely  into  2j-inch 
plank  would  show  considerably 
greater  waste  in  edging  than  where 
1-inch  boards  are  sawed  (§  21). 
The  results  shown  by  diagram  are 
confirmed  by  tests  in  the  mill. 

From  these  investigations  it  is 
evident  that  the  waste  from  slabs 
and  edgings  is  proportional,  approx- 
imately, to  the  surface  of  the  log 
inside  the  bark.  The  surface  of  a 
log  is  equal  to  the  circumference  or 
girth,  multiplied  by  the  length.  As 
circumference  equals  xD  for  all 
logs,  the  waste  from  slabs  and  edging 
is  then  proportional  to  the  diameter 
of  the  log  multiplied  by  its  length. 

But  the  volume  of  the  log  in- 
creases as  the  cross  sectional  area, 
which  is  proportional  to  the  square  of 
the  diameter  (§  27).  The  amount  of 
waste  in  slabs  and  edgings  from  a  log 
20  inches  in  diameter  is  just  twice 

that  for  a  10-inch  log,  since  the  diameter  and  the  surface  are  doubled. 
But  the  20-inch  log  contains  four  times  the  volume  of  the  smaller  piece, 
and  this  reduces  the  per  cent  of  waste  from  slabs  and  edgings  based  on 
the  volume  of  the  larger  log  to  one-half  that  for  the  10-inch  log. 

52.  The  Waste  from  Crook  or  Sweep.  Log  rules  apply  only  to 
straight  logs.  But  the  standard  as  to  what  constitutes  straight  logs 
requires  definition.  For  all  commercial  log  rules,  this  standard  permits 
of  "  normal  "  crook  (§  93).  This  is  best  defined  as  crook  averaging 
not  over  1|  inches  in  12  feet,  and  including  no  log  which  crooks  more 
than  4  inches  in  12  feet.  Crook  or  sweep  in  long  logs  is  reduced  by 
cutting  them  into  two  or  more  short  sections  before  sawing.     Where 


Fig 


— Relative  waste  in  slabs  and 
edgings  from  sawing  2j-inch  plank 
and  1-inch  boards.  If  1-inch  boards 
are  sawed,  the  waste  is  reduced  by 
the  amount  of  the  shaded  portion. 
The  greater  proportion  of  waste  in 
sawing  thick  boards  comes  from  the 
side  cuts,  hence  the  practice  is  to 
cut  1-inch  lumber  from  the  sides. 


52       THE  MEASUREMENT  OF  LOGS— BOARD-FOOT  CONTENTS 

very  short  material  such  as  box  boards  is  used,  crook  does  not  cause 
abnormal  waste  in  logs.  Care  in  laying  off  log  lengths  in  the  woods 
to  secure  the  maximum  length  of  straight  sections  by  dividing  the 
tree  at  the  points  of  greatest  crook  reduces  this  source  of  waste  to  small 
proportions. 

Waste  from  crook  is  deducted  in  scaling  on  the  assumption  that 
the  merchantable  portion  of  the  log  must  cut  boards  extending  its 
whole  length.  The  influence  of  length  of  log  upon  the  waste  due  to 
crook  is  very  pronounced,  and  where  long  logs  are  divided  into  shorter 
lengths  in  the  mill  they  should  never  be  discounted  for  crook  except 
to  the  extent  that  this  crook  will  affect  the  sawed  contents  of  the  shorter 
pieces.  For  lumber  longer  than  12  feet  the  influence  of  crook  rapidly 
increases. 

The  relation  of  normal  crook  to  taper  is  shown  in  Fig.  7  in  which  the 
line  DE  is  the  axis  of  the  cylinder  corresponding  to  a  straight  log.  The 
line  AB  is  parallel  to  this  axis  and  tangent  to  the  margin  at  the  small 


Fig.  7. — Method  of  measuring  amount  of  crook  in  a  log,  in  inches.  The  line  JM 
represents  the  proper  measurement,  coinciding  with  the  shaded  portion  J  A  or 
waste  in  the  circle  representing  small  end  of  log. 

end.  The  line  AC  is  a  straight  line  connecting  the  margins  of  both  ends 
of  the  log.  Were  the  log  cylindrical,  the  line  HJ  under  these  circum- 
stances would  represent  the  amount  of  crook.  But  the  taper  gives  a 
larger  cross-section  at  JL  than  at  AK.  Unless  crook  exceeds  the  taper 
for  half  the  log,  the  cross-section  JL  when  projected  upon  AK  would 
completely  cover  it,  permitting  as  much  lumber  to  be  sawed  as  if  the  log 
were  straight.  In  the  diagram  the  crook  exceeds  this  taper  and  the 
upper  shaded  portion  of  the  cross  section  which  represents  the  small 
end  must  be  wasted  in  slabs,  in  addition  to  the  normal  slabbing  of  a 
round  log. 

But  this  waste  is  incorrectly  measured  by  any  other  method  than 
that  shown  by  the  line  JM,  which  is  the  distance  to  the  surface  of  the 
log  from  a  line  parallel  to  the  axis,  and  tangent  to  the  margin  of  the  small 
end.     This  distance  gives  the  crook  in  inches. 

*  For  a  16-foot  log  tapering  2  inches,  a  crook  of  1  to  1|  inches  at  the 
middle  point  has  no  appreciable  effect  on  the  output. 


THE  WASTE  FROM  SAW  KERF 


53 


By  slabbing  in  the  direction  of  KN  this  waste  may  be  still  further 
reduced,  since  the  cylinder  sawed  is  not  parallel  with  the  axis  but  follows 
the  crook  at  the  small  end,  and  takes  maximum  advantage  of  taper  at 
butt.  Logs  so  crooked  that  their  sawed  contents  is  materially  reduced 
are  not  scaled  "  straight  and  sound  "  or  full.  Deductions  for  crook  are 
discussed  in  §  93.  The  waste  from  normal  crook  is  included  with  that 
for  slabbing  and  edging  and  is  in  proportion  to  surface,  and  hence  to 
diameter. 

53.  The  Waste  from  Saw  Kerf.  The  total  waste  in  sawdust,  unlike 
that  in  slabs  and  edgings,  takes  approximately  the  same  per  cent  of  the 
cubic  volume  of  all  logs,  regardless  of  their  size.  If  a  log  is  sawed  by  the 
method  called  slash  sawing,  in  parallel  saw  cuts  without  squaring  it, 
then,  after  the  first  slab  is  removed,  there  will  be  one  saw  kerf  to  each 


Fig.  8. — Waste  incurred  as  slabs  and  sawdust  in  sawing  round,  straight  logs. 

board.  The  initial  saw  kerf,  and  the  sawdust  wasted  in  edging,  and  in 
ripping  wide  boards  into  narrower  boards,  forms  an  additional  percentage 
of  waste  not  exactly  proportional  to  volume.  Disregarding  this  dis- 
crepancy, the  fixed  per  cent  of  waste  from  saw  kerf  for  the  log  is  the  same 
as  the  per  cent  wasted  in  sawing  one  board.  If  the  thickness  of  board 
plus  that  of  the  saw  is  taken  as  100  per  cent,  this  waste,  for  a  1-inch 
board  with  j-inch  saw  kerf  is  as  ^  to  1  j  or  20  per  cent,  while  for  a  |-inch 
saw  kerf  the  proportion  is  |  to  1|  or  11.1  per  cent.  A  general  formula 
applicable  to  saws  of  all  thicknesses  is  as  follows : 


Let       K  =  width  of  saw  kerf; 
T  =  thickness  of  lumber. 


Then 


T+-K^  =  total  volume  of  board  plus  kerf, 


54         THE  MEAStfREMENT  OF  LOGS— BOARD-FOOT  CONTENTS 
K 


T-VK 

T 
T+K 


per  cent  deduction  for  saw  kerf, 
per  cent  of  log  utilized  as  lumber. 


Efforts  to  account  for  the  exact  per  cent  of  waste  in  sawdust  have  been  made, 
by  including,  first  the  saw  kerf  required  for  ripping  or  edging  one  edge,  as  shown 
in  Fig.  8,'  and  second,  the  additional  saw  kerf  for  the  first  slab.  But  neither  method 
is  complete,  since  boards  are  edged  when  necessary  on  both  edges.  The  best  method 
is  probably  to  include  this  extra  saw  kerf,  together  with  the  edgings,  in  the  waste 
due  to  slabbing,  leaving  the  sawdust  as  a  straight  per  cent  of  volume.   ' 

Shrinkage.  Where  shrinkage  is  considered,  or  where  lumber  must  be 
sawed  a  trifle  full,  the  extra  thickness  which  is  not  measured  in  the 
green  lumber  constitutes  a  waste  exactly  similar  to  saw  kerf,  and  can  be 
added  to  the  latter  factor  in  the  formula  before  calculating  the  per 
cent  of  reduction. 

For  instance,  if  a  log  rule  is  intended  to  measure  the  output  of  1-inch 
lumber  after  seasoning,  and  the  average  shrinkage  on  inch  boards  is 
i^-inch,  and  saw  kerf  |-inch,  the  per  cent  of  waste  in  small  logs  is 

s+.Tfi-        .1875      ICO  J. 

15.8  per  cent. 


1+I+T6     1-1875 

1  By  the  inclusion  of  one  edge,  the  formula  for  sawdust  would  be: 

Volume  of  unit  {W+K){T+K), 

Saw  kerf  K{W  +  T+K), 

KiW  +  T-\-K) 
Per  cent  of  waste —^;;^y^--. 

H.  E.  McKenzie,  Bui.  5,  California  State  Board  of  Forestry,  Sacramento,  Cal., 
1915. 

By  inclusion  of  the  extra  saw  kerf  but  not  of  the  cut  for  edging. 

Number  of  cuts  =A'^, 


Average  saw  kerf  per 

board 

-■4 

Volume  of  unit 

=r+.+f, 

Per  cent  of  waste 

C.  M.  Hilton,  Bangor,  Me.,  1920. 


TOTAL  PER  CENT  OF  WASTE  IN  LOG  55 

Corrections  for  Saw  Kerfs  of  Different  Widths.  Since  the  per  cent  of 
waste  caused  by  saw  kerf  applies  directly  to  the  residual  volume  of  logs 
after  subtracting  the  waste  for  slabbing  and  edging,  the  effect  of  using 
a  saw  of  greater  or  lesser  width  than  that  used  in  constructing  the  rule 
can  be  found  in  terms  of  a  per  cent  of  the  values  of  the  log  rule.  This 
flat  correction  can  then  be  applied  if  desired,  to  correct  timber  estimates, 
convert  the  log  rule  into  one  which  eliminates  over-run  from  saw  kerf, 
or  correct  the  scale  of  logs  to  coincide  more  closely  with  sawed  output. 

For  instance,  the  above  rule  would  utilize  1  — .158  or  84.2  per  cent  of  the  net 
cubic  contents  of  the  cylinder.  A  saw  cutting  a  j-inch  kerf,  with  the  same  allowance 
for  shrinkage,  calls  for  the  formula, 

i+A  .3125 

=  23.8  per  cent, 


l+i+fe     1-3125 

giving  72.6  per  cent  utilized.     The  values  expressed  by  the  log  rule  made  for  the 

§-inch  kerf  must  now  be  taken  as  100  per  cent  to  which  the  correction  will  apply. 

76.2 

Then gives  90.5  per  cent.     The  second  rule  requires  values  equaling  90.5  per 

84 . 2 

cent  of  the  first,  or  a  straight  reduction  of  9.5  per  cent. 

That  this  conversion  can  be  accurately  made  was  demonstrated  on  diagrams  by 

H.  D.  Tiemann,  who  found  that  the  possible  error  was  less  than  one-half  of  one 

per  cent.^ 

54.  Total  Per  Cent  of  Waste  in  a  Log.  The  total  per  cent  of  waste  in 
a  log  is  the  sum  of  the  waste  from  slabbing  and  edging,  or  surface  waste, 
and  from  saw  kerf.  The  proportion  of  this  total  waste  represented 
respectively  by  slabbing  and  by  sawdust  will  depend  upon  which  of 
these  deductions  is  made  first,  and  whether  the  sawdust  made  in  slabbing 
and  edging  is  included  as  part  of  the  waste  in  slabs  and  edgings,  or  is 
counted  as  part  of  the  waste  in  sawdust.  If  the  deduction  for  sawdust 
is  made  first,  it  will  include  a  fixed  per  cent  of  the  cubic  volume  of  the 
log.  If  on  the  other  hand,  the  slab  waste  is  first  deducted  as  a  ring  or 
collar  of  a  given  thickness,  the  subsequent  deduction  for  saw  kerf, 
although  the  per  cent  is  the  same,  applies  only  to  the  residual  volume  of 
the  log. 

The  total  per  cent  of  waste,  and  its  distribution  between  these  two  factors  is 
illustrated  in  table  VIL  Let  slab  waste  equal  a  ring  f-inch  in  thickness  or  a 
reduction  of  1.5  inches  in  diameter.  Sawdust,  for  J-inch  kerf,  equals  20  per  cent. 
The  per  cent  of  waste  will  vary  with  diameter  of  logs,  as  shown : 

In  column  2  the  per  cent  of  waste  is  seen  to  be  approximately  one-half  as  great 
for  20-inch  logs  as  for  10-inch  logs. 

1  Proc.  Soc.  of  Am.  Foresters,  Vol.  V,  1909,  p.  29. 


56       THE  MEASUREMENT  OF  LOGS— BOARD-FOOT  CONTENTS 

TABLE  Vn 
Distribution  of  Waste  between  Slabbing  and  Sawdust 


1 

2 

3 

4 

5 

6 

7 

8 

Diameter 

at 

small 

end  of 

log. 

Inches 

Waste  in 
slabbing. 

Per  cent 

Waste  in 

sawdust 

20  per  cent 

of 

remainder 

of  log. 

Per  cent 

Total 

waste 

Columns 

2+3. 

Per  cent 

Waste 

saw  kerf 

in 

slabs. 

Per  cent 

Total 

waste 

saw  kerf, 

Columns 

3+5. 

Per  cent 

Waste  in 

slabs  less 

saw  kerf 

in 

slabs. 

Per  cent 

Utiliza- 
tion.* 

Per  cent 

10 
20 
40 

27.75 
14.44 

7.27 

14.45 
17.11 

18.54 

42.20 
31.55 
25.81 

5.55 
2.89 
1.45 

20 
20 
20 

22.20 
11.55 

5.82 

57.80 
68.45 
74.19 

*  Of  the  small  cylinder  not  including  taper. 


The  waste  in  slabbing  would  be  exactly  proportional  to  diameter  except  for  the 
fact  that  the  volume  of  the  hollow  cylinders  representing  the  collar  deducted  for 
slabs  is  not  directly  proportional  to  the  outer  surface  of  the  respective  cylinders  in 
logs  of  different  sizes.  The  same  relation  is  seen  to  hold  whether  or  not  the  slab 
waste  is  deducted  before  or  after  the  sawdust.     (Columns  2  and  7.) 

Since  the  per  cent  of  slab  waste  is  roughly  proportional  to  D,  while  that  from 
sawdust  is  as  D-,  the  sum  of  these  two  factors  causes  the  total  per  cent  of  waste  to 
decrease  as  shown  in  column  4,  instead  of  remaining  constant  as  in  column  6.  The 
rate  of  decrease  is  less  rapid  than  in  columns  2  or  7  since  only  a  -portion  of  the  waste 
decreases  in  per  cent  with  increasing  diameter  of  log. 

Were  the  total  waste  in  logs  proportional  to  D^  as  is  the  waste  from 
saw  kerf,  log  rules  could  be  converted  from  cubic  to  board  feet  by  a 
single  ratio.  But  since  the  part  of  this  waste  due  to  slabbing  is  pro- 
portional to  D,  the  per  cent  of  total  waste  decreases  with  increasing  diameter 
by  a  rate  which  is  the  sum  of  these  two  factors  and  is  therefore  directly 
proportional  to  neither  D  nor  D^.  This  explains  the  increasing  per  cent 
of  utilization  secured  in  sawing  larger  logs  and  the  need  for  log  rules 
based  directly  upon  the  board-foot  unit  and  not  derived  by  conversion 
of  cubic  units. 

To  derive  an  accurate  log  rule,  not  only  must  the  waste  from  slabs 
and  edgings  be  deducted  separately  from  the  waste  from  saw  kerf,  but 
the  correct  amount  must  be  deducted  for  each  source  of  waste.  A  rule 
which  deducts  too  much  for  slabs  and  too  little  for  saw  kerf  will  deduct 


TOTAL  PER  CENT  OF  WASTE  IN  LOG  57 

too  much  on  small  logs,  where  the  slab  waste  is  normally  high,  and  too 
little  on  large  logs,  where  the  greater  portion  of  the  deduction  is  for  saw 
kerf.  Such  a  rule  can  be  correct  only  for  a  single  diameter  class  where 
the  two  errors  happen  to  balance. 

On  the  other  hand,  if  too  small  a  deduction  is  made  for  slabs,  and 
too  large  for  sawdust,  small  logs  may  be  overscaled,  while  the  increasing 
per  cent  of  utilization  possible  in  larger  logs  will  not  be  shown  in  the 
scale  (Column  8),  and  the  rule  therefore  tends  to  under-scale  large  sizes. 


CHAPTER  VI 

THE  CONSTRUCTION  OF  LOG  RULES  FOR  BOARD-FOOT 
CONTENTS 

55.  Methods  Used  in  Constructing  Log  Rules  for  Board  Feet.     The 

great  variation  in  the  contents  of  different  log  rules  for  board  feet,  and 
the  variation  in  accuracy  and  consistency  of  these  rules  is  due  to  the 
methods  used  in  their  construction  as  well  as  to  the  factor  of  over-run 
resulting  from  closer  utilization. 

Four  general  methods  have  been  used  in  constructing  such  rules. 
These  are: 

1.  By  mathematical  formulae.  A  formula  is  used,  which  derives  the 
board-foot  contents  of  the  log  directly  from  its  diameter  and  length,  by 
allowing  for  reductions  from  D^XL  for  cubic  volume,  waste  in  saw 
kerf,  waste  in  slabs,  and  reduction  of  residual  volume  to  board  feet.  If 
the  principles  used  in  making  these  reductions  (§  54)  are  correct  and  the 
amounts  used  are  also  correct,  such  log  rules  are  superior  to  diagram 
rules,  but  if  errors  in  either  principles  or  amounts  of  deduction  are 
introduced  into  the  formula,  the  rule  is  worse  than  useless. 

2.  By  diagrams.  Full-sized  circles  of  all  diameters  are  drawn  on 
large  sheets  of  paper,  representing  the  top  ends  of  the  logs.  On  these 
cross  sections  of  the  log  the  ends  or  cross  sections  of  the  boards  which 
could  be  sawed  from  these  logs  are  drawn,  leaving  between  each  board  a 
space  equal  to  the  width  of  the  saw  kerf.  The  area  of  boards  in  square 
inches  is  then  reduced  to  board  feet  by  the  factor  i^X  length  in  feet,  for 
logs  of  a  standard  length,  and  from  this,  for  logs  of  all  lengths. 

3.  By  tallying  the  actual  sawed  contents  of  logs  at  the  mill  for  differ- 
ent diameters  and  lengths.  Owing  to  the  variables  introduced  by  the 
thickness  of  lumber  sawed,  and  by  taper,  this  method  has  seldom  been 
accepted  as  the  sole  basis  for  a  log  rule,  but  has  been  extensively  used 
to  check  the  accuracy  of  rules  made  by  the  preceding  two  methods. 

4.  By  conversion  of  the  cubic  contents  of  logs  into  board  feet,  after 
deducting  a  fixed  per  cent  of  this  total  cubic  contents  for  waste  in  saw- 
ing and  slabbing.  As  shown  in  Chapter  V,  all  board-foot  log  rules 
constructed  on  this  basis  are  fundamentally  wrong. 

A  fifth  method  has  been  used,  which  is  a  combination  of  methods 
1  and  2  or  3,  namely,  to  alter  or  correct  the  values  of  an  existing  log  rule, 
by  means  of  mill  tallies  obtained  in  sawing.     The  author  of  such  cor- 

58 


THE  CONSTRUCTION  OF  LOG  RULES  59 

rections  may  give  a  new  name  to  such  a  rule,  or  may  state  that  it  is 
an  old  rule  corrected.  Such  corrected  rules  while  undoubtedly  better 
than  the  originals  have  so  far  failed  of  adoption  in  place  of  the  rules 
from  which  they  were  made,  owing  to  the  force  of  custom  in  perpetuating 
established  standards  even  if  in  error. 

56.  The  Construction  of  Rules  Based  on  Mathematical  Formulae. 
Many  efforts  have  been  made  to  evolve  a  formula  which  will  give  an 
accurate  basis  for  a  board-foot  log  rule.  Of  these  the  erroneous  formulae, 
or  rules  of  thumb,  based  on  a  fixed  conversion  factor  are  most  common. 
Of  those  which  recognize  the  fundamental  difference  between  waste  from 
slabs,  and  waste  from  saw  kerf,  we  have  two  groups,  distinguished 
not  ])y  principle,  but  by  the  method  of  procedure  dependent  on  whether 
the  deduction  for  saw  kerf  is  made  first,  from  the  total  contents  of  the 
log,  or  whether  that  for  slabs  and  edgings  is  first  deducted,  and  the 
waste  from  saw  kerf  then  taken  from  the  residual  volume. 

Method  of  Deducting  Slobs  First.  When  the  first  plan  is  used,  a  constant,  a, 
representing  in  inches  the  double  width  or  thickness  of  the  hollow  cylinder  or  sur- 
face layer  wasted  in  slabs,  edgings  and  crook,  is  first  deducted  from  the  diameter  of 
the  log  at  small  end.  From  the  area  of  the  smaller  circle  thus  obtained,  the  required 
per  cent  is  subtracted  for  saw  kerf,  shrinkage  or  surplus  thickness  of  board  required 
in  sawing. 

The  residual  area  of  the  circle  in  square  inches  is  converted  into  board  feet  for 
logs  1  foot  long,  by  dividing  by  the  factor  12.  Disregarding  the  taper,  the  volume 
of  a  log  of  any  length  is  found  by  multiplying  the  contents  by  length  in  feet. 

D  =  diameter  of  log  in  inches; 
a  =  inches  subtracted  from  diameter,  a  constant; 
D— a  =  reduced  diameter  of  log  after  subtracting  waste  from  slabs  and  edgings; 
ir(/)-a)2 


reduced  area  of  small  end  of  log  in  square  inches; 
4 

6  =  per  cent  of  volume  deducted  for  saw  kerf; 

1  —  6=per  cent  remaining  after  deduction  for  saw  kerf; 

L  =  length  of  log  in  feet ; 

B.M.  =  volume  of  log  in  board  feet; 
then 

r(D-a)2   L 


B.M.  =  (1-6)- 

=  (l-fe)' 


4  12 

(D-ay 
48       ■ 


Illustration 

Let    a  =  1.5  inches,  representing  a  collar  of  .75  inch    thickness    deducted    for 
slabs,  etc. 
6  =  20  per  cent  representing  a  i-inch  saw  kerf. 


60  THE  CONSTRUCTION  OF  LOG  RULES 

Then  for  any  log, 


B.M.  =  (l-.20f'^-'-^''L. 


For  a  12-mch  log  16  feet  long, 

/3. 1416(12 - 
B.M.  =  .80' 


^)l6 


48 
=  92  board  feet. 

Method  of  Deducting  Saivdust  First. — By  the  second  method,  the  per  cent  of 
waste  in  saw  kerf  is  first  deducted  from  the  entire  volume  of  the  log.  From  the 
residual  volume  the  amount  to  be  further  subtracted  for  slabs,  edging  and  crook  is 
taken.  This  is  a  smaller  per  cent  than  by  the  first  method,  as  shown  in  Table  VII, 
column  7  since  the  sawdust  used  in  slabbing  is  not  included,  and  it  is  for  convenience 
computed  in  the  form  of  a  plank  of  width  and  length  equal  to  the  log,  and  whose 
thickness  is  varied  to  give  the  required  volume  of  waste. 

Let  A  equal  the  width  of  this  plank  in  inches.     This  is  taken  as  a  constant. 

Then, 

B.M.  =  (  (1-6)— -AD j-. 


Illustration 

Let  6  =  20  per  cent —sawdust  allowance, 

A=l .767  inches,  the  thickness  of  a  plank  whose  width  is  equal  to  D,  and 
length  to  L — for  slabbing  allowance. 
Then  for  any  log. 


B.M..|,8o('-f')-l,767D]^^ 


^12 

For  a  12-inch  log  16  feet  long, 

B.M.  =  [ .  80( .  7854  X 12=)  - 1 .  767  X  12]|f , 
B.M.=  92  board  feet. 

This  result  shows  that  for  12-inch  logs,  after  .subtracting  20  per  cent  from  log  for 
sawdust,  a  plank  1.767  inches  by  12  inches  gives  a  deduction  from  the  net  volume, 
equal  to  method  1  when  a  collar  .75  inch  thick  is  first  deducted  and  20  per  cent  for 
sawdust  taken  from  the  remainder. 

The  two  methods  are  not  absolutely  interchangeable.  Their  relation  may  be 
shown  by  algebraical  means. 

Substitute  C  for  (1-6). 

Then  C  =  per  cent  left  after  subtracting  saw  kerf. 

Since  D  is  in  inches,  and  L  exerts  no  influence  on  the  relative  values,  the  areas 
of  the  small  end  of  log,  left  after  subtracting  total  waste,  should  be  equal,  and  can 
be  e.vpressed  in  square  inches  for  each  formula  as : 

CTr(D-a)^     CwTP 

= AD. 

4  4 

Then, 

,     C(1.5708aD-.7854a2) 
A= ;r . 


COMPARISON  OF  LOG  RULES  BASED  ON  FORMULAE 
The  results,  for  certain  diameters  are  shown  below: 


61 


TABLE  VIII 

Thickness  of  Plank  to  be  Deducted  for  Slab  Waste  to    Coincide  with  a 
Collar  1.5  Inches  Thick.     Sawdust  Allowance  20  Per  Cent 


Double  thickness  of  col 

Corresponding     thick- 

Ratio  of  thickness  of 

Diameter  of 

lar  deducted  for  slab 

ness  of  plank  to  be 

of  plank  to  collar 

log. 

waste  previous  to  de- 

deducted   after    de- 

ducting sawdust. 

ducting  sawdust. 

Inches 

Inches 

Inches 

3 

1.5 

1.414 

0.940 

6 

1.5 

1.649 

1.099 

9 

1.5 

1.728 

1.152 

12 

1.5 

1.767 

1.178 

18 

1.5 

1.800 

1.200 

40 

1.5 

1.849 

1.233 

The  use  of  these  ratios  would  give  identical  results  by  both  methods.  But  in 
application  the  second  method  usually  stipulates  that  the  thickness  of  plank  shall 
be  constant  for  all  logs.  This  results  in  a  greater  proportionate  deduction  for  slabs 
on  small  logs  than  by  the  first  method.  This  deduction  is  more  in  accordance  with 
the  actual  results  of  sawing,  owing  to  the  increasing  effect  of  minimum  widths  of 
board  on  per  cent  of  loss  in  slabbing  (§  51).  The  best  application  is  to  adopt  a 
ratio  which  applies  to  medium-sized  logs,  and  use  thi§  for  all  logs,  large  and  small. 

If  a  log  rule  is  constructed  to  deduct  the  waste  which  actually  occurs  in  sawing, 
it  must  be  based  on  one  or  the  other  of  these  two  formulae.  If  the  waste  allowances 
are  correct  for  the  conditions  assumed,  there  will  still  be  over-run  when  other  condi- 
tions apply,  but  the  per  cent  of  over-run  will  be  practically  the  same  for  all  sizes, 
the  rule  is  consistent,  and  the  results  are  subject  to  correction  by  a  fixed  ratio  or 
per  cent. 

If  the  waste  allowance  for  either  slabbing  or  sawing,  or  both,  are  incorrect  for 
the  conditions  assumed,  the  rule  will  not  only  give  over-  or  under-run,  but  will  also 
be  inconsistent,  the  per  cent  will  differ  with  diameter,  and  the  rule  will  not  be  subject 
to  correction  by  a  fixed  ratio,  and  will  lack  the  basic  requirements  of  a  standard  of 
measure. 

57.  Comparison  of  Log  Rules  Based  on  Formulae.  In  constructing 
a  formula  log  rule,  the  correct  application  of  the  deduction  for  saw  kerf 
presents  no  great  difficulty.  In  the  International  rule,  an  extra  deduc- 
tion of  Ye-inch  was  made  for  shrinkage.  Other  rules  neglect  all  factors 
but  the  actual  width  of  saw  kerf  (§  53). 

The  deduction  for  slabs,  edging  and  normal  crook  requires  determination  not 
only  from  diagrams  but  from  practical  tests.  The  following  amounts  are  deducted 
by  the  log  rules  given  below,  exTjressed  both  as  a  "collar"  deduction  from  diameter, 
(o),  and  as  a  thickness  of  plank  (A),  to  correspond  with  the  two  methods  describod 
(§56). 


62  THE  CONSTRUCTION  OF  LOG  RULES 

TABLE  IX 

Deductions  for  Slabbing  and  for  Saw  Iverf,  for  12-inch  Logs,  in  Ten  Log 
Rules  Based  on  Formul.-e.  The  Basis  Used  in  the  Rule  is  Shown  in 
Heavy  Type. 


Log  Rule. 

Deduction 

from  diameter 

for 

slabbing. 

Inches 

Equivalent 

deduction  in 

form  of  a 

plank 

thickness. 

Inches 

Saw  kerf 

plus 
shrinkage. 

Inches 

Deduction 

for 
saw  kerf. 

Per  cent 

International 

1.73 
1.66 
1  75 
1  50 
1  50 
1  25 
1.18 
1.00 
1  00 
0.87 
0.83 
4  00 
1.00 

2.12 
2  00 

2.04 

1.77 

1.77 

1.42  ' 

1.32 

1.17 

1.17 

1.05 

1.00 

5.00 

1.00 

15.8 
20.0 

Preston :  Large  logs 

Small  logs 

British  Columbia 

20.0 
20.0 
27.3 

CUck 

Clement 

Wilson             

23.6 
25.0 

22.2 

Thomas 

Baughman  * 

Champlain 

Doyle 

Baxter                    

22.0 
20.0 
20.0 

4.5 
33.8 

*  Diagram  rule. 

Of  the  rules  above  cited,  the  British  Columbia  and  Doyle  are  the  only  ones  used 
extensively  at  present.  The  table  is  instructive  as  an  indication  of  the  proper  allow- 
ances to  make  for  slabbing.  The  test  of  a  formula  is  actual  comparison  with  sawed 
output.  The  deductions  in  the  International  rule  were  determined  by  careful 
measurement  on  logs  actually  sawed.  The  Champlain  rule  is  known  to  be  too 
close  a  rule,  with  too  small  an  allowance  for  slabs.  The  British  Columbia  rule 
neglects  shrinkage  and  is  a  good  standard.  The  Click  rule  was  carefully  checked 
by  sawed  output.  These  results  indicate  that  for  1-inch  lumber  sawed  to  exact 
dimensions,  an  allowance  for  slabbing  of  1.5  to  1.75  inches  subtracted  from  diameter, 
or  one-half  this  deduction  as  the  single  thickness  of  the  collar,  is  a  fair  allowance 
for  slabbing.  This  allowance  would  be  too  small  for  lumber  of  greater  average 
thickness  than  1  inch  or  for  very  small  logs. 

When  the  deduction  is  made  in  the  form  of  a  plank  whose  width  equals  the 
diameter,  D,  of  the  log,  the  thickness  of  plank  required  to  make  it  equivalent  to  the 
collar  deduction  is  from  1.75  to  2  inches  for  12-inch  logs,  slightly  more  for  larger 
logs,  and  decreasing  in  thickness  for  smaller  logs.  But  where  the  deduction  is  made 
in  this  form,  as  in  the  International  and  Champlain  rules,  it  is  used  as  a  constant 
for  all  dimensions  (§  59  and  §  62)  with  results  corresponding  more  closely  to  actual 
waste  than  by  the  first  method. 

The  allowance  for  saw  kerf,  on  all  log  rules  in  commercial  use,  is  i^-inch  or  over. 
The  International  rule  in  its  original  form  gives  values  for  a  |-inch  saw  kerf,  which, 
with  the  other  allowances,  gives  a  rule  intended  to  measure  the  output  of  modem 
band  mills. 


McKENZIE  LOG  RULE,  1915  63 

58.  McKenzie  Log  Rule,  1915.  This  log  rule  is  a  universal  formula 
and  not  a  commercial  standard  or  true  log  rule.  It  is  intended  to 
reduce  all  the  variable  factors  in  the  production  of  sawed  lumber  to 
elements  in  a  formula,  which  will  permit  the  determination  of  a  local 
rule  that  will  accurately  measure  the  sawed  output  in  the  log  for  any 
condition,  and  eliminate  over-run. 

The  factor  of  taper  is  treated  by  building  up  the  log  in  8-foot  sections, 
permitting  the  use  of  whatever  actual  average  taper  coincides  with  that 
of  the  logs  sawed.  The  allowance  for  slabs,  edging  and  crook  is  made  by 
the  first  method,  that  of  deduction  from  the  diameter  previous  to  sub- 
tracting saw  kerf.  Shrinkage  could  be  included  with  saw  kerf,  if  neces- 
sary, but  the  author  does  not  mention  it. 

The  formula  is  the  one  already  shown  to  be  correct  and  universal  for  board-foot 
log  rules, 

L 

B.M.  =  (l-fe).7854(D-o)2— . 

The  saw  kerf  allowance,  h,  is  computed  to  include  width  as  well  as  thickness  of 
lumber  sawed  ( §  53) .  To  this  general  formula  the  author  adds  a  constant,  c,  to 
offset  excessive  taper  on  small  logs. 

The  principal  utility  of  this  log  rule  will  be  found  in  determining,  in  advance  of 
sawing,  the  amount  of  over-run  which  may  be  obtained  from  logs  scaled  by  a  com- 
mercial rule,  or  to  test  the  results  in  over-run  to  be  expected  by  the  use  of  different 
log  rules  and  different  methods  of  manufacture.  The  objections  to  adopting  it  as  a 
standard  of  measure  arc  stated  in  §  49. 

Reference 
Bui.  5,  California  State  Board  of  Forestry,  by  H.  E.  McKenzie. 

59.  International  Log  Rule  for  |-inch  Kerf,  Judson  F.  Clark,   1900. 

In  constructing  this  rule,  modern  conditions  of  manufacture  in  large 
mills  were  presupposed.  The  values  of  the  rule  as  published  are  for  a 
band  saw  cutting  a  |-inch  kerf  and  are  rounded  off  to  5  and  10  board 
feet,  thus  approaching  the  principle  of  a  decimal  rule.  Saw  kerf  is 
first  subtracted,  allowing  ^-inch  for  shrinkage,  or  a  total  of  y&  inch. 
The  deduction  for  slabs  and  edging,  including  a  normal  crook  of  from 
1  to  1|  inches  is  then  made  in  the  form  of  a  plank  measuring  2.12D. 


The  formula  reads: 


L 
B.M.  =  (.66D2-2.12D)— . 


The  rule  was  constructed  as  follows:    Since  the  per  cent  of  waste  in  saw  kerf  plus 
K  "^ 

shrinkage  is  this  becomes  for  inch  boards  or  3  parts  in  19,  which  gives 

\+K  16+3  *  '  ^ 

.158,  and  the  factor  for  residual  volume  is  .842.     Then, 
.842(.7854D2)  =  .66D2. 


64  THE  CONSTRUCTION  OF  LOG  RULES 

The  deduction  2.12D  was  determined  from  tests  of  sawed  logs,  including  all  crook 
of  4  inches  or  less. 

Since  the  log  is  divided  into  4-foot  lengths,  the  sum  of  which  gives  the  scale, 
the  formula  reads  for  each  length, 

B.M.  =  (.66Z)2-2.12D)y% 

=  .22D2-.71D. 

A  taper  of  |-inch  in  4  feet  is  allowed.  D  is  thus  increased  by  ^-inch  for  each  succes- 
sive section  and  the  sum  of  the  scale  of  the  separate  4-foot  cylinders  gives  the  scale 
of  the  log  (§  43).  On  account  of  the  allowance  for  shrinkage  the  rule  is  based  in 
reality  on  the  production  of  lye-inch  boards  measured  as  inch  boards.  A  minimum 
width  of  3  inches,  and  a  minimum  length  of  2  feet  are  adopted  as  standard,  no  piece 
to  contain  less  than  2  board  feet.  Standard  values  were  published,  it  being  the  inten- 
tion of  the  author  to  furnish  a  commercial  log  rule  that  could  be  accepted  as  a  com- 
mon standard  for  the  measurement  of  logs  as  sawed  in  modern  mills  using  a  band 
saw  cutting  a  J-inch  kerf. 

60.  International  Log  Rule  for  i-inch  Kerf,  Judson  F.  Clark,  1917. 

For  general  adoption  as  a  standard  commercial  log  rule,  the  |-inch  rule 
is  open  to  the  objection  that  it  over-scales  the  product  of  most  small 
mills,  since  it  is  seldom  that  such  mills  use  saws  cutting  less  than  j-inch 
kerf,  or  make  close  use  of  the  taper  of  the  log.  A  log  rule  which  gives 
a  safe  margin,  and  which  permits  mills  using  thin  band  saws  and  up-to- 
date  equipment  to  secure  an  over-run  of  about  10  per  cent  is  more 
acceptable  as  a  commercial  standard  than  one  which  scales  for  the 
closest  possible  standard  of  utilization.  For  this  reason,  Mr.  Clark 
has  computed  values  for  the  International  rule,  for  j-inch  saw  kerf. 
This  form  of  the  rule  is  here  published  for  the  first  time  from  values 
furnished  by  its  author  (Appendix  C,  Table  LXXX).  To  obtain  this 
rule,  the  original  values  for  the  |-inch  rule  were  reduced  by  9.5  per  cent 
and  then  rounded  off  to  the  nearest  5  or  10  board  feet.  The  rule  is 
recommended  as  a  standard  for  scientific  measurements  of  volume  and 
growth  in  terms  of  board  feet,  for  regions  where  the  product  is  manufac- 
tured by  small  mills  using  circular  saws  cutting  a  I -inch  kerf. 

61.  British  Columbia  Log  Rule,  1902.  This  is  the  only  case  of  the 
legal  adoption  and  application  in  commercial  scaling  of  a  new  log  rule 
based  on  sound  scientific  principles,  as  the  direct  result  of  a  thorough 
investigation.  In  1902  a  commission  of  three  men  prepared  from  dia- 
grams a  rule  to  suceed  the  Doyle  Rule  for  the  province,  which  was 
adopted  in  1909  as  the  Statute  rule. 

Their  results  were  embodied  in  a  formula  reading: 

"For  logs  up  to  40  feet  in  length  deduct  1^  inches  from  the  diameter  of  the  small 
end  inside  the  bark;    square  the  result  and  multiply  by  the  decimal  .7854;    from 


OTHER  FORMULA  RULES  65 

the  product  deduct  three-elevenths;    multiply  the  remainder  by  the  length  of  the 
log  and  divide  by  twelve."    Or, 

B.M.  =  (l-i3j-)  .7854(1) -1.5)2— 

The  minimum  width  of  board  used  was  3  inches. 

For  logs  over  40  feet  in  length,  an  increase  in  diameter  is  allowed  on  half  the 
length  of  the  log  amounting  to  1  inch  on  the  diameter  at  the  small  end,  for  each 
10  feet  in  length  over  40  feet.  Thus  for  logs  from  41  to  50  feet  long  the  contents 
of  the  butt  cylinder  is  scaled  by  a  diameter  1  inch  larger  than  the  top  end;  for  logs 
from  51  to  60  feet  long,  the  rise  allowed  is  2  inches,  etc. 

This  allowance  for  taper  is  absurdly  small  and  constitutes  the  only  weak  point 
in  the  rule.  It  is  a  concession  to  the  low  standards  of  utilization  practiced  in  the 
province  at  the  time. 

62.  Other  Formula  Rules,  Approximately  Accurate,  Both  in  Princi- 
ples and  Quantities.  When  a  log  rule  is  constructed  by  using  the  prin- 
ciples embodied  in  the  standard  formula,  and  when  in  addition,  the 
amount  of  deduction  for  both  saw  kerf  and  slabbing  is  approximately 
correct,  the  resultant  log  rule  will  be  far  more  accurate  and  consistent 
than  any  of  the  commercial  rules  in  common  use  except  the  last  men- 
tioned. Several  rules  have  been  constructed,  whose  values  differ  only 
because  of  slightly  different  allowances  for  waste,  as  shown  in  Table  IX. 
Seven  such  rules  are  given  below.  This  completes  the  list  of  log  rules 
known  to  the  author,  and  based  on  diameter  at  small  end  of  log,  which 
deserve  to  be  classed  as  fundamentally  correct  standards  for  board-foot 
contents  of  saw  logs. 

Champlain  Log  Rule,  A.  L.  Daniels,  1902.  This  log  rule,  intended  as  a  perfect 
rule  for  1-inch  boards,  is  based  on  ^-inch  saw  kerf  and  neglects  taper.  It  is  for 
perfect  logs.  The  deduction  for  slabs  and  edging,  without  normal  crook,  is  made 
equal  to  a  1-inch  plank  or  ID.  No  shrinkage  is  considered.  The  diameter  is  taken 
at  small  end.  Were  it  not  for  an  over-run  secured  from  taper  or  the  methods  of 
sawing  used,  logs  would  never  saw  out  what  this  rule  calls  for.  The  quantities 
given  are  above  normal  in  cylindrical  contents  for.  short  logs.  This  error  is  offset 
by  neglect  of  taper,  so  that  in  long  logs  the  rule  falls  below  the  International. 

This  rule  has  not  been  used  commercially,  except  in  a  few  instances  in  Vermont. 
The  formula  is: 

L 

B.M.  =  (.62832Z)-D)"— . 

The  author  of  the  Champlain  log  rule  realized  that  the  slab  allowance  was  too 
small  for  actual  conditions.  By  increasing  the  width  of  plank  deducted  for  slabbing 
to  2D,  a  modification,  termed  the  Universal  log  rule  was  computed,  using  the  formula, 

B.  M.  =  (.62832D2-2D)^. 


66  THE  CONSTRUCTION  OF  LOG  RULES 

This  rule  compares  favorably  with  other  theoretically  accurate  rules  except  that 
it  shares  the  common  fault  of  neglecting  taper.     Mr.  Daniels  states  (1917),  that  he 
favors  the  use  of  the  Champlain  rule  as  the  more  accurate  of  the  two. 
Wilson  Log  Rule,  1825. 

Tr(D-iy-L 

B.M.  =  .807-^—  -. 

By  Clark  Wilson,  Swanzey,  N.  H.  Originated  in  1825,  and  computed  for  |-inch 
boards.  Now  obsolete.  This  was  vmquestionably  the  first  formula  rule.  The  author 
was  a  mathematician,  and  "estimated  the  difference  in  yield  in  gain  of  the  large 
logs  over  the  small  ones,  and  then  calculated  the  intermediate  spaces  by  nearly 
regular  integral  differences  as  logs  increase  in  size.  The  author  intended  it  for 
|-inch  boards.  It  is  recorded  that  E.  A.  Parks  later  used  it  for  1-inch  boards,  which 
use  resulted  in  a  lawsuit."  (John  Humphrey,  Keene,  N.  H.) 
Preston  Log  Rule,  An  Old  Rule. 

7r(D-1.75)2L 
Large  logs,     B.M.  =  .80 


Small  logs:     B.M. 


4  12 

r{D-1.5y-L 
4  12' 


Still  used  in  Florida.  Known  locally  as  a  seller's  rule.  Sold  in  Jacksonville,  Fla., 
by  H.  &  W.  B.  Drew  Co. 

Thomas'  Accurate  Log  Rule. 

^_         _7r(D-l)2L 

B.M.  =  .78-^-. 

For  J-inch  saw  kerf.     Also  computed  for  |-inch  kerf. 
Click's  Log  Rule,  1909. 

By  A.  C.  Click,  Elkin,  N.  C,  1909.  This  rule  was  based  on  1-inch  boards  averaging 
6  inches  in  width  and  makes  reduction  for  saw  kerf  of  i-inch  as  per  the  formula 
(§  58),  used  by  McKenzie.  Other  rules  for  different  widths  of  saw  kerf  were  worked 
out  by  the  author.     (Forestry  Quarterly,  Vol.  VH,  1909,  p.  145.) 

Carey  Rule,  Date  Unknown.  This  was  a  cahper  rule  to  be  applied  to  middle 
diameter,  and  was  used  for  round  edge  boards  1-inch  thick.  The  values  given  are 
almost  identical  with  the  Wilson  ruie.     Formerly  used  in  Massachusetts. 

Clement's  Log  Rule,  1904. 


B.M.=  |  (  .75--)-1.18D 


\i 


This  log  rule  illustrates  the  use  of  a  rule  of  thumb,  based  on  correct  mathematics. 
The  above  formula  is  expressed  thus:  Multiply  half  the  diameter  by  half  the  circum- 
ference, then  subtract  half  the  circumference.     The  remainder  will  be  the  total 
amount  of  feet  board  measure,  in  a  16-foot  log. 
This  becomes: 

L 
B.M.  =  (.7854D2-1.57D)— , 
lb 

from  which  the  above  formula  is  derived. 

With  the  exception  of  the  Preston,  none  of  these  rules  is  in  commercial  use. 


TIEMANN  LOG  RULE  1910  67 

63.  Tiemann  Log  Rule,  H.  D.  Tiemann,  1910.  All  of  the  com- 
mercial log  rules  in  use  are  open  to  the  criticism  that  the  taper  is  dis- 
regarded, thus  causing  the  over-run  to  vary  according  to  the  length 
and  amount  of  total  taper  of  the  log.  The  International  rule,  in  which 
taper  is  included,  is  not  in  commercial  use  to  any  extent.  But  one 
attempt  has  been  made  to  take  proper  cognizance  of  taper  by  the  method 
of  applying  a  log  rule  for  board  feet  to  the  middle  diameter  instead  of  the 
small  end.  Most  rules  employing  this  method  are  cubic-foot  rules  or 
based  on  cubic  contents.  The  Tiemann  log  rule  on  the  other  hand  is 
a  true  board-foot  rule  based  on  a  j^-inch  saw  kerf.  The  rule  was  made 
from  actual  mill  tallies  accurately  adjusted  for  saw  kerf  and  for  exact 
thicknesses  and  the  results  worked  out  graphically  by  curves.  Quite 
remarkably  the  curves  were  found  to  correspond  very  closely  to  the 
exceedingly  simple  formula 

B.M.  =  (.751)2  _2Z))^, 
lb 

which  equals  ( -716—7 1.5Z)  j— . 

The  application  of  the  rule  is  limited  by  its  author  to  lengths  not 
exceeding  24  feet. 

This  log  rule  applies  to  logs  scaled  in  the  middle.  When  this  is 
possible,  the  rule  is  more  accurate  than  any  other  board  foot  log  rule, 
since  neither  the  variation  in  taper  nor  length  of  log  affects  it.  It  can 
be  adjusted  to  apply  to  the  small  end  just  as  well  as  any  other  rule  can, 
but  it  is  intended  primarily  for  middle  diameter  as  this  largely  elimi- 
nates errors  in  estimates  of  taper.  For  scientific  records  it  is  of  distinct 
value.  It  is  superior  to  the  International  rule  as  it  eliminates  taper 
as  a  variable  instead  of  averaging  it.  The  obstacles  to  converting  this 
rule  or  any  other  rule  into  equivalent  values  at  small  end  are  discussed 
in  §  31.     The  rule  is  given  in  Appendix  C,  Table  LXXXIV. 

64.  Formula  Rules  Inaccurately  Constructed.  Baxter  Rule.  If 
the  allowance  for  slabbing  in  a  formula  rule  is  excessive,  and  that  for 
sawdust  too  small,  the  resultant  volumes  will  be  too  small  for  logs  of 
small  diameters  and  too  large  for  large  logs,  thus  giving  not  only  an 
inaccurate  but  an  inconsistent  rule.  If  these  errors  in  deducting  waste 
are  reversed,  slabbing  allowance  being  too  small,  and  that  for  sawdust 
too  large,  the  reverse  is  true,  and  the  large  logs  will  be  under-scaled. 

Baxter  Log  Rule.  In  adopting  a  rule  of  thumb  for  the  construction  of  a  log  rule, 
the  author  may  have  in  mind  a  certain  result,  but  the  rule  when  expressed  in  a  formula 
may  give  quite  a  different  result. 

The  Baxter  Log  Rule  was  constructed  by  the  rule  "Subtract  1  from  the  diameter 
inside  bark  at  the  small  end,  square  the  remainder,  and  multiply  by  .52.     The  result 


68  THE  CONSTRUCTION  OF  LOG  RULES 

is  the  contents  of  a  12-foot  log"  (hence  —  gives  the  contents  of  any  log) .  This  squar- 
ing and  subsequent  subtraction  of  one-half  the  square  was  intended  to  give  suffi- 
cient deduction  for  both  slabs  and  saw  kerf.     But  it  actually  gives, 

4        12 

The  factor  1,  for  yl,  is  insufficient  for  slabs  and  the  factor  .338  for  C  is  far  too  great 
for  sawdust,  corresponding  in  fact  to  a  kerf  of  ^.inch.  The  rule  therefore  greatly 
underscales  large  logs.     Its  inconsistency  makes  it  worthless. 

65.  Doyle  Log  Rule.  Synonyms:  Connecticut  River,  St.  Croix, 
Thurber,  Vannoy,  Moore-Beeman  (in  part),  Ontario,  Scribner  (erro- 
neously) . 

This  rule  is  used  almost  to  the  exclusion  of  all  other  rules  for  hard- 
woods in  parts  of  the  Ohio  Valley,  and  for  Southern  yellow  pine.  Its 
use  is  extensive  in  every  eastern  state  outside  of  New  England  and 
Minnesota.     In  the  West,  it  is  not  used  to  any  extent. 

The  Doyle  rule  reverses  the  error  of  the  Baxter  rule  by  deducting 
too  large  a  per  cent  for  slabbing  and  not  enough  for  sawdust.  The  wide 
use  of  this  rule  has  caused  losses  of  millions  of  dollars  to  owners  selling 
logs  and  standing  timber,  by  improper  and  defective  measurement  of 
contents.  The  prevalence  of  its  use  is  due  first  to  the  simplicity 
of  its  application  as  a  rule  of  thumb.  The  rule  reads:  Deduct  4  inches 
from  the  diameter  of  the  log  as  an  allowance  for  slab.  Square  one- 
quarter  of  the  remainder  and  multiply  the  result  by  the  length  of  the  log 
in  feet.  The  result  is  the  contents  in  board  feet.  Timber  cruisers 
estimate  logs  in  16-foot  lengths.  For  this  length  of  log  the  rule  would 
read:  Deduct  4  inches  from  the  diameter  of  the  log  inside  bark,  and 
square  the  remainder.  The  result  is  the  contents  of  the  log  in  board 
feet,  by  the  Doyle  rule.  A  rule  as  easily  applied  as  this  was  sure  to  be 
popular. 

The  second  reason  for  its  wide  use  was  its  substitution  for  the  old 
Scribner  rule  in  Scribner's  Log  and  Lumber  Book,  after  this  publication 
had  already  attained  a  large  circulation.  As  this  book  was  widely 
accepted  as  a  standard  and  almost  the  only  publication  on  log  rules, 
the  impetus  given  to  the  use  of  this  inaccurate  rule  by  this  substitution 
was  tremendous. 

The  third  reason  for  the  continued  use  of  the  Doyle  rule  is  the  same 
which  operates  to  prevent  reform  in  the  use  of  log  rules  in  general. 
Custom,  or  habit  of  using  it,  is  fixed.  So  far  has  this  gone  that  the 
States  of  Arkansas,  Florida  and  Mississippi  prescrilje  its  use  by  statute. 
Added  to  this  is  the  fact  that  a  rule  favoring  the  buyer  will  be  advocated 
by  this  class  to  its  own  advantage. 


DOYLE  LOG  RULE  69 

The  seller  can  defend  himself  against  the  use  of  a  short  measure  if 
the  latter  is  consistent  and  its  per  cent  of  error  is  known.  But  with  a 
log  rule  like  the  Doyle,  the  per  cent  of  error  differs  with  every  scale  of 
logs  or  stand  of  timber  and  it  is  practically  impossible  to  determine  the 
actual  loss  without  remeasuring  the  logs  by  a  correct  log  rule  or  tally- 
ing the  sawed  contents. 

Since  it  will  be  impossible  to  displace  this  log  rule  by  better  standards  unless 
its  vicious  character  is  fully  understood,  the  exact  nature  of  the  error  should  be  made 
clear.  The  original  form  of  this  rule  read  "Deduct  -i  inches  from  the  diameter 
for  slabs,  then  squaring  the  remainder,  subtract  one-fourth  Jor  saw  kerf  and  the 
balance  will  be  the  contents  of  a  log  12  feet  long."  The  sawdust  allowance  as 
intended,  would  have  corresponded  to  a  i^-inch  saw  kerf.  The  author  evidently 
figured  that  4  inches  of  slab  would  square  the  log  sufficiently  so  that  the  sawdust 


Fig.  9. — Actual  deductions  for  slabs  and  for  .saw^  kerf  made  by  the  formula  of  the 
Doyle  rule,  for  logs  6  inches,  and  28  inches  in  diameter  respectively. 

The  square  A  BCD  is  the  supposed  residue  after  deduction  for  slabs,  while  the 
outer  inscribed  circle  represents  the  actual  residue.  The  inner  inscribed  circle 
represents  the  residual  percentage  showu  as  board  feet  by  the  rule.  The  sawdust 
allowance  is,  therefore,  the  difference  between  the  outer  and  inner  inscribed  circles, 
whose  area  is  but  4.5  per  cent  of  the  contents  of  the  cylinder. 


allowance  could  be  appUed  in  this  manner  to  the  squared  or  partially  squared  stick. 
His  fundamental  error  lay  in  his  method  of  deducting  for  slabbing  and  edging.  As 
shown,  the  waste  from  slabs  and  edging  does  not  amount  to  a  reduction  of  4  inches 
in  the  diameter,  but  to  about  1.75  inches,  and  instead  of  being  slabbed  from  four 
sides,  it  is  distributed  evenly  over  the  entire  surface  as  a  collar.  The  assumption 
made  re.sulted  in  an  actual  deduction  for  slab  far  in  excess  of  what  was  intended, 
this  excess  in  turn  reducing  the  sawdust  allowance  from  an  a.ssumed  25  per  cent  to 
negligible   proportions. 

The  above  diagrams  (Fig.  9)  will  explain  the  reason  for  this  inconsistency. 

The  diagram  for  the  larger  log  shows  that  the  squaring  of  the  timber  would  not 

require  a  4-inch  slab  allowance.     The  standard  formula  -fD— 4)^  gives  the  volume 

4 

.7854(D— 4)-  as  the  actual  net  result  of  deducting  4  inches  from  the  diameter  of  the 


70  THE  COXSTRUCTIOX  OF  LOG  RULES 

log.  This  was  the  point  overlooked  in  constructing  the  rule.  The  deduction  so 
made  is  in  its  effect  a  deduction  for  slabbing  and  edging  although  not  so  intended. 

That  it  was  not  intended  is  shown  by  the  instructions  for  next  deducting  one- 
fourth  of  {D—Ay  "for  saw  kerf."  But  this  leaves  .75(Z)— 4)-  for  all  logs,  instead 
of  .7854(Z)— 4)-,  which  is  a  further  reduction  of  but  .0354(D— 4)^,  the  actual  reduc- 

0354 
tion  for  saw  kerf  _        =  .045  or  4.5  per  cent  of  the  cylindrical  contents  for  saw  kerf 
.7854 

instead  of  the  20  per  cent  of  the  same  cylinder  required  by  a  j-inch  saw  kerf.     The 

remaining  21.5  per  cent  of  the  supposed  saw  kerf  is  a  true  slab  deduction  of  4  inches 

from  diameter.     Thus  the  amounts  and  proportions  of  slab  deductions  are  grossly 

out  of  balance  and  this  ruins  the  rule. 

This  early  form  was  not  kno-mi  as  the  Doyle  rule.  The  present  form,  first 
published  in  the  decade  1870-80  was  advertised  as  a  new  rule.  The  scale  is  identical 
with  the  older  form  but  the  change  in  the  wording  of  the  rule  to  its  present  form 
still  further  concealed  the  flaw  in  its  construction. 

The  formula  for  the  Doyle  rule  is: 

B.M.(^)=. 

corresponding  to  the  standard  formula : 

^_  7r(D-4)2L 

B.M.  =  .955 -—. 

4         12 

The  true  sawdust  allowance  can  be  shown  by  the  follo^-ing  comparison: 

- — )  L=.0625(D-4)2L. 
The  area  contents  of  the  cylinder  D— 4, 

^"(0-4)2^=  .06.547(D-4)=L. 

0625 
Since  the  cylinder  D— 4  represents  the  log  minus  true  slab  deduction,— --—— = 

.0654/ 

95.5  per  cent  or  the  log  minus  both  slabs  and  sawdust. ' 

66.  Effect  of  Errors  in  Doyle  Rule  upon  Scaling    and  Over-nin. 

The  effect  of  this  overbalancing  of  the  respective  allowances  is  to  cause 
this  rule  to  give  zero  for  the  contents  of  logs  5  inches  in  diameter  while 
for  logs  above  47  inches,  the  scale  yields  more  than  80  per  cent  of  the 
cubic  contents,  thus,  for  j-inch  kerf,  eliminating  slab  waste  altogether. 
The  over-run  would  thus  vary  with  increasing  diameter,  from  infinit}- 
to  zero. 

When  the  Doyle  rule  is  applied  to  long  logs,  with  a  small  top  or  scaling  diameter, 
the  over-run  becomes  proportionally  greater.  A  careful  test,  imder  direction  of 
the  courts  in  Te.xas  where  logs  of  given  sizes  were  actually  sawed  (Extending  a 
Log  Rule,  E.  A.  Braniff,  Forestry-  Quarterly,  Vol.  VI,  1908,  p.  47),  showed  that 
for  24-foot  logs  sawed  by  circular  saw.  the  Doyle  rule  gave  an  over-nm  for  different 
diameters,  as  shown  in  Table  X. 

1  The  author  is  indebted  to  material  published  by  H.  E.  McKenzie  in  Bui.  5, 
California  State  Board  of  Forestry,  for  this  discussion  of  the  error  in  the  Doyle  rule. 


EFFECT  OF  ERRORS  IN  DOYLE  RULE 


71 


TABLE  X 

Over-run,  Doyle  Rule.     Texas 


Diameter  at 
small  end. 

Sawed  product. 

Scale 
Doyle  Rule 

Per  cent  of 
over-run 

Inches 

Board  feet 

6-  61 

35 

6 

483 

7-7f 

49 

14 

250 

8-  81 

61 

24 

150 

9-  9f 

76 

37 

105 

10-lOf 

95 

54 

76 

11-1 If 

112 

74 

51 

The  over-run  steadily  diminishes  with  increasing  diameter  until  at  from  36  to  40 
inches  the  rule  gives  practically  full  scale  for  J-inch  kerf  and  normal  allowance  for 
slab,  disregarding  taper. 

An  investigation  made  in  1904  for  the  Province  of  Ontario  by  Judson  F.  Clark, 
showed  that  the  volume  of  the  average  log  cut  in  the  Province  had  decreased  in 
25  years  by  63  per  cent  and  at  that  time  averaged  61  board  feet  and  12  inches  in 
diameter.  From  mill  tests  of  pine  logs  sawed  with  i^-inch  kerf,  the  per  cent  of 
ov«r-run  was  as  follows,  for  12-foot  logs : 


TABLE  XI 
Over-run,  Doyle  Rule.     Ontario 


Diameter  of 

Per  cent 

log  at  small 
end. 

Scale  by  Doyle  rule. 

Actual  output  of 
inch  lumber. 

of 

over-run 

Inches 

Board  feet 

Board  feet 

6 

3 

14 

366 

8 

12 

30. 

150 

10 

27 

50 

85 

12 

48 

76 

58 

14 

75 

108 

44 

16 

108 

144 

33 

18 

147 

186 

26 

20 

192 

234 

22 

When  the  average  log  ran  between  18  and  31  inches,  the  defects  of  this  rule  were 
not  so  apparent,  and  the  over-run  was  not  excessive.  But  as  the  size  of  the  logs 
cut  grows  less  with  the  advent  of  second-growth  and  closer  utilization,  the  rule 
becomes  impossible.  Its  continued  use  in  many  regions  is  due  largely  to  the  fact 
that  logs  are  not  often  bought  and  sold,  but  the  timber  is  purchased  on  the  stump 
and  the  owner  is  unaware  of  his  losses.  This  rule  must  eventually  be  superseded 
either  by  a  more  consistent  standard  or  by  the  rejection  of  board-foot  measure 


72  THE  CONSTRUCTION  OF  LOG  RULES 

altogether.  No  owner  of  small  logs  or  of  young  standing  timber  can  afford  to  sell 
on  the  basis  of  a  scale  or  estimate  made  by  the  Doyle  rule.  As  it  stands,  this  rule 
is  a  serious  obstacle  to  the  profitable  marketing  of  second-growth  timber,  hence  to 
the  practice  of  forestry. 

67.  The  Construction  of  Log  Rules  Based  on  Diagrams.  In  con- 
structing log  rules  based  on  diagrams  (§  55),  the  quantity  of  1-inch 
boards  contained  within  a  given  diagram  may  vary,  due  to  four  different 
factors.  The  first  is  whether  a  1-inch  board  or  a  saw  kerf  is  placed  on 
the  center  line.  For  some  diameters  the  one  method  gives  the  most 
lumber,  for  others  the  alternate  plan,  depending  upon  the  relation  of 
the  total  diameter  to  the  sum  of  the  diameters  of  boards  plus  saw  kerf. 
The  second  factor  is  the  minimum  width  of  the  boards  to  be  sawed.  The 
narrower  the  board,  the  greater  will  be  the  product  from  circles  of  a 
given  diameter.  The  third  source  of  variation  lies  in  the  choice  of 
plotting  all  boards  as  if  slash  sawed,  or  else  arbitrarily  choosing  a  given 
method  of  sawing  around  or  squaring  the  log  on  the  diagram,  with 
boards  taken  from  the  slabs.  The  fourth  factor  is  the  acceptance  or 
rejection  of  fractional  inches  in  the  boards  inscribed  in  the  circle.  When 
all  boards  are  read  to  the  nearest  full  inch  in  width,  dropping  all  frac- 
tions, some  diagrams  will  lose  a  much  larger  per  cent  than  others — while 
in  actual  sawing,  these  variations  tend  to  even  up. 

For  circles  of  the  same  diameter  and  with  the  same  minimum  width 
of  board  and  saw  kerf,  the  board-foot  contents  wiU  evidently  vary  con- 
siderably according  to  the  treatment  of  these  four  factors  in  construction 
of  the  diagram.  In  a  well-constructed  consistent  set  of  diagrams,  the 
values  in  board  feet  should  increase  by  a  regular  progression.  This 
can  be  shown  by  plotting  the  original  quantities  on  cross-section  paper 
and  connecting  the  consecutive  points  by  straight  lines.  Irregularities 
are  revealed  by  sharp  angles  in  this  continuous  line.  Most  diagram 
log  rules  show  considerable  irregularity,  which  the  authors  made  no 
attempt  to  smooth  out,  as  could  have  been  done  by  means  of  this  graphic 
plotting.  A  wholly  inexcusable  variation  of  such  rules  is  caused  by 
increasing  the  average  width  of  slab  allowed  on  large  logs.  This  increase 
does  not  conform  to  the  actual  practice  in  sawing  and  results  in  a  larger 
over-run  on  large  logs.  It  is  the  principal  defect  in  both  the  Scribner 
and  the  Spaulding  diagram  log  rules.  The  Maine  or  Holland  rule, 
by  avoiding  this  error,  secured  a  more  consistent  result. 

Diagram  log  rules  tend  to  give  the  scale  of  perfect  logs  under  a  given  standard 
for  saw  kerf  and  width  of  slab.  The  waste  for  normal  crook  and  irregular  form 
cannot  be  shown.  Since  the  commercial  rules  have  ordinarily  allowed  too  thick  a 
slab  or  too  wide  a  minimum  board  or  have  rejected  fractions,  this  loss  is  compen- 
sated, but  formula  rules  if  accurate  are  more  practical  and  convenient. 

Baughnan  Log  Rules.  As  an  example  of  a  diagram  rule  which  is  too  perfect 
for  commercial  use,  since  it  neglects  shrinkage  and  normal  crook  and  includes  frac- 


SCRIBNER  LOG  RULE,  1846  73 

tional  inches,  can  be  cited  the  Baughman  log  rules  for  J-inch  and  |-inch  saw  kerfs 
respectively.  The  results  obtained  from  these  diagrams  are  so  consistent  that  they 
conform  to  the  typical  formula  for  a  perfect  log  rule. 

B.M.  =  .Sl'^— ^^-^ for  Hnch  kerf, 


and 


12 


B.M.  =  .90^ ~  —  for  1-inch  kerf. 


In  practice  the  use  of  these  rules  would  give  an  under-run:    i.e.,  the  logs  would  not 
saw  out  the  scale. 

In  these  diagrams  the  minimum  board  was  4  inches,  the  lumber  exactly  1  inch. 
The  1-inch  board  was  always  placed  in  middle  of  diagram.  Taper  was  neglected. 
H.  R.  A.  Baughman,  Indianapolis,  Ind. 

68.  Scribner  Log  Rule,  1846.  Synonym:  Old  Scribner.  The 
Scribner  log  rule  is  the  oldest  diagram  rule  now  in  general  use.  But  for 
the  unfortunate  substitution  of  the  Doyle  rule  for  this  rule  in  Scribner's 
Log  and  Lumber  Book,  its  use  would  now  be  practically  universal. 
The  rule  held  its  own  in  the  North  and  West,  and  is  the  legal  standard 
for  Minnesota,  Wisconsin,  West  Virginia,  Oregon,  Idaho,  and  Nevada. 
It  is  the  standard  prescribed  in  timber  sales  on  National  Forests  through- 
out the  West  and  by  the  Dominion  Forestrj^  Branch  of  Canada. 

The  rule  was  published  previous  to  1846.  The  diagrams  are  for 
1-inch  lumber,  and  j  inch  saw  kerf.  The  width  of  the  minimum  board 
was  not  stated  but  the  author  modified  an  earlier  edition  of  his  rule  by 
increasing  the  allowance  for  slab  on  larger  logs.  As  a  result  of  this 
unfortunate  error,  the  rule  gives  a  larger  over-run  on  logs  above  28  inches 
than  on  smaller  logs.  The  products  of  the  diagrams  were  evidently 
not  evened  off.  The  values,  when  plotted,  show  great  irregularities, 
but  except  for  the  factor  just  noted,  the  general  tendency  of  the  rule  is 
consistent. 

The  original  values  were  for  logs  from  12  to  44  inches  in  diameter  in 
sections  15  feet  long,  "  the  fractions  of  an  inch  inside  the  bark  not 
taken  into  the  measurement."  Taper  is  not  considered  on  logs  of  the 
lengths  used.  These  factors  the  author  intended  to  offset  normal  crook 
and  concealed  defects.  Values  were  then  given  for  logs  from  10  to  24 
feet  in  length. 

Modification  to  a  Decimal  Rule.  Two  important  changes  in  this  rule 
have  been  made  to  meet  the  demands  for  a  universal  log  rule.  It  has 
been  changed  to  a  decimal  rule,  and  values  for  logs  below  12  inches, 
and  above  44  inches  have  been  added.  The  practice  of  modifying  a  log 
rule  in  scaling  by  reducing  it  to  even  tens,  in  order  to  eliminate  the  col- 
umn of  unit  feet  in  adding,  is  found  in  connection  with  several  rules. 
With  the  Scribner,  instead  of  dropping  odd  feet,  thus  reducing  the  scale, 


74 


THE  CONSTRUCTION  OF  LOG  RULES 


the  odd  feet  were  rounded  off  to  the  nearest  ten,  values  over  5  feet 
being  raised,  while  5  feet  and  under  are  dropped.  The  average  scale 
of  even  a  few  logs  by  this  method  is  practically  identical  with  that 
obtained  by  the  original  rule  as  the  errors  are  compensating.  This  modi- 
fied rule  is  known  as  the  Scribner  decimal  rule. 

Exiensimi  below  12  Inches.  For  values  below  12  inches,  the  original  rule  pro- 
vided no  figures.  The  lack  of  a  formula  permitted  individuals  to  supply  their  own 
values  for  these  sizes.  As  early  as  1900,  the  Lufkin  Rule  Company  tabulated  the 
decimal  values  then  in  use,  under  three  schedules,  termed  A,  B  and  C,  shown  below. 

To  read  in  board  feet,  add  a  cipher  to  each  figure. 

TABLE  XII 
Decimal  Values  Below  12  inches  fok  Scribner  Log  Rule 


Decimal  A 

Decimal  B 

Decimal  C 

Length. 

Diameter — inches 

6     7     8     9 

10 

11 

6     7     8    9     10     11 

6     7     8    9 

10 

11 

Feet 

Board  feet,  in  tens 

12 
14 

16 

18 
20 
22 
24 

112     3 
112     3 
12     3     4 
12     3     4 
12     3     4 

12  3     5 

13  4     5 

4 
4 
5 
5 
6 
7 
7 

5 
6 
6 
7 
8 
9 
10 

12     2     3       4       4 
12     3     3       4       6 
2     3     3     4       5       7 
2     3     4     5       6       8 

2  3     4     6       7       8 

3  4     5     7       8       9 

4  5     6     7       9     10 

12     2     3 
12     2     3 
2     3     3     4 
2     3     3     4 

2  3     3     4 

3  4     4     5 
3     4     4     6 

3 
4 
6 
6 

7 
8 
9 

4 
5 
7 
8 
8 
9 
10 

Still  other  values  resulted  from  the  use  of  the  full  scale,  rather  than  the  decimal 
form.  In  the  Woodsman's  Handbook,  (1910  Forest  Service),  values  for  16-foot  logs 
used  by  a  company  in  New  York  (Santa  Clara  Lumber  Co.)  were  published.  These 
values  were  adopted  by  the  Canadian  Forestry  Branch  in  1914.  The  State  of  Minne- 
sota adopted  standard  values  differing  slightly  from  these  figures.  Wisconsin 
adopted  definite  values  by  law  for  these  sizes,  conforming  exactly  to  the  Decimal  "C" 
scale  given  above.  Idaho  prescribes  that  the  Scribner  Decimal  Scale  be  used  with- 
out specifying  values  and  both  "A"  and  "C"  scales  are  in  use  in  the  state.  In 
Oregon  and  West  Virginia  the  "Scribner  Scale"  is  called  for  by  statute,  leaving  the 
question  open  for  values  below  12  inches. 

The  weight  of  custom  is  at  present  in  favor  of  the  use  of  the  Decimal  "C"  values 
for  this  rule,  and  the  utility  of  the  Scribner  Decimal  Rule  would  be  improved  by  a 
universal  adoption  of  this  standard. 

Extension  above  44  Inches.  With  the  adoption  of  the  rule  by  the  Forest  Service, 
its  use  on  the  Pacific  coast  required  an  extension  from  44  to  120  inches.     In  this 


SPAULDING  LOG  RULE,  1868  75 

instance  a  similar  but  worse  confusion  might  have  resulted,  but  was  avoided  by  the 
adoption  of  a  single  standard  of  values  prepared  by  the  U.  S.  Forest  Service  about 
1905,  and  published  in  the  Woodsman's  Handbook,  1910  edition.  The  extension 
(made  by  E.  A.  Ziegler)  was  based  on  a  comparison  of  the  curve  formed  by  the 
plotted  values  of  the  rule  with  similar  curves  for  the  formula  rules  such  as  the 
International,  and  for  the  Spaulding  rule.  Ziegler  states,  "It  might  be  described 
as  an  extension  built  on  an  old  rule  by  graphic  methods  checked  with  the  correct 
mathematical  formula  in  which  the  slab  waste  varies  with  D  and  the  kerf  with  D^, 
and  compared  with  the  accepted  rules  in  the  Northwest,  notably  the  Spaulding." 
The  extension  was  built  up  on  a  12-foot  log,  and  applied  to  lengths  of  from  8  to 
16  feet.  As  a  concession  to  logging  methods  in  the  Northwest,  logs  up  to  32  feet 
were  scaled  without  taper  by  this  rule. 

No  such  difficulties  in  extension  are  encountered  with  rules  constructed  by  the 
use  of  correct  formulae,  since  the  values  of  logs  of  all  sizes  are  in  this  way  determined. 

Attempt  to  Improve  the  Rule.  Further  efforts  to  modify  this  log  rule  have  been 
made  in  order  to  even  off  the  irregularities  of  value  between  contiguous  sizes. 
Examples  of  this  are  the  Hanna  log  rule,  1885  (John  S.  Hanna,  Lock  Haven,  Pa.), 
the  White  rule,  1898  (J.  A.  White,  Augusta,  Mont.)  and  a  local  rule  used  by  M.  E. 
Ballou  &  Son,  Becket,  Mass.,  1888,  adopted  from  Scribner  rule,  for  small  logs.  Such 
modifications  unquestionably  improve  the  rule,  but  the  minor  irregularities  do  not 
appreciably  modify  the  scale  of  a  large  number  of  logs  of  different  sizes.  The  con- 
fusion which  would  result  in  attempting  to  secure  universal  agreement  on  any  change 
in  accepted  values  for  this  rule  has  prevented  their  adoption,  and  the  values  still 
stand  as  they  were  originally  determined,  subject  only  to  the  conversion  to  decimal 
form. 


The  Scribner  Decimal  "  C  "  log  rule  in  spite  of  its  imperfections 
comes  the  nearest  at  present  to  fulfilling  the  demand  for  a  universal 
commercial  log  rule,  because  of  its  present  wide  acceptance  and  use 
(§  13),  and  reasonable  consistency  in  over-run.  The  latter  reason  alone 
makes  it  preferable  to  the  Doyle  rule.  "  Not  even  this  rule,  however, 
does  justice  to  logs  below  12  inches  in  diameter;  and  in  regions  of  second 
growth  and  small  logs,  a  closer  and  more  accurate  rule  is  preferable. 

69.  Spaulding  Log  Rule,  1868.  Synonym:  California  Rule.  The 
Spaulding  Log  Rule  was  adopted  by  statute  in  1878  as  the  standard  for 
California,  and  the  values  were  given.  It  was  constructed  by  N.  W. 
Spaulding  of  San  Francisco  in  1868  from  diagrams  of  logs  from  10  to  96 
inches  in  diameter,  using  an  ^-inch  saw  kerf,  and  1-inch  lumber,  and 
afterwards  tested  by  sawing  logs  of  each  size  in  two  mills.  The  size  of 
the  slab  (width  of  minimum  board)  was  varied  according  to  the  size  of 
the  log.  This  error  of  construction  tends  to  increase  the  over-run  in 
large  logs.  The  values  were  given  for  lengths  from  12  to  24  feet.  The 
author  directed  that  longer  logs  be  scaled  by  doubling  the  values  in  the 
table,  and  this  practice  was  incorporated  in  the  statute.  Thus  the 
rule  neglects  taper  altogether.  In  scaling,  this  principle  is  not  applied 
to  logs  longer  than  40  feet.  It  constitutes  the  most  serious  defect  of  the 
rule  at  present.     Owing  to  the  large  saw  kerf  considerable  over-run  is 


76  THE  CONSTRUCTION  OF  LOG  RULES 

secured  by  modern  band  saws  but  the  rule  is  fairl}-  consistent,  as  are 
all  well-constructed  diagram  rules. 

70.  Maine  or  Holland  Rule,  1856.  Sjmonjan:  Fabian's.  This 
is  the  most  accurate  and  consistent  diagram  rule  in  common  use  (§55). 
It  was  constructed  in  1856  b}'  Chas.  T.  Holland  for  1-inch  boards, 
allowing  for  a  j-inch  saw  kerf  and  for  a  minimum  width  of  board  of  6 
inches.  Fractional  parts  of  a  foot  amounting  to  over  .5  are  reckoned  as 
a  whole  foot,  those  less  than  .5  are  rejected.  This  resulted  in  a  more 
consistent  rule  from  the  diagrams.  The  rule  is  applied  at  the  small 
end  of  log  and  disregards  taper,  so  cannot  be  applied  to  the  scaling  of 
long  logs  without  considering  them  as  sections.  The  best  practice  now 
limits  the  length  of  these  sections  to  16  feet  (§  43). 

71.  Canadian  Log  Rules.  The  practice  of  adopting  standard  log 
rules  by  statute  has  been  followed  by  New  Brunswick,  Quebec,  Ontario 
and  British  Columbia.  Theu*  use  is  practically  universal  in  the  pro- 
vinces. 

The  New  Brunswick  Rule,  1854.  This  rule,  is  the  statute  rule  of 
the  Province  and  is  probably  based  on  diagrams.  Values  for  from  5  to 
10  inches  were  added  by  later  regulations.  Logs  26  feet  and  over  are 
measured  in  two  lengths.  The  small  end  is  used  and  the  rule  is  based 
on  1-inch  lumber. 

Quebec  Log  Rule,  1889.  To  construct  this  rule,  diagrams  of  logs 
from  6  to  40  inches  in  diameter  were  divided  into  1-inch  boards.  A 
second  set  was  divided  into  3-inch  deals,  using  |-inch  kerf.  The  mean 
of  the  two  resultant  contents  was  taken,  and  from  this  an  arbitrary 
deduction  was  made,  ranging  from  0  to  17  feet.  Taper  was  neglected. 
This  scale  is  applied  at  the  small  end  for  logs  up  to  18  feet  in  length, 
above  which  the  average  diameter  of  the  two  ends  is  taken.  The  rule 
is  the  statute  rule  of  the  Province.^ 

The  British  Columbia  Rule  is  discussed  in  §  61. 

72.  Hybrid  or  Combination  Log  Rules.  The  inconsistency  of  the 
Dojde  rule  by  which  small  logs  are  under-scaled  and  large  logs  over- 
scaled  has  led  to  its  combination  with  the  Scribner  rule.  The  values 
of  the  latter  rule  drop  below  the  Doyle  rule  at  28  inches. 

Low  values  in  the  log  rule  favor  the  buyer  of  logs.  In  purchasing 
large  logs,  especially  hardwoods,  the  Doyle  rule  was  considered  unsafe. 
The  combined  rule,  termed  the  Doyle-Scribner,  retains  the  low  values  of 

^  The  statute  rule  of  the  province  of  Ontario  is  the  Doyle  Rule  which  was 
adopted  in  1879.  In  spite  of  the  facts  brought  out  in  an  investigation  in  1904, 
that  in  that  one  year  the  Province  lost  134  million  board  feet  on  the  scale,  equiv- 
alent to  28  per  cent  of  the  contents  of  the  logs  cut,  by  reason  of  this  rule,  the 
influences  in  favor  of  its  retention  were  too  strong  to  be  overcome  and  it  is  still 
the  standard  rule  of  the  Province. 


GENERAL  FORIMUL.E  FOR  ALL  LOG  RULES  77 

the  Doyle  rule  up  to  28  inches,  and  substitutes  the  low  values  of  the 
Scribner  rule  above  that  point. 

The  reverse  of  this  process  was  adopted  by  the  State  of  Louisiana 
in  1914.  The  values  of  the  Scribner  rule  below  28  inches  were  combined 
with  those  of  the  Doyle  rule  for  29  inches  and  over,  and  the  resultant 
hybrid  rule,  known  as  the  Scribner-Doyle  rule  is  the  official  rule  of  the 
state. 

The  Doyle  and  Baxter  rules  were  also  combined,  using  the  Doyle 
values  up  to  19  inches,  with  those  of  the  Baxter  rule  for  the  remaining 
diameters.  Both  the  Doyle-Scribner  and  the  Doyle-Baxter  are  cut- 
throat rules  calculated  to  give  the  buyer  the  maximum  advantage  of 
the  defects  of  both  rules.  The  Scribner-Doyle  rule  has  no  advantage 
over  the  straight  Scribner  rule  since  most  logs  are  below  28  inches  in 
diameter. 

73.  General  Formulae  for  All  Log  Rules.  Wlien  log  rules  have  not 
been  constructed  by  a  formula,  but  from  diagrams  or  mill  tallies,  no 
formula  can  be  found  which  will  give  the  exact  values  of  the  rule.  But, 
consciously  or  not,  the  authors  of  log  rules  have  attempted  to  deduct 
the  waste  from  saw  kerf  and  from  slabbing  and  edging  and  the  average 
results  which  they  obtained,  or  the  actual  treatment  of  these  two  fac- 
tors is  revealed  by  reducing  these  rules  to  the  nearest  approximate 
formula. 

The  general  form  of  such  a  formula  is: 

BM.  =  iaD'-+bD+C)— 

in  which  aD^  covers  the  per  cent  reduction  of  volume  for  sawdust  after  reducing  the 
square  to  a  circle,  bD  gives  the  reduction  of  diameter  or  surface  for  slabbing  and  edg- 
ing, while  C  is  a  constant  added  in  an  effort  to  correct  irregularities  in  the  rule  itself. 

L 
The  factor  —  reduces  square  inches  to  board  feet. 

Cubic  rules  converted  to  board  feet  correspond  exactly  to  the  formula, 


or  to 


B.M.  =  (aD2)— 


B.M.  =  (l-6)-^^L. 
4X12 


Perfect  formula  rules  correspond  to  the  formula, 

L 


or  to 


BM.  =  {aD^+bD)- 


'   4X12 


78  THE  CONSTRUCTION  OF  LOG  RULES 

But  imperfect  or  irregular  diagram  or  formula  rules  require  the  formula, 

B.M.  =  {aD'+bD+C)~ 
or 

B,M.  =  (  (l-6)^^-C)L- 

\  4X12       / 

The  first  of  these  sets  of  formulae  was  originated  by  A.  L.  Daniels,  the  second  by 
H.  E.  McKenzie.  By  Daniels'  formula,  the  values  of  logs  of  three  sizes  will  give 
the  formula.     For  the  following  rules,  the  formula;  read: 

Doyle,  B.M.  =  (.75Z)-'-6D+12)— , 

Scribner,       B.M.  =  (.5550=- .55D-23)— ; 

Maine,  B.M.  =  (.635D2-1 .45D+2)— ; 

Champlain,  B.M.  =  (,62832Z)=-D)— ; 

Vermont,      B.M.  =  (.50D2)— . 

By  the  McKenzie  formula,  adding  the  constant  C  gives  the  following  for: 

Spaulding,     B.M.  =  (  (1- .266)^^ -2  |L; 
\  4X12       / 

Scribner,       B.M.  =  (  (1  -  .266)^'^^ -3  )L; 
V  4X12       /    ' 

Maine,  B.M.  =  f  (1  -  .222)-"^^  -  .67  )L. 

\  4X12  / 

These  formula^  permit  of  analysis  and  comparison  of  different  log  rules. 

74.  The  Construction  of  Log  Rules  from  Mill  Tallies.  Graded 
Log  Rules.  A  log  rule  based  directly  on  mill  tallies  or  the  measured 
product  of  sawing  logs  into  lumber  will  have  no  over-run  provided  the 
variable  conditions  of  manufacture  coincide  with  those  which  determined 
the  contents  of  the  logs  from  which  the  rule  was  made.  But  this  is 
never  the  case.  Standard  log  rules  made  for  1-inch  boards  do  not  con- 
form to  mill  tally  of  lumber  sawed  partly  into  2-inch  plank,  or  even  if 
sawed  full  or  Ij^-inch  in  thickness.  Standard  rules  for  square-edged 
lumber  fall  far  short  of  measuring  the  product  of  small  logs  sawed  and 
tallied  as  round-edged  boards.  The  board  foot  as  a  cubic  measure  will 
not  indicate  the  quantity  of  surface  or  superficial  feet  of  lumber  pro- 
duced in  sawing  f-inch  boards. 

Where  it  is  desired  to  obtain,  in  the  log,  the  probable  actual  contents 
in  boards,  and  existing  rules  are  unsatisfactory,  a  new  rule  may  be  worked 


THE  MASSACHUSETTS  LOG  RULE  79 

out  based  directly  on  mill  tallies.  Unfortunately,  most  of  the  rules  so 
obtained  are  not  standardized  for  lumber  of  a  given  width,  as  1-inch 
boards,  but  include  the  mill  run,  with  varying  per  cents  of  thicker  plank. 
This  requires  a  statement  as  to  the  basis  of  the  rule.  Even  when  based 
on  arbitrary  per  cents  of  1-inch  and  thicker  lumber  such  a  rule  may  be 
superior,  for  local  use,  to  one  of  the  older  commercial  rules. 

A  mill  tally,  upon  which  a  local  log  rule  can  be  based,  will  also  serve 
two  other  purposes  if  rightly  conducted,  namely,  a  check  on  the  amount 
of  over-run  to  be  obtained  from  logs  of  different  sizes  if  scaled  by  an 
existing  log  rule  (Doyle  rule,  §  65),  and  an  analysis  of  the  product  of 
the  log  by  grades  of  lumber,  leading  to  the  construction  of  graded  log 
rules. 

For  the  single  purpose  of  constructing  a  log  rule  for  sound  logs  with 
normal  crook  (§  52)  but  two  operations  are  required.  Each  log  is  meas- 
ured, preferably  at  both  the  small  end,  inside  bark,  and  the  middle 
diameter  outside  bark,  and  its  length  recorded.  The  contents  of  each 
board  sawed  from  the  log  is  then  tallied,  and  the  total  found,  from  which, 
by  averaging  for  logs  of  the  same  dimensions,  and  the  use  of  graphic 
plotting  (§  138)  the  log  rule  may  be  obtained. 

When  mill-scale  studies  are  made  to  check  a  given  log  rule,  and  to  determine 
contents  of  logs  by  grades,  from  which  a  graded  log  rule  is  constructed  (§  87),  the 
work  is  planned  as  follows:  Each  log  is  given  a  number,  and  is  scaled  as  it  enters 
the  mill.  A  second  man  stationed  at  the  edger  places  this  number  on  the  first  and 
last  board  sawed  from  the  log.  A  lumber  grader  at  the  grading  table  indicates  the 
grade  of  each  board,  while  a  fourth  man  tallies  the  board-foot  contents  of  the  piece 
on  a  ruled  blank  which  contains  columns  for  each  standard  grade.  As  the  scaler 
and  grader  are  usually  employees  of  the  mill  the  work  requires  two  extra  men  in 
the  mill. 

The  study  is  usually  extended  to  include  defective  logs,  which  are  kept  separate 
in  the  final  averages,  since  the  original  scale  of  such  logs  is  a  matter  of  judgment 
subject  to  wide  errors.     (Appendix  A,  §  361.) 

By  a  proper  system  of  numbering  the  logs  in  the  woods,  a  mill  scale  study  may 
be  applied  to  determine  the  graded  contents  of  entire  trees  for  the  construction  of 
graded  volume  tables  (§  165). 

Reference 

A  Mill-scale  Study  of  Western  Yellow  Pine,  H.  E.  McKenzie,  Bui.  6,  Cali- 
fornia State  Board  of  Forestry,  Sacramento,  Cat,  1915. 

75.  The  Massachusetts  Log  Rule  for  Round-edged  Lumber.  This 
log  rule  is  constructed  for  round-edged  and  square-edged  boards  as 
sawed  from  small  logs  for  close  utilization  of  second-growth  timber. 

The  per  cent  of  square-edged  lumber  sawed  varies  from  0  to  50  per  cent,  increas- 
ing with  diameter  of  log.  The  rest  of  the  cut  was  round-edged.  The  rule  is  for 
i-inch  saw  kerf,  varying  in  the  per  cent  of  round-  or  square-edged  boards  included. 
It  is  based  on  mill  taUies  of  1200  logs  down  to  4  inches  at  small  end.     The  rule  is 


80  THE  CONSTRUCTION  OF  LOG  RULES 

expressed  in  two  forms,  one  for  application  to  diameter  at  small  end,  inside  bark, 
the  other  to  diameter  outside  bark  at  middle  of  log.  The  latter  form  would  apply 
only  to  species  with  bark  of  similar  average  thickness  to  the  second-growth  white 
pine  on  which  the  latter  is  based.  The  utility  of  this  rule  as  a  standard  is  inter- 
fered with  by  the  fact  that  a  certain  per  cent,  not  stated,  of  IJ-inch  and  2i-inch 
lumber  was  included  with  1-inch  boards  in  its  construction.  The  results  are  there- 
fore somewhat  too  high  for  1-inch  lumber. 

This  log  rule  indicates  that  the  contents  of  logs  measuring  from  4  to  10  inches 
in  diameter  at  small  end  are  from  20  to  50  per  cent  greater  when  scaled  by  this  rule 
than  by  the  International  |-inch  rule.  Above  12  inches,  the  excess  is  not  over 
10  per  cent.  Since  these  boards  are  measured  at  their  average  face,  taper  is  fully 
utilized,  while  waste  from  slabs  and  edging  is  reduced  to  a  minimum.  The  result- 
ant per  cent  of  utilization  is  very  consistent  for  logs  of  all  sizes;  hence  it  shows  a 
marked  gain  in  the  small  sizes  over  the  per  cents  utilized  in  square-edged  boards  as 
shown  in  Table  III. 

The  importance  of  a  log  rule  of  this  character  in  scaling  the  boardrfoot  contents 
of  second-growth  timber  in  regions  utilizing  round-edged  boards  is  obvious.  Rules 
of  this  character  are  nearly  as  satisfactory  as  the  cubic  foot  in  measuring  small  timber. 
For  complete  accuracy  in  applying  this  rule  to  other  species,  the  average  taper 
must  be  known,  or  the  average  thickness  of  bark.  Similar  local  log  rules  have 
been  made  for  loblolly  or  old  field  pine  in  the  Atlantic  Coast  States. 

76.  Conversion  of  Values  of  a  Standard  Rule  to  Apply  to  Different 
Widths  of  Saw  Kerf  and  Thickness  of  Lumber.  Where  over-run  or 
under-run  is  caused  by  a  difference  in  the  width  of  saw  kerf  used,  or  in 
the  thickness  of  lumber  sawed,  from  the  standards  used  in  the  log  rule, 
the  per  cent  of  this  difference  between  scaled  and  sawed  contents  due  to 
these  factors  may  be  easily  determined,  and  applied,  if  desired,  to  the 
scale;  or  it  may  be  incorporated  in  a  new  set  of  values  or  local  log  rule 
similar  to  those  made  from  mill  tallies. 

For  saws  of  different  widths. 

Let       iv  =  width  of  saw  'kerf  in  standard  rule; 

K'  =  width  of  saw  kerf  used  in  sawing. 
Then 

—  =per  cent  of  lumber,  minus  saw  kerf  by  standard  rule; 

1-l-A. 

—  =per  cent  of  lumber  using  different  saw  kerf. 

1+A 

The  correction  to  apply  to  the  standard  rule  in  terms  of  per  cent  is: 

1 

Per  cent  correction  =  100  X , 

T+A' 
e.g.,  the  International  rule,  j-inch  kerf  plus  iV-inch  shrinkage  =  i^-inch  =  .3125,  . 

1 

100 X =76. 3  per  cent. 

1.3125  ^ 


CONVERSION  OF  VALUES  OF  A  STANDARD  RULE 


81 


For  a  1%-inch  saw  kerf  plus  jig-inch  shrinkage  =  j^g  =  .25, 
1 


100  X =80  per  cent. 

1.25 


Then, 


'""^^S-a"'"^ 


+4.8  per  cent. 


The  following  table  will  convert  values  for  the  International  j-inch  log  rule  to 
products  of  saw  kerfs  of  other  widths,  allowing  j^-inch  shrinkage  in  each  case  as 
for  the  original  rule. 

TABLE  XIII 

Conversion  of  International  Rule  j-incii  Saw  Kerf  for  Other 

Widths  of  Kerf 


Width  of  saw 
kerf. 

Per  cent 

Per  cent  correc- 
tion to  obtain 

utilized* 

product  for 

desired  kerf 

A 

85.4 

+  11.9 

i 

84.3 

+  10.5 

A 

80.0 

+  4.8 

i 

76.3 

0 

A 

72.7 

-  4.7 

t 

69.6 

-  8.8 

A 

66.7 

-12.6 

*  This  per  cent  applies  only  to  the  residual  portion  of  the  log  after  deducting  the  waste  for 
slabbing  and  edging.  The  ratio  between  the  per  cents  utilized  is  the  basis  for  correcting  for  saw 
kerf. 

Log  rules  which  make  no  allowance  for  shrinkage  may  be  adjusted  in  the  same 
manner  by  omitting  this  factor.     Table  XIV,  Page  82. 

Correction  for  lumber  thicker  than  the  standard.  For  this  purpose  the  same 
formula  as  for  saw  kerf  is  used,  substituting  the  actual  thickness  of  lumber  (0  for 
1  inch,  and  using  i^  as  a  constant  representing  saw  kerf. 

Let     1  =  standard  thickness  of  lumber; 

/=  actual  thickness  of  lumber. 
Then, 
1 
l+K 

t 
T+K 


=  per  cent  of  lumber,  minus  saw  kerf  by  standard  rule; 
=  per  cent  of  lumber,  with  thickness  of  t; 


and 


=per  cent  correction. 


1 
l+K 

t 

t+K 
For  ^-inch  saw  kerf  the  results  obtained  are  given  in  Table  XV,  Page  82  (§  48) : 


82 


THE  CONSTRUCTION  OF  LOG  RULES 


TABLE  XIV 

Conversion  of  Log  Rules  with  5-inch  Saw  Kerf  and  No  Shrinkage 
Allowance  to  Other  Widths  of  Saw  Kerf 


Width  of 
saw  kerf. 
Inches  * 

Per  cent 

Per  cent  correc- 
tion to  obtain 

Utihzed 

product   for   de- 
desired  saw  kerf 

A 

90.2 

+  12.7 

i 

88.8 

+  11.1 

1^ 

84.3 

+  5.4 

i 

80.0 

0 

A 

76.2 

-  4.8 

f 

72.7 

-  9.1 

1^ 

69.6 

-13.0 

*  Rules  made  by  first  subtracting  slabbing  and  edging  may  evidently  be  altered  for  different 
widths  of  saw  kerf,  as  these  deductions  are  directly  proportional  to  volume,  and  are  applied  to  the 
reduced  cylinder  only.  Where,  as  with  the  International  rule,  the  deduction  for  saw  kerf  is  made 
before  subtracting  AD  for  slabs  and  edging,  this  rule  still  holds  good,  since  the  per  cent  of  cor- 
rection is  not  applied  to  the  entire  log,  but  to  the  values  in  the  rule,  which  already  exclude  AD. 
If  worked  out  for  the  log,  independent  of  the  rule,  the  sawdust  in  the  slabs  is  deducted  before 
the  factor  AD  is  found,  and  for  larger  saw  kerfs  this  factor  AD  would  be  proportionally  smaller, 
so  that  the  total  net  product  in  lumber  is  the  same  as  if  computed  by  the  above  correction. 

TABLE  XV 

Per  Cent  of  Increase  in  Sawed    Lumber  Caused  by  Sawing 
Lumber  of  Different  Thicknesses  f 


1 
Increase  in  sawed 

Thickness  of  kimber. 

product  over  1  inch 

lumber. 

Inches 

Per  cent 

U 

4.1 

U 

7.1 

If 

9.4       .. 

2 

11.1 

21 

12.5 

3 

13.6 

t  In  preparing  tables  of  volume  for  Connecticut  hardwoods  (Bui.  96,  Forest  Service),  Frothing- 
ham  used  the  International  rule,  reduced  for  a  j-inch  saw  kerf  by  subtracting  the  required  9.5 
per  cent  of  volume  from-values  for  J-inch  saw  kerf.  Complaint  was  later  made  that  in  applying 
these  tables  to  logs  sawed  in  mills  using  j-inch  saw  kerf,  the  output  over-ran  the  tables.  This 
was  due  not  to  error  in  the  tables,  but  to  the  production  of  a  large  proportion  of  thick  planks, 
thus  reducing  the  sawdust  waste. 

These  per  cents  are  applied  to  the  scale  of  1-inch  lumber.  When  50  per  cent  of 
the  output  is  in  2-inch  plank,  the  correction  would  be  50  per  cent  of  11.1  per  cent, 


LIMITATIONS  TO  CONVERSION  OF  BOARD-FOOT  LOG   RULES    83 

or  5.55  per  cent.  As  the  increase  in  per  cent  of  correction  in  the  total  scale  becomes 
less  with  increasing  thickness  of  boards  sawed,  this  method  is  more  accurate  than 
that  of  computing  the  average  dimensions  of  the  products  sawed.  In  the  above 
case  the  latter  would  have  been  I5  inches,  calling  for  a  correction  of  7.1  per  cent 
instead  of  5.55  per  cent. 

Correction  for  thin  lumber  based  on  superficial  contents.  In  a  similar  way, 
log  rules  for  1-inch  lumber  may  be  corrected  to  give  the  product  in  superficial  board 
feet  for  lumber  sawed  to  thicknesses  less  than  1  inch.     Since  the  board,  of  whatever 

thickness,  measures  1  superficial  foot,  the  "per  cent  of  utiUzation"  will  be ,  t  being 

t-\-K. 

thickness  of  board,  K,  saw  kerf.     For  5-inch  kerf  and  1-inch  lumber,  the  standard 


per  cent  is  7;  =  80  per  cent.     Then  the  correction  per  cent  is 

1+A 


t+K 

1 
1+X 


TABLE  XVI 

Correction  Per  Cents  for  Contents  of  Logs  in  Superficial  Board    Feet 
FOR  Lumber  Saw^d  Less  than  1  Inch  in  Thickness 


Thickness   ' 

of                  Saw^  kerf, 
lumber.     1 

Inches      1           Inches 

Per  cent  of 
UtiUzation 

Per  cent  for 
inch  lumber 

Correction  per 

cent  to  add  to 

log  rule  for 

1-inch  boards 

Per  cent 

1 
i 

1 

\ 

1 

133.3 
114.3 
100.0 

88.8 

80 
80 
80 
80 

66.6 
42.9 
25.0 
11.1 

77.  Limitations  to  Conversion  of  Board-foot  Log  Rules.  It  is  thus 
seen  that  a  correction  of  the  total  scale  of  logs  regardless  of  diameter  or 
length  can  be  made  whenever  thio  correction  takes  the  form  of  a  straight 
per  cent  of  the  volunie  of  Jthe  scale.  In  addition  to  the  effect  of  saw  kerf 
and  thickness  of  boards,  this  principle  applies  to  cubic  rules  erroneously 
used  for  board  feet  (§  38).  But  no  true  board-foot  log  rule  can  be  con- 
verted by  a  constant  or  flat  per  cent  into  the  values  of  any  other  log 
rule,  unless  the  deduction  for  waste  from  slabs  and  edgings  is  identical 
for  both  rules,  and  the  difference  is  wholly  due  to  the  use  of  different  per 
cents  of  waste  for  saw  kerf.  Otherwise,  the  conversion  factor  will  vary 
with  diameter  of  log.  Since  tables  of  tree  volumes  and  the  scale  of  a 
number  of  logs  include  logs  of  different  sizes,  such  volume  tables  or 
scale  totals  must  be  remeasured  in  the  log  in  order  to  determine  the 
values  for  any  other  than  the  log  rule  originally  used. 


84 


THE  CONSTRUCTION  OF  LOG  RULES 


78.  Choice  of  a  Board-foot  Log  Rule  for  a  Universal  Standard.     As 

long  as  opinions  and  customs  differ  witli  regard  to  tlie  measurement  of 
taper,  scaling  length,  saw-kerf  allowance  and  amount  of  waste  in  slabbing 
which  should  be  expressed  in  log  rules,  it  will  be  impossible  to  reach 
an  agreement  on  a  common  standard.  Meanwhile,  custom  is  working 
towards  the  elimination  of  rules  which  have  not  found  favor  and  all  but 
about  ten  log  rules  in  the  United  States  can  already  be  classed  as  obsolete. 

A  log  rule  becomes  obsolete  when  it  ceases  to  be  used,  regardless  of 
the  reasons  for  its  disuse.  Poor  rules  should,  and  sometimes  do,  become 
obsolete  because  they  do  not  give  satisfaction.  But  good  and  con- 
sistent rules  may  also  become  obsolete  or  may  never  be  taken  up,  because 
the  use  of  other  and  inferior  rules  is  so  firml}^  intrenched  that  a  substitu- 
tion is  impractical.  Rules  which  scale  so  closely  as  to  permit  no  over- 
run will  be  verj^  difficult  to  bring  into  common  use,  owing  to  the  opposi- 
tion of  buyers  w^ho  prefer  lower  standards  even  if  inaccurate. 

The  log  rules  whose  use  is  sufficiently  extensive  to  justify  their  con- 
sideration, on  this  basis  alone,  for  universal  adoption  include  only  the 
following : 


Basis  of  Rule  United  States 

Formula  Doyle 


Canada 

Doyle 

British  Columbia 


Diagram  Scribner  Quebec 

Scribner  Decimal  C       New  Brunswick 

Spaulding 

Maine 

Hybrid  Doj-le-Scribner 

Mill  Tallies  Massachusetts 


Of  these,  the  DoA'le  must  be  rejected  because  of  its  glaring  inconsis- 
tencies and  the  Doyle-Scribner  because  it  combines  the  worst  features 
of  both  rules.  The  use  of  the  Maine  and  the  Spaulding  rules  is  confined 
to  single  states,  and  the  Massachusetts  rule  is  for  a  special  form  of 
product;  i.e.,  round-edged  timber. 

This  leaves  the  Scribner,  preferably  in  Decimal  C  form,  as  the  only 
logical  rule  now  in  wide  use,  which  is  applicable  to  the  measurement  of 
square-edged  lumber. 

If  the  admitted  irregularities  of  the  Scribner  rule  are  deemed  so  seri- 
ous as  to  justify  its  rejection,  its  successor  should  not  be  chosen  from 
among  the  other  rules  in  common  use,  but  should  rather  be  a  rule  based 
on  a  formula  and  tested  to  conform  to  actual  conditions  of  sawing.  For 
such  a  purpose,  the  International  |-inch  Rule  is  probably  as  perfect  a 


UNUSED  AND  OBSOLETE  LOG  RULES  85 

rule  as  will  ever  be  required  in  commerce.  This  rule  is  especially  valu- 
able for  logs  below  12  inches  and  above  28  inches,  in  which  classes  the 
Scribner  rule  is  defective.  There  is  nothing  to  be  gained  by  further 
efforts  to  construct  new  "  perfect  "  log  rules. 

79.  Unused  and  Obsolete  Log  Rules.  In  addition  to  the  rules  described  in 
this  chapter  we  may  mention  the  following  rules,  all  of  which  are  now  obsolete. 

Bangor  Rule.  Synonyms:  Miller,  Penobscot.  The  Bangor  Rule  was  constructed 
from  diagrams,  and  gives  slightly  higher  and  more  consistent  values  than  the  Maine 
rule.  It  shows  more  care  in  construction  and  is  probably  the  best  of  the  diagram 
rules.     Owing  to  the  more  extensive  use  of  the  Maine  rule,  this  rule  is  ahnost  obsolete. 

Parson's  Rule.  This  rule  is  of  similar  construction  to  the  Bangor  and  Maine 
rules  and  its  values  are  almost  identical  but  a  little  below  the  Maine  rule.  The 
difference  is  about  2  per  cent.     It  is  a  local  rule,  still  used  to  some  extent. 

Boynton  Rule,  1899  (Vermont,  local).  Made  up  from  values  taken  from  Scrib- 
ner and  Vermont  ruies  checked  by  mill  tallies.  A  fair  rule  but  of  no  general  value. 
D.  J.  Boynton,  of  Springfield,  Vermont. 

Brubaker  Rule.     No  detailed  knowledge. 

Chapin  Rule,  188.3.  The  most  erratic  of  all  log  rules,  made  up  apparently  by 
selecting  values  from  existing  rules  to  suit  thfe  author. 

Drew  Rule,  1896.  The  Drew  rule  has  been  the  statute  log  rule  of  the  State  of 
Washington  since  1898  but  is  used  'practically  nowhere  in  the  state.  Instead,  the 
Scribner  rule  is  universally  used,  except  along  the  Columbia  River,  where  the  Spauld- 
ing  rule  is  in  use. 

This  rule  (by  Fred  Drew,  Port  Gamble,  Wash.)  was  made  from  diagrams  checked 
by  tallies  of  logs  as  sawed.  The  value.?  are  given  for  diameters  from  12  to  60  inches 
and  lengths  of  from  20  to  48  feet.  Taper  is  not  considered.  The  values  are  said 
to  have  been  reduced  to  allow  for  hidden  defects.  The  rule  is  inconsistent  in  scale, 
resembling  the  Doyle  in  tendency  on  large  logs.     Its  use  is  practically  discontinued. 

Dusenberry  Rule,  183.5.  This  rule  was  made  in  1835  by  a  Mr.  May,  and  adopted 
by  Dusenberry-Wheeler  Co.,  of  Portville,  N.  Y.  It  was  probably  constructed 
from  mill  tallies,  and  was  intended  to  measure  the  output  of  pine  sawed  I5  inches 
thick  with  some  1^-  and  2-inch  pieces.  The  saw  kerf  was  Ye  inch.  The  rule  is 
very  consistent  and  was  generally  adopted  in  the  Alleghany  Waters  in  Penn- 
sylvania. It  is  still  used  in  that  and  adjoining  states.  Owing  to  the  wide  saw 
kerf  used,  this  rule  under-scales  Scribner  from  15  to  20  per  cent  and  is  not  suited 
to  pre.sent  conditions. 

Favorite  Rule.  Synonym:  Lumberman's  Favorite.  A  diagram  rule,  made 
by  W.  B.  Judson  in  1877  and  published  in  Lumberman's  Handbook,  1880,  The 
values  for  small  logs  are  lower  by  15  per  cent  than  Scribner's.  The  rule  is  now 
practically  obsolete. 

Finch  and  Apgar  Rule.  Date  unknown.  A  diagram  rule,  erratic,  for  i^-inch 
saw  kerf.     Gives  low  values. 

Forty  Five  Rule.  About  1870.  Based  on  an  inaccurate  rule  of  thumb  formula 
which  gives  high  values  for  small  and  large  logs  and  low  values  between  these 
extremes. 

Herring  Rule,  1871.  Synonym:  Beaumont.  The  values  in  the  Herring  rule 
as  originally  made,  to  include  from  12-  to  44-inch  logs,  are  practically  identical 
with  the  Dusenberry  rule.  The  rule  was  applied  at  the  small  end  to  logs  up  to 
20  feet  in  length.  Above  20  feet  a  rise  of  1  inch  was  added,  and  was  applied  at 
middle  point  of  logs  up  to  40  feet  in  length.     Here  another  inch  was  added,  and  the 


86  THE  CONSTRUCTION  OF  LOG  RULES 

scale  carried  to  60-foot  logs.  The  taper  allowed  in  this  was  is  about  half  of  the 
average  taper. 

The  rule  is  used  extensively  in  the  pine  regions  of  Texas  and  gives  a  large  over- 
run. 

The  same  trouble  was  ex-perienced  with  this  rule  as  with  the  Scribner,  in  agreeing 
upon  an  extension  of  values  to  cover  logs  less  than  12  inches  in  diameter.  The 
values  most  commonly  used  are  the  so-called  Devant  extension,  based  upon  the 
Orange  River  rule,  and  agreeing  closely  with  the  Scribner  extension. 

Licking  River  Rule.     No  detailed  knowledge. 

Northwesiern  Rule.  A  diagram  rule  for  |-inch  saw  kerf.  Erratic,  and  similar 
to  Scribner's. 

Ropp's  Rule.  A  rule  pubhshed  by  C.  Ropp  &  Sons,  Chicago.  Based  originally 
on  diagrams  of  1-inch  lumber  for  a  j-inch  saw  kerf,  it  was  reduced  to  a  rule  of 
thumb  which  gives  erroneous  results  especially  for  small  logs,  which  are  severely 
under-scaled.     The  rule  is  therefore  of  no  value. 

Warner  Rule.  A  diagram  rule  with  excessive  allowance  of  |  inch  for  saw  kerf. 
Worthless. 

Wheeler  Rule.     No  detailed  knowledge. 

Wilcox  Rule.     A  diagram  rule  for  f-ineh  saw  kerf.     Irregular.     Low  values. 

Younglove  Rule.^  Fitchburg,  Mass.,  1840.  A  caliper  rule  resembhng  the  Baxter 
in  values. 

References 

General  Treatises  on  Log  Rules 

Relative  Value  of  Round  and  Sawn  Timber,  James  Rait,  p.  114,   Wm.  Blackwood 

Sons,  London,  1862. 
The  Measurement  of  Saw  Logs  (Universal  Rule),  A.  L.  Daniels,  Bui.  102  Vermont 

Exp.  Sta.,  1903. 
The  Measurement  of  Saw  Logs  and  Round  Timber  (Champlain  Rule),  A.  L.  Daniels, 

Forestry  Quarterly,  Vol.  Ill,  1905,  p.  339. 
The  Measurement  of  Saw  Logs   (International  Rule),  Judson  F.  Clark,  Forestry 

Quarterly,  Vol.  IV,  1906,  p.  79. 
The  Standardizing  of   Log   Measures,    E.   A.   Ziegler,    Proc.   Soc.   Am.   Foresters, 

Vol.  IV,  1909,  p.  172. 
The  Log  Scale  in  Theory  and  Practice  (Tiemann  Log  Rule),  H.  D.  Tiemann,  Proc. 

Soc.  Am.  Foresters,  Vol.  V,  1910,  p.  18. 
A  Discussion  of  Log  Rules,  H.  E.  McKenzie,  Bui.  5,  California    State  Board  of 

Forestry,  1915. 
Review  of  Bui.  5,  California  State  Board  of  Forestry,  by  H.  D.  Tiemann.  Proc. 
Soc.  Am.  Foresters,  Vol.  XI,  1916,  p.  93. 

Specific  Log  Rules 

Scribner's  Log  and  Lumber  Book  (Cubic  Measure,  Two-thirds  Rule,  Doyle  Rule), 

S.  E.  Fisher,  Rochester,  N.  Y.,  1900. 
Extending  a  Log  Rule  (Devant  Extension  of  Herring  Rule  vs.  Doyle  Rule),  E.  A. 

Braniff,  Forestry  Quarterly,  Vol.  VI,  1908,  p.  47. 
Report  of  Commission  to  Investigate  Methods  of  Scaling  Logs  in  Maine  (Holland 

Rule,  Blodgett  Rule,  Hollingsworth  &  Wliitney  Rule),  House  Document  No.  43, 

74th  Legislature,  Maine,  1909. 

1  Reference,  Forestry  Quarterly,  Vol.  XII,  1914,  p.  395. 


UNUSED  AND  OBSOLETE  LOG  RULES  87 

A  Comparison  of  the  Maine  and  Blodgett  Log  Rules,  Ii-ving  G.  Stetson,  Forestry 

Quarterly,  Vol.  VIII,  1910,  p.  427. 
Woodsman's  Handbook,  Henry  S.  Graves  and  E.  A.  Ziegler  (Scribner  Decimal  C, 

Doyle,  Inscribed  Square  Log  Rules,  and  Table  of  Comparisons  of  44  log  rules 

for  16-foot  logs),  Bui.  36,  U.  S.  Dept.  Agr.  Forest  Service,  1910. 
Comparative  Study  of  Log  Rules  (Champlain,  Vermont  and  Doyle  Rules),  Austin 

F.  Hawes,  Bull.  161,  Vermont  Agr.  Exp.  Sta.,  Part  II,  1912. 

Log  Rules  Based  on  Mill  Tallies 

Log  Rules  for  Second-growth  Hardwood  from    Mill   TalUes.     j-inch  Saw  Kerf, 

Round-edged  Boards  cut  \\  inches  thick.     Based  on  Small  End,  Inside  Bark, 

and  on  Middle  Diameter   Outside  Bark,  C.  A.  Lyford,  Reports   of  Forestry 

Commission,  N.  H.,  1905  and  1907. 
Log  Rule  for  White  Pine,  from  Mill  Tallies,  j-inch  Saw  Kerf,  for  60  per  cent  Roimd- 

edged,  40  per  cent  Square-edged  Boards,  70  per  cent  1-inch  Lumber,  remainder 

2g-inch  Plank,  C.  A.  Lyford,  Reports  of  Forestry  Commission,  New  Hampshire, 

1905  and  1907. 
Log  Rules  for  12-ft.  logs  from  Mill  Talhes  of  Round  and  Square  Edge  Lumber, 

separately  for  White  Pine,   and   Hardwoods,    L.    Margolin,    Proc.   Soc.  Am. 

Foresters,  Vol.  IV,  1909,  p.  182. 
Comparison  of  Round-edged  and  Square-edged   Sawing  for  2|-inch  planks,  H.  O. 

Cook,  Forest  Mensuration  of  White  Pme  in  Mass.,  1908,  pp.  38-43. 
Contrast  of  Output  by  Different  IMethods  of  Sawing,  H.  D.  Tiemann,  Proc.  Soc. 

Am.  Foresters,  Vol.  IV,  1909,  p.  173. 
Log  Rule  for  Hickories,  in  Cubic  Feet,  Bui.  80,  Forest  Service,  1910,  p.  39. 
Log  Rule  for  Hardwood  Logs  from  Mill  Tally,  Yellow  Birch,  Maple,  Beech,  I.  W. 

Bailey  and  P.  C.  Heald,  Forestry  Quarterly,  Vol.  XII,  1914,  p.  17. 
Log  Rule  for  Loblolly  Pine,  based  on  Mill  Tallies,  Logs  with  less  than  2-inch  Crook, 

i-inch  Kerf.     W.  W.  Ashe,  Table  23a.  Bui.  24,    North  CaroUna  Geological 

Survey,  1915,  p.  76. 


CHAPTER  VII 
LOG  SCALING  FOR  BOARD  MEASURE 

80.  The  Log  Scale.  The  scale  of  a  given  quantity  of  logs  is  their 
total  contents  expressed  in  the  unit  of  measurement  employed.  The 
term  "  scale  "  also  refers  to  the  general  rules  or  customs  of  scaling 
adopted  in  a  given  region  or  locality,  upon  which  depend  the  liberality 
or  closeness  of  the  measurement  (§  83).  Differences  in  the  method  of 
scaling  may  make  from  5  to  50  per  cent  difference  in  the  scaled  contents 
of  the  same  logs  (Table  XVII). 

To  determine  the  contents  of  logs  in  board  feet,  the  diameter  of  the 
log  is  measured  with  a  stick  marked  in  inches,  the  length  in  feet  is  deter- 
mined by  measuring  it  with  the  above  stick  or  by  a  tape  or  wheel 
(§  34),  and  the  volume  corresponding  to  these  dimensions  looked  up  in 
the  log  rule.^  This  process  is  simplified  by  placing  upon  the  sides  and 
edges  of  this  stick,  opposite  each  diameter,  rows  of  figm-es  giving  the 
values  of  the  rule  for  each  of  several  standard  lengths.  The  volume  in 
board  feet  is  then  read  directly  from  the  stick,  and  recorded.  A  stick 
so  graduated  is  termed  a  scale  stick  or  scale  rule. 

Scale  sticks  are  made  of  hickory  or  maple  about  1  by  ^  inch  in  cross  section, 
graduated  in  inches,  with  the  figures  burnt  into  the  wood  (Fig.  10).  Metal  sticks 
are  also  in  use  and  in  some  regions  cahper  rules  are  used.  The  inch  scale  is  on 
one  or  both  edges  and  the  stick  easily  accommodates  six  or  seven  other  rows  of 
figures  corresponding  to  the  contents  in  board  feet  of  logs  of  as  many  different 
standard  2-foot  lengths.  A  metal  tip  aids  in  measuring  the  diameter  inside  the 
bark.  Other  forms  are  made  for  scaling  logs  in  water,  or  logs  with  ends  rounded 
or  sniped.  Lengths  of  scale  sticks  in  inches  correspond  to  the  maximum  diameters 
of  the  logs  to  be  scaled.  Hexagonal  scale  sticks  are  sometimes  used.  Scale  sticks 
have  been  made  which  are  graduated  at  points  giving  volumes  to  exact  tens  or 
hundreds  of  units,  but  these  rules  have  never  become  popular  as  the  basis  of  the 
rule  is  not  indicated  (§  111). 

The  purpose  of  a  log  scale  depends  upon  the  ownership  of  the  timber 
or  logs.  Where  the  logs  are  to  be  sold  the  scale  is  the  basis  of  settle- 
ment and  must  be  far  more  carefully  made  than  when  the  timber  is 

1  Experienced  scalers  sometimes  substitute  ocular  or  paced  lengths  on  short 
logs.  The  scale  of  logs  shorter  than  the  minimum  length  given  in  the  rule  is  taken 
as  equaling  one- half  the  scale  of  a  log  twice  as  long  as  the  one  in  question,  i.e., 
when  the  shortest  length  given  on  the  scale  is  10  feet,  an  8-foot  log  is  scaled  as 
one-half  of  a  16-foot  log. 


THE  LOG  SCALE 


owned,  logged  and  manufactured  by  the  same  firm.  In  the  latter  case, 
the  purpose  of  the  scale  is  merely  to  provide  a  basis  for  the  payment 
of  contractors  for  logging  or  sawyers  for  felling,  or  for  checking  the  com- 


Forms  of  scale  sticks  in  use. 


parative  efficiency  of  crews  or  camps.  Finally,  the  woods  scale  deter- 
mines the  quantity  of  timber  felled,  thus  keeping  track  of  the  operation, 
while  a  re-scale  at  the  mill  permits  the  keeping  of  costs  and  credits 
separately,  on  the  basis  of  the  volume  of  logs  delivered,  between  the 


90 


LOG  SCALING  FOR  BOARD  MEASURE 


logging  and  milling  ends  of  the  business,  as  if  they  were  under  separate 
management.  Woods  scaling  also  checks  the  accuracy  of  timber  esti- 
mates, whenever  the  timber  from  given  areas  is  scaled  separately  in 
logging. 

When  the  purjjose  is  to  determine  the  basis  for  paying  saw  crews,  logs  are 
scaled  in  the  woods  before  skidding.  When  standing  timber  is  sold  on  the  basis 
of  the  log  scale,  the  scaling  is  done  at  the  skidways  or  landings  before  removal 
from  the  tract  or  vicinity.  The  mixing  of  logs  cut  from  two  or  more  tracts  must 
be  avoided  by  any  necessary  measure  such  as  sawyers'  marks,  or  scahng  in  the 
woods.  Where  no  question  of  sale  is  involved,  the  logs  are  scaled  wherever  it  is 
most  convenient.  Logs  are  usually  re-scaled  on  the  log  deck.  Where  logs  are 
rafted  and  sold,  they  usually  are  scaled  in  the  water. 

81.  The  Cylinder  as  the  Standard  of  Scaling.  A  log  rule  does  not 
give  an  exact  scale  of  lumber  which  will  be  or  can  be  sawed  from  logs 

(§  46).  The  log  rule  is  an  arbitrary 
standard  fixing  the  quantity  of  1-inch 
lumber  said  to  be  contained  in  logs  of  given 
diameters  and  lengths.  When  the  top  or 
small  end  of  the  log  inside  the  bark  deter- 
mines the  diameter,  as  it  does  for  all  board- 
foot  log  rules  in  common  use,  these  rules  do 
not  include  any  boards  or  pieces  sawed 
from  the  taper  or  swell  of  the  log.  The 
scaler  must  therefore  pay  no  attention  to 
that  portion  of  the  contents  of  the  log 
which  lies  outside  of  this  cylinder,  no 
matter  whether  this  portion  be  sound  or 
defective.  On  the  butt  end  of  a  log,  the 
contents  to  be  scaled  lies  within  a  smaller 
circle  representing  the  area  of  the  top  end 
of  the  log,  or  the  cross-section  of  the 
cylinder  whose  diameter  is  this  top  end. 
This  cylinder  must  coincide  in  position 
with  the  axis  of  the  log,  so  that  the  center 
of  the  cross-section  or  area  to  be  scaled 
coincides  with  the  center  of  the  butt  or 
larger  end  of  the  log.  Common  errors  in  scaling  are  the  shifting  of  the 
scaled  cylinder  towards  one  side  to  avoid  defects,  and  the  offsetting  of 
defects  within  the  cylinder  against  sound  short  lumber  which  may  be 
scaled  from  the  taper. 

82.  Deductions  from  Sound  Scale  versus  Over-run.  Log  rules 
give  the  scale  of  this  cylinder  in  sound  lumber  and  do  not  allow  for 
defects.     The  standard  scaling  practice  is  to  make  deductions  from 


Fig.  11. — Projection  of  area 
of  top  end  of  log  on  butt 
section,  showing  portion  of 
butt  to  be  scaled.  The 
circle  A  represents  the  area 
to  be  scaled.  The  presence 
of  defect  in  area  C  does  not 
justify  the  shifting  of  this 
circle  to  position  B  but  de- 
ductions for  defect  must  be 
made  from  A.  D  is  the 
geometric  center  of  the  log 
and  of  the  scaled  area  A . 


SCALING  PRACTICE  91 

the  scale  for  all  visible  defects  which  lie  within  the  cylinder  in  each 
log  separately,  of  the  amount  of  lumber  which  would  be  lost  because  of 
the  defect. 

This  rule  is  not  always  observed.  In  many  species,  certain  defects  may  exist 
without  visible  external  indications  either  on  the  surface  or  at  the  exposed  ends. 
When  the  logs  are  in  water  it  is  difficult  to  detect  defects.  There  has  been  a 
tendency  on  the  part  of  makers  of  log  rules  to  reduce  the  standard  volumes  of  the 
log  rule  in  order  to  offset  these  invisible  defects  (Scribner  rule,  §  68).  Log  rules, 
like  the  Cumberland  River  rule  which  gives  but  45  per  cent  of  the  cubic  contents, 
permit  the  buyer  to  ignore  most  defects  with  perfect  safety. 

The  use  of  a  log  rule  which  is  known  to  give  a  large  over-run  (§  47)  usually 
gives  rise  to  the  practice  of  scaling  "sound"  and  ignoring  defects.  The  buyer 
can  afford  to  be  lenient,  and  the  seller  objects  to  any  further  discounts  than  those 
inherent  in  the  rule  itself. 

Except  for  a  few  species  and  regions,  defects  may  usually  be  seen  and 
deducted.  Where  the  opposite  is  true,  custom  sometimes  permits  a 
reduction  of  the  final  scale  by  a  straight  per  cent  to  allow  for  such 
invisible  defects. 

Over-run  (§  46)  is  therefore  an  element  which  should  not  influence 
in  any  way  the  practice  of  log  scaling.  Where  an  admittedly  defective 
rule  is  offset  by  lenient  but  inaccurate  scaling  practice,  the  entire 
technique  and  standard  of  scaling  suffers,  and  such  conditions  should 
sooner  or  later  yield  to  accurate  standards,  both  in  the  rule  used  and 
in  its  application. 

83.  Scaling  Practice,  Based  on  Measurement  of  Diameter  at  Small 
End  of  Log.  The  advantages  of  measurement  of  the  log  at  the  small 
end,  which  have  made  this  custom  practically  universal  in  scaling,  are 
that  the  scaling  diameter  inside  the  bark  can  be  directly  measured 
without  guessing  at  bark  thickness,  and  no  matter  how  high  a  skidway 
or  roUway  is  piled,  the  ends  of  the  logs  are  usually  visible  for  scaling. 
By  contrast,  logs  to  be  calipered  at  the  middle  point  can  be  measured 
only  when  lying  separately  or  before  being  placed  on  rollways,  and  the 
bark  thickness  is  usually  guessed  at. 

The  per  cent  of  over-run  on  the  log  scale  is  affected  by  three  main 
factors.  Two  of  these,  namely,  the  elements  affecting  manufacture  of 
lumber  and  the  character  of  the  log  rule  itself,  have  been  discussed  in 
Chapter  V.  The  third  is  the  practice  of  scaling,  and  the  customs  which 
govern  it,  collectively  termed  the  "  scale."  This  practice  affects,  first, 
the  method  of  determining  scaling  diameters  and  lengths,  for  when 
these  are  once  ascertained  the  rule  permits  no  variation  in  contents  for 
sound  logs;  and  second,  the  deductions  from  this  scale  for  defects,  as 
interpreted  by  the  scaler. 

Scaling  Lengths.  The  total  length  of  a  log  must  be  accurately  deter- 
mined.    For  log  rules  which  are  based  on  diameter  at  the  small  end, 


92  LOG  SCALING  FOR  BOARD  MEASURE 

logs  whose  length  exceeds  a  givep  maximum  are  scaled  as  two  or  more 
sections  or  shorter  logs  (§  43).  Custom  or  "  scale  "  determines  the 
maximum  length  to  be  scaled  as  one  section  and  the  method  of  deter- 
mining the  taper  or  diameter  of  the  second  or  remaining  sections  to  be 
scaled.  Short  sections  scaled  to  full  or  actual  top  diameter  give  the 
maximum  scale,  while  the  loss  from  scaling  long  logs  as  one  piece  based 
on  diameter  at  top  end  may  be  very  large,  due  to  the  increasing  per  cent 
of  volume  in  long  logs  which  lies  outside  the  cylinder  and  is  thrown  into 
the  over-run. 

The  standard  lengths  of  softwood  or  coniferous  logs  are  multiples  of 
2  feet,  to  which  is  added  an  allowance  for  trimming.  Where  long  logs 
are  divided  into  two  or  more  lengths  for  scaling,  this  rule  is  still  adhered 
to;  e.g.,  a  26-foot  log  is  scaled  as  a  14-  and  a  12-foot.  Usually  the 
longer  length  is  scaled  as  the  butt  log. 

The  tremendous  variations  in  scale  which  may  result  from  different 
treatment  of  scaling  lengths  and  taper  in  long  logs  is  illustrated  in  Table 
V  (§  44).  In  order  to  secure  a  consistent  scale  between  long  and  short 
logs,  the  scaling  length  should  be  limited  to  not  over  16  feet,  and  the 
actual  diameter  of  each  section  taken  as  the  scaling  diameter. 

Trimming  Allowance.  The  trimming  allowance  varies  according  to  the  method 
of  transportation  used.  For  logs  hauled  by  rail  or  driven  down  sluggish  streams, 
from  2  to  3  inches  is  allowed  for  each  16  feet  of  length.  Large  logs  require  the 
greater  allowance,  to  guard  against  slanting  cross  cuts  which  might  give  a  short 
length  on  one  side.  Where  logs  are  driven  down  swift  rocky  streams  the  trimming 
length  must  be  sufficient  to  allow  for  the  brooming  of  the  ends.  In  very  bad  waters, 
the  exact  length  of  a  log  is  immaterial  and  the  loss  from  brooming  a  heavy  item. 
Odd  lengths,  i.e.,  lengths  measured  in  odd  feet  as  1.3  feet,  are  permitted  in  hard- 
woods and  to  a  limited  extent  in  softwoods. 

In  ordinary  scaling,  trimming  lengths  in  excess  of  standard  2-foot  gradations 
are  not  scaled.  But  sellers  of  logs,  to  reduce  loss  from  careless  cutting  of  log  lengths, 
may  stipulate  that  when  trimming  lengths  are  in  excess  of  the  margin  agreed 
upon,  the  log  shall  be  scaled  as  if  cut  from  1  to  2  feet  longer.  The  U.  S.  Forest 
Service  adopts  this  practice  as  a  penalty  scale. 

Scaling  Diameters.  In  the  apparently  simple  process  of  measuring 
the  diameter  inside  the  bark  at  the  top  end  of  the  log,  there  are  two  ways 
in  which  the  buyer  may  be  given  the  advantage  of  a  smaller  scale.  Owing 
to  the  irregular  cross  sections  of  logs,  an  average  diameter  should  be 
found  by  taking  two  measurements  at  right  angles.  Instead,  the 
practice  of  scaling  the  smallest  diameter  is  common.  The  difference, 
in  large  logs,  sometimes  amounts  to  2  or  3  inches.  The  second  choice 
lies  in  the  treatment  of  fractional  inches.  These  fractions  should  be 
rounded  oE  to  the  nearest  inch;  e.g.,  the  18-inch  log  class  should  include 
diameters  from  17.6  inches  to  18.5  inches.     Instead,  all  fractions  may 


SCALING  PRACTICE 


93 


be  dropped,  throwing  logs  from  17.6  inches  to  17.9  inches  into  the  17- 
inch  instead  of  the  18-inch  class.^ 

The  variations  in  scaling  practice  or  local  "scale"  for  the  different  regions  in 
the  United  States  and  Canada  are  shown  in  Table  XVII,  p.  94. 

It  is  seen  that  the  standard  set  by  the  U.  S.  Forest  Service  is  almost  nowhere 
complied  with  in  private  operations,  and  that  the  departures  from  this  standard 
work  uniformly  in  favor  of  the  buyer.  Except  for  hardwoods,  there  is  no  vaHd 
reason  for  rejecting  fractional  inches,  since  these  are  in  most  instances  already 
rejected  in  the  construction  of  the  log  rule  itself  (Scribner,  §  68),  and  in  any  case, 
the  contents  of  logs  of  exact  inch  diameters  represent  a  fair  average  for  logs  varying 
up  to  5  inch  larger  or  smaller.  In  the  same  way,  it  is  unfair  to  measure  the 
smallest  diameter  instead  of  the  average,  for  the  sawed  contents  of  logs  with 
eccentric  cross-sections  is  little  if  any  less  than  for  round  logs,  and  certainly 
does  not  diminish  in  proportion  to  the  ratio  between  smallest  and  average  diameter. ^ 


Fig.  12. — Effect  of  rapid  taper  at  small  end  upon  scaling  diameter  and 
scaled  contents  of  a  log. 


1  The  adoption  of  these  two  buyers'  practices  in  the  scale  will  result  in  a  loss 
to  the  seller  which,  by  the  Scribner  log  rule,  amounts  to  from  5  to  15  per  cent, 
averaging  8  per  cent  for  logs  running  10  to  the  thousand  board  feet,  and  13  per 
cent  for  logs  rimning  20  per  thousand.  The  use  of  the  average  diameter,  and  the 
rounding  off  of  fractional  inches  are  practices  fair  alike  to  buyer  and  seller,  and 
are  required  by  the  U.  S.  Forest  Service  in  selling  public  timber. 

The  practice  of  reducing  unit  feet  in  a  log  rule  to  tens,  or  converting  the  rule 
into  a  "decimal"  rule  gives  a  third  opportunity  for  discrimination  in  favor  of 
the  buyer.  The  correct  method  Ls  that  employed  in  the  Scribner  Decimal  rule  where 
all  fractions  above  5  feet  are  thrown  to  the  10-foot  value  above,  while  those  less  than 
5  feet  are  dropped.  But  in  one  section  of  Marae  it  is  the  custom  to  drop  all  unit 
feet  scaled  by  the  Maine  rule.  Thus  a  log  scaling  19  feet  would  be  entered  as 
10  feet.     The  effect  of  such  a  custom  on  the  scale  is  self  evident. 

-  In  a  contract  for  sale  of  logs,  the  log  rule  to  be  used  must  be  mentioned. 
The  practice  regarding  scaling  length,  trimming  allowance,  method  of  measuring 
taper  or  rise  on  logs  of  greater  than  scahng  lengths,  measurement  of  diameter  and 
treatment  fractional  inches  should  be  specified.  Otherwise,  common  custom  or 
scale  in  the  locality  will  determine  what  constitutes  a  proper  method.  The  method 
of  deducting  for  defects  whether  by  each  log  separately  or  by  a  straight  per  cent 
should  be  agreed  upon,  and  if  possible,  standard  instructions  adopted  for  culling 
defects.  The  minimum  dimensions  of  a  merchantable  log  should  be  defined,  both 
as  to  length  and  diameter,  and  as  to  per  cent  of  total  scale  which  must  be  obtained 
after  deducting  for  defects. 


94 


LOG  SCALING  FOR  BOARD  MEASURE 


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SCALING  PRACTICE  95 


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96 


LOG  SCALING  FOR  BOARD  MEASURE 


1 

Chief  defect  is  log  length 
and  taper 

Tolerated  because  of  in- 
complete utilization 

Tendency  (Scribner)  to 
correct,  as  utilization  be- 
comes closer 

Concealed  defects  demand 
a  conservative  scale. 

Incomplete  utilization  tol- 
erates neglect  of  taper 

On  each  log 
Judgment  of  scaler 

Ditto 
Ditto 

1.  25  to  30  per  cent 
cull  deducted  from 
total  scale 

2.  On  each  log,  plus 
8   to    10   per    cent 
cull  for  unseen  de- 
fects 

1  ? 

1" 

Dropped 

British  Colum- 
bia; dropped 

Dropped 

1.  Dropped 

2.  Sometimes 
averaged     to 
nearest  inch 

Hi 

1  i  ^ 

Q   "  o 

Smallest,      inside 
bark 

Average,    inside 
bark 

Either       method, 
inside  bark 

Average,       inside 
bark,  and  some- 
times inside  sap 
as  well 

Trimming 
allowance 

Logs   under   36 

inches  allow  4 

inches 
Logs     over     36 

inches  allow  6 

inches 

4  to  6  inches,  6 
inches    on    all 
large  logs 

Taper  on  long 
logs,  how 
measured 

1  inch  for  butt 
log  for  each  10 
feet     of    total 
length    above 
40  feet 

Ditto 

Various    o  u  s  - 
toms 

As    in    Pacific 
Northwest 

^1 

40  to  50  feet 

British  Colum- 
bia, 40  to  50 
feet 

40  to  50  feet 

40  feet 

2 

Spaulding 

Scribner 
Spaulding 

•a 

Pacific 
Northwest 

Redwoods 
California 

SCALING  PRACTICE  BASED  ON  ME.\SUREMENT  OF  DIAMETER    97 


Abnormal  Diameters.  The  practice  of  basing  the  scaling  diameter  on  that  of 
the  small  end  of  the  log,  with  its  consequent  disregard  of  taper,  gives  rise  to  diffi- 
culties on  'ogs  which  taper  rapidly  at  the  small  end,  as  for  instance,  rough  or  limby 
logs  on  the  basis  of  their  top  diameters  may  result  in  loss  of  scale  when  in  reaUty 
a  gi-eater  volume  of  the  tree  has  been  utilized.  Fig.  12,  p.  93. 

By  the   International  i-inch  rule   this   log   would   scale,    in   actual   diameter 


Length.      [  Scaling  diameter. 
Feet         I  Inches 


Scale. 
Feet  B.M. 


12 


Rigid  adherence  to  the  scaling  practice  on  such  logs  results  in  the  refusal  of 
contractors  to  cut  them.  There  are  two  possible  modifications  of  the  end  diameter 
rule  which  will  meet  this  condition:  First,  to  scale  the  log  as  a  shorter  log,  at  the 
point  which  will  give  the  largest  total  scale,  in  the  above  instance  at  12  feet  giving 
a  scale  of  70  board  feet;  second,  to  scale  it  as  two  logs,  including  the  short  tapering 
portion  as  a  separate  piece  from  the  main  portion.  In  the  above  case,  the  6-inch 
top,  with  a  length  of  4  feet  would  add  one-fourth  of  the  scale  of  a  16-foot  log  of 
that  diameter,  or  5  board  feet,  giving  a  total  scale  of  75  board  feet.  The  latter 
method  is  the  most  equitable,  otherwise  there  is  no  object  to  the  contractor  in 
going  into  the  top  to  secure  closer  utilization. 

Abnormally  large  diameters,  occurring  at  the  small  ends  of  logs  are  the  result 
of  cross  cutting  through  crotches  or  swellings  caused  by  limbs,  or  by  defects  or 
cankers.  Such  diameters  must  always  be  reduced  to  a  size  representing  the  normal 
diameter  of  the  cross  section  as  determined  by  average  taper.  For  shght  .swellings 
this  is  judged  by  eye.  For  crotches,  the  diameter  at  butt  end  is  sometimes  taken 
and  average  taper  deducted.^ 

84.  Scaling  Practice  Based  on  Measurement  of  Diameter  at  Middle 
of  Log  or  Caliper  Scale.  Xone  of  the  true  board-foot  log  rules  in  common 
use  are  applied  at  the  middle  of  the  log.  By  the  Blodgett  Rule,  a  cubic 
rule  expressed  in  board  feet  (§  33)  the  log  is  usually  measured  in  the 
middle,  outside  the  bark.  When  taper  is  taken  on  long  logs  by  the  ordi- 
nary rules,  the  scaler  depends  upon  his  scale  stick  and  ocular  judgment 
for  the  measurement  of  the  upper  diameters.  But  if  logs  are  customarily 
cut  long,  and  must  be  scaled  by  getting  actual  taper  rather  than  assumed 

1  The  following  court  decisions  are  important  as  defining  the  bearing  of  the 
"scale"  on  agreements: 

"In  the  absence  of  any  agreed  standard  of  measure  in  a  contract,  that  of  the 
place  where  a  commodity  is  purchased  will  govern  the  contract."  Supreme  Court 
of  New  York,  Dunberic  vs.  Spaubenberg,  121  N.  Y.  299. 

"Where  a  contract  involves  the  measurement  of  logs  by  specified  rule,  but 
does  not  indicate  the  manner  of  measuring  whether  by  end,  average  or  middle 
diameter,  local  custom  shall  determine  such  manner."  Supreme  Court  of  Louisiana, 
13  So.  230. 


98  LOG  SCALING  FOR  BOARD  MEASURE 

standard  tapers,  calipers  must  be  brought  into  use  in  scaling.  The 
calipers  employed  in  scaling  logs  by  the  Blodgett  rule  are  equipped  with 
a  wheel  of  10  spokes,  one  revolution  measuring  5  feet  in  length  (§34), 

The  greatest  drawback  to  a  caliper  scale  is  the  necessity  of  determin- 
ing the  width  of  bark,  doubling  this,  and  subtracting  to  get  the  scaling 
diameter  of  the  log.  When  all  logs  are  calipered,  it  is  a  common  prac- 
tice to  determine  the  average  width  of  bark  of  the  species  and  region, 
and  deduct  twice  this  fixed  amount  on  all  logs  regardless  of  variations 
in  actual  bark  thickness,  relying  on  the  law  of  averages  to  secure  a  true 
scale.  For  the  Blodgett  rule,  |-inch  for  each  bark  is  allowed  and  the 
calipers  are  adjusted  to  read  the  diameter  inside  bark  direct.  On  the 
Big  Sandy  River  in  Kentucky  (Big  Sandy  Cube  Rule)  the  allowance  is 
1  inch  for  each  bark.^ 

85.  Scale  Records.  The  tally  is  the  record  kept  of  the  logs  by  the  scaler  or  his 
assistant,  the  tally  man.^  The  tally  may  consist  merely  of  a  record  of  diameter 
and  length  of  each  log.  From  this  the  full  scale  is  easily  computed  at  camp.  But 
the  system  prevents  deductions  for  defects  from  each  log  separately,  and  is  used 
only  where  such  discounts  are  not  made,  or  are  made  either  as  a  per  cent  of  total 
scale,  or  by  reducing  the  length  or  diameter  of  the  log.  This  primitive  method 
of  scaUng  has  been  largely  replaced  by  the  plan  of  recording  the  board-foot  contents 
of  each  log  when  scaled.  From  the  full  scale,  deduction  is  made  for  defect,  and  the 
net  or  sound  scale  recorded.  For  long  logs  scaled  in  two  or  more  sections,  only 
the  sum  of  these  volumes  is  set  down,  giving  the  total  scale  for  the  log  as  one  piece 
and  thus  keeping  the  count  intact.  The  purpose  in  this  is  to  obtain  a  tally  of 
the  exact  number  of  pieces  scaled  as  well  as  their  total  contents. 

To  still  further  insure  an  accurate  record,  logs  are  numbered  serially,  with 
crayon,  coinciding  with  printed  numbers  in  the  scale-book.  This  enables  a  check 
scaler  to  re-scale  and  compare  individual  logs,  or  any  number  of  logs,  with  the 
original  scale  to  determine  the  per  cent  of  error  and  the  specific  faults  in  practice. 
Without  such  enumeration,  the  entire  number  must  be  re-scaled  to  obtain  a  check, 
and  specific  errors  are  not  shown.  The  method  of  numbering  is  cumbersome  where 
large  quantities  of  very  small  logs  are  handled,  but  it  is  the  only  plan  by  which  a 
uniform  standard  of  scaling  may  be  attained  by  a  force  of  several  scalers. 

1  A  second  method,  employed  in  Maine  in  scaling  cubic  contents,  is  to  assume 
that  the  volume  of  bark  is  12§  per  cent  of  the  total  volume  of  the  tree  with  bark. 
The  diameter  outside  bark  is  measured  direct,  and  the  volumes  given  on  the  rule 
are  computed  to  express  the  contents  of  wood  alone. 

Bark  is  never  removed,  in  scaling,  to  permit  the  calipering  of  the  direct  measure- 
ment inside  bark,  as  this  process  is  too  time  consuming.  The  Tiemann  log  rule 
(§  63)  which  applies  to  middle  diameter  inside  bark,  if  used  commercially,  would 
probably  be  applied  by  the  common  method  of  deducting  fixed  widths  of  bark, 
to  be  regulated  by  measurements  taken  of  the  species  and  locality.  This  practice 
permits  of  an  additional  source  of  variation  in  measuring  diameters  (§  29)  through 
the  bark  on  individual  logs  being  thicker  or  thinner  than  the  arbitrary  measure- 
ment. 

2  Scalers  usually  work  alone,  preferring  the  extra  labor  to  the  risk  of  errors 
made  in  the  record  by  incompetent  tally  men. 


SCALE  RECORDS  99 

The  scaler  marks  the  logs  with  crayon  as  he  scales  them.  If  not  numbered, 
they  are  check  marked. 

Where  logs  are  piled  in  rollways,  unevenly,  and  cut  different  lengths,  the  count 
must  be  checked  carefully  to  see  that  none  is  missed.  This  is  best  done  by  making 
a  recoimt  after  scahng  a  rollway,  and  check  marking  the  butts  of  the  logs,  the 
tops  having  been  marked  in  the  scaling.  Logs  piled  in  high  rollways  can  best  be 
scaled  by  two  men,  one  working  at  each  side  of  the  rollway. 

Cull  logs  which  are  not  scaled  are  given  a  distinguishing  mark.  If  already 
skidded,  they  should  be  counted  and  recorded  as  culls.  The  scaling  of  logs  in 
the  woods  eliminates  the  culls  from  the  scale  altogether  and  saves  the  expense  of 
logging  them. 

Log  Brands,  Termed  Stamps  and  Bark  Marks.  When  the  practice  is  necessary 
the  scaler  must  see  that  the  logs  have  been  properly  stamped  and  bark  marked. 
A  stamp  is  a  pattern  or  die  stamped  into  the  end  of  a  log  with  a  marking  hammer. 
A  bark  mark  is  a  pattern  cut  into  the  bark,  usually  near  an  end,  with  an  axe. 
Stamps  and  bark  marks  are  used  to  distinguish  logs  when  driven  with  those  of 
other  owners  down  a  common  stream.  These  marks  are  recorded  by  scalers  and 
determine  the  ownership  of  the  logs. 

The  Scale  Book.  A  form  of  scale  book  is  shown  on  p.  100  containing  100  printed 
numbers  on  a  page  with  spaces  for  entering  the  contents  of  logs,  and  for  totahng 
each  column  separately  and  adding  these  totals  for  the  page. 

The  scale  record  shown  in  this  sample  page  is  for  the  Scribner  Decimal  C  Scale. 
The  original  records  give  the  scale  in  tens  of  feet.  At  the  foot  of  each  column,  the 
total  is  entered  parallel  to  the  base,  and  the  zero  added  to  obtain  full  scale. 

Logs  whose  scale  has  been  culled  show  the  net  scale,  and  also  the  amount 
culled  enclosed  in  a  circle  as,  ®,  which  permits  checking  the  cull. 

Other  forms  of  scale  records  are  in  use  following  these  general  principles.^ 

86.  The  Determination  of  What  Constitutes  a  Merchantable  Log. 

A  merchantable  log  is  one  which  it  is  profitable  to  log.  Logs  whose  con- 
tents will  not  return  the  cost  of  logging  and  manufacture  are  unmer- 
chantable. This  may  be  due  either  to  small  size,  to  defects  which 
reduce  the  scaled  contents  of  the  log,  or  to  high  cost  of  logging. 

Minimum  Size.  The  costs  of  producing  lumber  are  separated  into 
logging  cost  and  milling  cost.  Both  depend  on  the  cubic  volume  of  the 
log.  But  both  are  modified  by  the  time  required  in  handling  separate 
pieces.  This  causes  the  cost  per  cubic  foot  to  increase  for  small  logs. 
In  logging,  and  in  small  mills,  the  cost  also  increases  per  cubic  foot  when 
logs  reach  large  sizes  difficult  to  handle. 

The  value  of  the  product  depends  not  upon  the  cubic  contents  of 
the  log,  but  on  the  quantity  of  sawed  lumber  which  it  contains,  and 

1  The  following  court  decisions  are  of  interest:  "When  record  of  scale  is  kept 
on  temporary  paper  and  transferred  every  evening  to  permanent  record,  this 
record  holds  in  court  as  original  evidence."  Court  of  Appeals,  Alabama,  68  South. 
698. 

The  U.  S.  Forest  Service  instructs  its  scalers  to  make  the  original  and  final 
record  of  scale  in  the  field  because  of  the  liability  of  error  in  copying  figures. 

"Parties  must  abide  by  the  official  scaler's  report  except  that  fraud  or  gross 
mistake  can  be  shown."    Supreme  Court,  Michigan,  Brook  vs.  Bellows,  146  N.  W.  311. 


100  LOG  SCALING  FOR  BOARD  MEASURE 


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WHAT  CONSTITUTES  A  MERCHANTABLE  LOG  101 

finally,  upon  the  qualities  or  grades,  and  price  of  this  lumber.  The 
ratio  of  board  feet  per  cubic  foot  (§  41),  the  quality  and  value,  all 
increase  with  increasing  size  of  log.  Due  to  these  factors,  logs  below  a 
given  diameter  and  length,  or  total  scale,  even  if  sound,  become  unprofit- 
able or  unmerchantable.  This  minimum  diameter  and  length,  when 
specified,  reheves  the  logger  or  purchaser  of  the  requu-ement  of  remov- 
ing such  logs  from  the  woods,  cutting  them  from  tops,  or  felhng  trees 
which  will  not  yield  larger  sizes.  If  he  chooses  to  take  these  sizes, 
especially  from  the  tops,  the  logs  are  customarily  scaled  and  paid  for. 

Defective  Logs.  Defective  logs,  which  wUl  produce  only  a  portion  of 
the  normal  contents  of  sound  logs  of  the  same  size,  cost  just  as  much  to 
log  and  saw  as  if  sound.  But  the  ratio  of  lumber  secured  per  cubic 
foot  is  reduced  in  proportion  to  the  amount  of  cull,  and  the  margin 
between  cost  and  value  shrinks  accordingly,  until  it  disappears  and  the 
log  is  classed  as  a  cull  and  not  scaled  even  if  taken  by  the  logger.  Defects 
occur  most  frequently  in  large  logs,  whose  quality  and  value  are  high. 

A  defective  log  which  produces  a  small  per  cent  of  its  contents  but 
of  clear  lumber  or  high  grades  may  be  merchantable,  while  a  rough  log 
with  a  much  smaller  per  cent  of  defect  va&y  not  show  a  profit  in  handling. 
Millmen  who  log  their  own  timber  can  base  their  standard  for  culls 
directly  upon  this  margin  of  profit,  and  can  afford  to  accept  very-  defect- 
ive logs  for  a  few  high-grade  boards.  Value  or  margin  of  profit,  if 
applied  as  a  standard  in  selecting  or  rejecting  logs,  means  an  elastic 
per  cent  of  cull  dependent  on  the  character  of  the  log  itself.  But  the 
logger  or  logging  contractor  is  paid  not  by  value  or  grade  of  sawed  lum- 
ber, but  by  the  scale.  Since  his  costs  are  determined  by  cubic  volume 
and  size,  he  would  prefer  a  cubic  log  scale,  but  in  accepting  payment  on 
the  basis  of  board-foot  contents,  his  profit  in  logging  depends  instead  on 
the  ratio  of  board  feet  to  cubic  feet  independent  of  qualit}-,  and  is 
diminished  by  reduction  in  scale  caused  by  cull.  On  the  other  hand 
the  loggers'  costs  vary-  with  the  distance  which  the  log  must  be  skidded 
or  hauled.  A  log  with  a  given  per  cent  of  sound  scale  if  near  the  point 
of  delivery  wQl  show  a  profit,  while  the  same  log  is  unmerchantable  if 
located  at  a  greater  distance  from  the  track.  For  defective  logs,  then, 
the  merchantability  is  determined,  for  the  millman,  by  comparing  the 
combined  cost  of  logging  and  milling  with  the  value  of  the  product, 
but  for  the  logger  it  is  determined  by  comparing  the  price  per  thou- 
sand board  feet  secured  for  the  scaled  contents  of  the  log  with  the  cost 
of  delivering  it  to  the  point  agreed  upon. 

Where  firms  are  doing  their  own  logging,  sawders  and  loggers  are 
frequently  paid  on  basis  of  full  scale  disregarding  cull.  But  in  contract 
logging,  the  scaler  usually  f ejects  cull,  thus  requiring  an  agreement  on 
the  per  cent  of  sound  contents  which  constitutes  a  merchantable  log. 


102 


LOG  SCALING  FOR  BOARD  MEASURE 


This  per  cent  cannot  be  varied  from  log  to  log  according  to  value  of 
contents  to  favor  the  millman,  or  to  location  of  log  to  favor  the  logger, 
but  is  arbitrarily  set  at  an  average  figure  applicable  to  all  logs  of  a  given 
species.  Different  per  cents  are  permitted  for  species  having  different 
average  values,  the  greater  the  value  the  lower  the  per  cent  of  sound 
lumber  accepted.  As  between  the  logger  and  the  millman,  the  use  of 
the  board-foot  scale  favors  the  latter,  but  its  application  regardless  of 
grades  of  lumber  in  the  log  is  a  concession  to  the  logger.  The  rejection 
of  cull  logs  is  a  concession  to  the  millman  but  the  adoption  of  a  fixed 
percentage  for  each  species  simplifies  administration  and  aids  the  logger, 
who  does  not  have  to  determine  the  profit  in  a  log  but  only  the  cost  of 
logging.  Contract  loggers  are  favored,  then,  by  a  cubic  basis,  no 
deductions  for  cull,  and  reduction  of  logging  costs  by  leaving  inaccess- 
ible logs  in  the  woods.  The  manufacturer  considers  the  additional 
factor  of  profit  or  value  of  the  log,  which  the  logger  himself  would 
have  to  consider  if  he  were  selling  his  logs.  Only  by  determining  aver- 
age total  costs  and  average  values  for  a  given  logging  operation  can 
the  actual  specifications  of  a  merchantable  log  be  determined,  and  the 
average  agreed  upon.  In  the  U.  S.  Forest  Service  the  custom  is  quite 
widely  adopted  that  logs  of  the  more  valuable  species  must  scale  33^ 
per  cent  of  their  sound  contents,  and  those  of  inferior  species,  50  per 
cent  to  be  merchantable. 

The  limits  of  merchantability  will  vary  widely  in  every  region,  unless  standard- 
ized as  is  the  case  in  the  Pacific  Northwest.  The  average  conditions  for  different 
regions  for  the  year  1917  are  indicated  below: 


Region 

Smallest  diameter. 
Inches 

Per  cent  of  sound 
scale  accepted 

Central,  hardwoods 

Southern  pine 

8  to  12 
7  to    8 

4  to    5 

5  to    8 

12 

6  to    9 

40  to  70,  average  60 

25  to  75,  average  50 

10  to  25,  average  20 

20  to  33,  average  25 

33§ 

30  to  40,  average  33 

White  pine.  Lake  States 

Idaho 

Southwest 

These  limits  apply  to  saw  logs.  For  pulpwood,  bolts  are  taken  down  to  between 
3  and  4  inches. 

Tests  on  spruce  logs  in  the  Adirondacks  showed  that  5-inch  logs  had  a  relative 
value  per  board  foot  of  56  per  cent  compared  with  11-inch  logs  at  100  per  cent, 
while  the  relative  value  of  20-inch  logs  was  126  per  cent.^ 


The  following  legal  decision  is  interesting: 
'A  merchantable  log  is  one  that  contains  sufficient  lumber  to  make  it  profitable 


GRADES  OF  LUMBER  AND  LOG  GRADES.  103 

87.  Grades  of  Lumber  and  Log  Grades.^  In  the  scaling  of  logs 
the  primary  object  is  to  determine  the  contents  in  board  feet  of  sound 
lumber  as  fixed  by  the  arbitrary  standard  of  the  log  rule,  based  solely 
on  dimensions  of  the  log,  and  modified  only  by  deductions  for  unsound 
lumber  (Chapter  VIII). 

But  as  shown  in  §  86,  the  purchaser  of  logs,  or  millman,  is  even 
more  concerned  with  the  value  per  1000  board  feet  of  the  scaled  contents. 
This  value  will  depend  directly  upon  the  amount,  by  per  cent  of  the 
total  scale,  of  each  of  several  standard  or  recognized  grades  of  lumber 
which  the  logs  will  yield  when  sawed,  and  the  resultant  weighted  aver- 
age value  which  this  gives  to  the  logs  as  a  whole. 

When  the  value  of  logs  must  be  determined  before  sawing,  as  is 
required  when  logs  are  purchased,  and  in  the  sale  of  standing  timber, 
the  relative  percentages  of  these  standard  grades  which  will  probably  be 
produced  from  these  logs  or  the  stands  in  question  must  be  estimated. 
It  is  evident  that  this  can  only  be  done  with  approximate  accuracy, 
since  a  mere  inspection  of  the  surface  and  ends  of  logs  will  not  reveal 
exactly  the  condition  of  the  interior  as  to  texture,  extent  of  defects 
and  per  cent  of  better  and  poorer  grades  present. 

In  scaling,  no  attempt  is  ever  made  to  divide  or  separate  the  total 
scale  of  a  log  as  indicated  by  the  log  rule,  into  the  amounts  or  per  cents 
of  different  grades  of  lumber  in  the  log.  Not  only  would  such  a  process 
be  too  expensive  and  time  consuming,  but  it  would  not  be  sufficiently 
exact  to  pay  for  the  effort  of  calculating  the  results  separately  log  by 
log  to  get  the  total  scale  for  each  grade  of  lumber. 

Instead,  a  system  has  been  substituted  of  establishing  so-called  log 
grades,  usually  three  in  number,  based  on  the  average  value  of  the  con- 
tents of  logs  as  determined  by  the  grades  of  lumber  which  they  contain. 
This  classification  permits  of  the  fixing  of  separate  prices  for  each  log 
grade.  The  total  scale  of  each  log  is  thrown  to  the  log  grade  in  which 
it  is  classed. 

Defects  in  lumber  (§  352-353)  may  be  separated  into  two  classes, 
unsound  defects  which  reduce  the  scale  of  the  log  as  described  above,  and 
sound  defects  which  reduce  the  grades  of  sound  lumber  but  do  not  reduce 
the  scale  of  the  log.  The  effect  of  the  first  class  is  to  render  the  log 
unmerchantable  if  in  excess  of  the  determined  limit;  the  effect  of  the 
second  class  is  to  lower  the  value  and  consequently  the  grade  of  the 

to  take  it  to  a  mill  and  have  it  sawed."  Gordon  vs.  Cleveland  Sawmill  Co.,  82 
N.  W.  Rep.  230,  Supreme  Court,  Michigan. 

This  ruling  is  based  on  the  millman 's  point  of  view,  which,  in  the  absence  of 
contract  specifications  protecting  the  logger,  will  always  determine  the  standard  of 
merchantability. ' 

*  Ref.  Appendix  A, 


104  LOG  SCALING  FOR  BOARD  MEASURE 

log.  The  fact  that,  with  increasing  prices  unsound  lumber  is  sold  and 
is  graded  does  not  change  the  standard  scaling  practice,  which  takes 
no  account  of  these  unsound  grades  and  excludes  them  from  the  scale. 
Such  lumber  merely  increases  the  amount  of  the  over-run. 

The  characteristic  sound  defects  are  tight  or  sound  knots,  pitch 
and  stain.  Sound  tight  knots  never  reduce  the  scale  unless  present  in 
such  size  and  quantity  as  to  cause  the  lumber  to  fall  apart  or  to  be 
rejected.  Stained  sap,  which  is  still  firm,  or  red  heart,  the  precursor 
of  red  rot,  are  scaled.  Pitch  is  usually  classed  as  a  sound  defect  for 
which  no  deduction  in  scale  is  made.  But  these  defects,  especially 
knots,  and  others  such  as  twisted  grain  and  wide  rings  do  serve  to  reduce 
the  grade  of  the  log.  The  presence  of  unsound  defects,  such  as  rot, 
shake  and  break,  does  not  reduce  the  grade  of  a  log,  provided  there  is 
sufl&cient  sound  lumber  remaining  to  permit  the  log  to  meet  the  mini- 
mum requirements  of  the  grade.  Since  the  purpose  of  log  grades 
is  to  establish  value,  log  grading  specifications  are  drawn  so  as  to  permit 
logs  of  the  same  average  value  to  be  placed  in  the  same  grade,  and  too 
detailed  specifications  are  avoided. 

By  thus  simplifying  the  classification  of  logs  by  grade,  the  total 
log  scale  is  easily  separated  into  log  grades,  and  any  variation  in  the 
average  quality  of  logs  within  the  grade  can  be  adjusted  in  the  price 
of  the  grade  (§359). 

For  any  given  region,  and  class  of  timber,  the  actual  average  per 
cents  of  different  standard  grades  of  lumber  contained  in  log  grades 
can  then  be  determined  by  mill-grade  or  mill-scale  studies  (§361). 
These  per  cents  can  then  be  applied  to  the  total  scale  for  each  log  grade 
with  far  greater  accuracy  than  could  be  attained  by  attempting  to  ana- 
lyze the  scale  of  each  log. 

Log  grades,  as  analj'zed  by  such  mill-grade  studies,  have  become  the 
basis  of  determining  the  stumpage  value  of  standing  timber  in  appraisals 
as  conducted  by  the  U.  S.  Forest  Service  (§  234). 

References 

Cost  of  Logging  Large  and  Small  Timber,  W.  W.  Ashe,  Forestry  Quarterly,  Vol.  XIV, 

1916,  p.  441. 
Cost  of  Logging  Small  Timber,  R.  D.  Forbes,  American  Lumberman,  Nov.   1.5, 

1919,  p.  52. 
Cost  of  Cutting  Large  and  Small  Timber,  W.  W.  Ashe  and  R.  C.  Hall,  Southern 

Lumberman,  Dec.  16,  1916. 
Inland  Empire  Sawing  and  Skidding  Studies  J.  W.  Girard,  Timbermau,  September, 

1920. 


CHAPTER  VIII 
THE  SCALING  OF  DEFECTIVE  LOGS 

88.  Deductions  from  Scale  for  Unsound  Defects.  No  deduction 
will  be  made  from  the  scale  of  a  log  unless  there  is  some  visible  indica- 
tion of  unsound  defect  such  as  will  reduce  the  quantity  of  sound  lumber 
that  can  be  sawed  from  the  log.  The  character  and  extent  of  the  deduc- 
tion to  be  made  for  the  indicated  defect  is  judged  by  the  scaler  based 
on  his  knowledge  of  the  given  species  and  region  and  his  experience  in 
observing  the  way  such  logs  open  up  in  sawing.  Defects  visible  at  the 
ends  of  the  log  give  a  basis  for  judging  the  remaining  contents.  When 
logs  must  be  scaled  as  they  lie  after  bucking,  with  ends  still  in  contact, 
as  sometimes  happens  with  overhead  skidder  operations,  it  is  difficult 
to  make  correct  deductions  for  defects. 

The  surface  of  the  log  offers  additional  evidence  of  unsound  defects, 
especially  the  character  of  the  knots.  Sound  knots  from  live  limbs 
do  not  affect  the  scale,  but  the  knots  of  dead  stubs,  if  they  show  rot, 
and  especially  the  presence  of  rotten  knot  holes,  with  exudations  of 
pitch,  indicate  the  presence  of  advanced  stages  of  rot,  which  a  little 
experience  in  the  mill  will  teach  the  scaler  to  allow  for  in  full  measure. 
The  mere  suspicion  that  logs  may  be  rotten  does  not  justify  deductions. 
When  timber  is  full  of  concealed  defects  with  no  surface  indications, 
the  method  of  deducting  a  given  per  cent  of  the  total  scale  may  be 
adopted  instead  of  attempting  to  reduce  the  scale  of  each  log  separately. 

89.  Methods  of  Making  Deductions.  There  are  four  methods  of 
reducing  the  scale  of  a  log;  by  length,  by  diameter,  by  diagram  or 
specific  quantity  of  lumber  and  by  a  per  cent  of  the  gross  scale.  The 
reduction  in  either  length  or  diameter  enables  the  scaler  to  read  the 
reduced  scale  from  his  stick  as  for  a  log  of  smaller  dimensions  and  is 
the  simplest  form  of  discount,  but  least  accurate  except  for  certain 
forms  of  defect. 

Reduction  in  Length.  A  redliction  in  length  gives  a  proportionate 
reduction  in  per  cent  of  total  contents.  The  per  cent  taken  depends 
on  the  relation  between  the  lengths  of  the  log  before  and  after  reduc- 
tion. For  a  16-foot  log,  12|  per  cent  of  the  total  scale  is  deducted 
for  each  2-foot  reduction.  This  deduction  becomes  10  per  cent  for 
a  20-foot  log  or  16|  per  cent  for  a  12-foot  log. 

Reduction  in  Diameter.  Reduction  in  diameter  is  not  a  satisfactory 
method  of  making  deductions  except  for  rotten  sap  found  on  logs  cut 

105 


106 


THE  SCALING  OF  DEFECTIVE  LOGS 


from  dead  trees,  or  for  surface  checking.  The  per  cent  of  the  scale 
thus  deducted  varies  for  every  diameter  of  log,  and  for  each  difference 
in  the  number  of  inches  subtracted.  This  method  of  deduction  should 
not  be  used  to  offset  some  interior  defect.  By  this  method,  a  20-inch 
log  by  Scribner's  Rule  would  give  the  following  deductions  from  scale 
in  per  cents.     For  other  diameters,  the  per  cents  would  differ: 


Reduction  of 

Per  cent  deduc- 

Per cent  loss 

diameter. 

tion  in  diameter 

in  scale 

Inches 

1 

5 

14.2 

2 

10 

25.0 

3 

15 

36.7 

4 

20 

42.8 

This  method  should  usually  be  rejected  in  favor  of  one  of  the  other 
three,  since  it  substitutes  a  guess  for  an  accurate  deduction. 

Use  of  Diagrams.  The  diagram  method  is  the  most  accurate  way 
of  computing  the  actual  number  of  board  feet  to  deduct  from  a  log 
for  a  given  defect.  The  cross  section  of  the  defective  area  is  blocked 
out  as  a  square  or  rectangle,  and  its  length  decided  upon,  whether 
running  completely  through  the  log  or  only  part  way  through.  For 
rules  based  on  j-inch  saw  kerf,  20  per  cent  of  the  cross  section  of  this 
area  must  be  deducted  to  get  the  net  volume  of  1-inch  boards  to  be 
deducted  from  the  scale. 


This  is  expressed  by  formula  when 
a  •  6  =  cross  sectional  area  in  inches, 
Z  =  length  of  defective  section  in  feet, 
y  =  cubic  contents  of  the  section  in  board  feet, 
a;  =  volume  of  section,  sawed  into  1-in.  boards,  \-m.  saw  kerf. 

ah-l 
12"* 


Then 


y- 


x=^y-.20y=.80y, 
or 

abl 

In  using  a  decimal  rule,  the  resultant  volume  is  rounded  off  to  the 
nearest  10  or  "decimal  value"  before  subtracting  it  from  the  log  scale. 


EFFECT  OF  MINIMUM  DIMENSIONS 


107 


As  a  substitute  for  this  calculation  and  to  save  time,  scalers  frequently 
approximate  the  amount  of  deduction  by  guess,  based  on  experience. 

Deducting  a  Per  Cent  of  Total  Scale.  The  method  of  deducting  a 
per  cent  of  the  total  scale,  as  distinguished  from  the  above  methods 
is  chiefly  applied  to  logs  containing  defects  within  the  log,  evidenced 
by  rotten  knots,  punk,  conks,  or  other  indications  and  whose  amount 
can  only  be  guessed  at  on  the  basis  of  experience  obtained  by  observing 
such  logs  as  they  are  sawed  in  a  mill. 

Influence  of  Log  Rule  on  Deductions  for  Defects.  A  log  rule  based  either  upon 
diagrams  of  1-inch  boards  and  definite  saw  kerf,  or  upon  a  formula  in  which  the 
proper  deductions  are  made  both  for  saw  kerf  and  slabbing,  permits  the  scaler 
to  make  deductions  from  the  scale  of  each  log  separately  on  the  basis  of  the  actual 
loss  in  1-inch  boards  from  that  portion  of  the  log  included  in  the  scale  or  log  rule. 
But  when  a  log  rule  is  inaccurate,  either  because  of  excessively  low  valuations, 
false  basis  as  in  converted  cubic  rules,  or  erroneous  values  in  formula;  as  in  Doyle 
or  Baxter  rules,  such  deductions  when  applied  to  logs  already  scaled  too  low  would 
take  from  the  scale  more  than  the  proper  per  cent  of  defect,  as  the  following  com- 
parison will  show. 

A  log  10  inches  in  diameter  and  16  feet  long,  which  will  saw  out  but  one-half 
of  its  scaled  contents  due  to  defect  (and  omitting  boards  sawed  from  outside  the 
cyHnder),  if  scaled  by  the  Scribner  and  Doyle  rules  respectively  will  give: 


Log  rule 

Sound 
scale. 

Feet  B.M. 

If  actual  loss  in 

sawed  content 

is 

Feet  B.M. 

Net  scale 

deducting  actual 

loss. 

Feet  B.M. 

Net  scale 

deducting  50  per 

cent  of  sound 

scale. 

Feet  B.M. 

Scribner 

Doyle 

54 
36 

27 
27 

27 
9 

27 
18 

If  the  log  is  sawed  by  a  mill  whose  output  coincides  with  the  Scribner  rule, 
the  over-run  on  a  sound  log  by  the  Doyle  rule  will  be  50  per  cent.  The  defective 
log  will  give  no  over-run  of  sound  lumber  by  Scribner.  But  if  27  feet,  or  one-half 
of  the  actual  sawed  contents,  is  deducted  from  the  scale  by  Doyle  rule  the  over-run 
will  be  18  feet,  which  is  200  per  cent  of  the  residual  scale  of  9  feet,  on  this  scale,  or 
four  times  as  great  on  the  defective  as  on  the  sound  log.  By  deducting  50  per  cent 
of  the  Doyle  scale  for  the  log,  the  over-run  remains  at  50  per  cent  of  the  scale  as 
for  sound  logs. 

Although  the  method  last  mentioned  gives  a  consistent  basis  for  making  deduc- 
tions in  rules  like  the  Doyle,  while  the  deduction  of  actual  loss  in  lumber  gives 
far  too  great  an  over-run,  it  is  evident  that  when  log  rules  are  used  capable  of  giv- 
ing a  scale  equaling  but  two-thirds  of  the  actual  contents,  the  tendency  will  be  to 
overlook  the  defects  in  scaling  unless  very  serious  and  numerous. 

90.  Efifect  of  Minimum  Dimensions  of  Merchantable  Boards  upon 
these  Deductions.     Log  rules  made  from  diagrams,  such  as  the  Scrib- 


108 


THE  SCALING  OF  DEFECTIME  LOGS 


ner  and  Spaulding  Rules,  were  based  on  a  minimum  width  of  board  of 
not  less  than  6  inches.  Present  practice  permits  the  sawing  of  4-inch 
strips.  In  deducting  for  defects  by  diagram,  the  latter  practice  is 
used,  and  portions  of  the  log  which  will  yield  4-inch  strips  are  scaled, 
provided  these  dimensions  lie  within  the  cyhn- 
der  and  do  not  include  taper.  A  rotten  butt 
with  6  inches  of  sound  wood  will  be  a  total  cull 
unless  the  inscribed  area  of  the  top  or  small 
end  of  the  log  contains  within  it  at  least  4  inches 
of  sound  wood. 

In  theory,  this  rule  must  be  modified  for 
deductions  which  take  the  form  of  slabs,  since 
the  original  diagram  or  scale  rejected  all  boards 
below  6  inches  in  width.  This  case  is  illustrated 
in  Fig.  14. 

The  minimum  length  of  merchantable  board 
should  first  be  standardized  or  agreed  on  in 
scaling.  Formerly  a  defect  at  one  end  of  a 
standard  log,  say  16  feet  long,  would  cull  the 
boards  affected  for  their  whole  length.  But 
where  boards  of  6-  or  8-foot  length  are  merchant- 
able, defects  which  leave  a  sound  length  equal 
to  these  minimum  boards  will  be  scaled  only 
for  the  actual  length  of  the  part  affected.  This 
rule  affects  the  results  for  nearly  all  forms  of 
defect.  Standard  minimum  lengths  are  im- 
portant in  scaling  crooked  logs.  The  standards 
now  in  use  for  saw  timber  vary  from  6  to  10 
feet  with  a  tendency  to  become  shorter. 

91.  Interior  Defects.  Unsound  defects  may 
be  classed  as  interior,  causing  waste  in  the  interior 
of  log;  side  or  exterior  defects,  causing  waste 
at  the  surface  or  outside;  and  defects  in  form, 
i.e.,  crook,  in  otherwise  sound  logs,  causing 
waste  in  sawing  straight  lumber.  Interior  defects  are  due  to  rot, 
shake,  seams  or  checks,  and  worm-holes.  The  defect  may  extend 
through  the  entire  log,  or  be  present  only  at  one  end.  It  may  be  cir- 
cular, and  regular  in  form,  or  irregular  in  form  and  extent. 

Center  Rot.  Circular  defects  in  the  form  of  either  rotten  or  hollow 
logs,  or  ring  shake,  if  they  extend  through  the  log,  will  be  measured  not 
at  the  small  but  at  the  large  end,  provided  the  log  is  not  over  16  feet 
long.  For  longer  logs  the  average  of  the  dimensions  at  butt  and  top  is 
taken.     If  only  one  end  is  affected,  the  diameter  of  the  defective  portion 


Fig.  14.— The  boards 
lost  are  measured  in- 
side the  smaller  in- 
scribed circle  repre- 
senting the  top  diam- 
eter. Three  boards 
are  affected,  4  inches, 
6  inches,  and  8  inches. 
The  6-inch  board  is 
deducted.  If  the  min- 
imum width  of  board 
utilized  is  4  inches,  a 
4-inch  strip  is  de- 
ducted from  the  8- inch 
board.  But  the  4-inch 
strip  on  the  margin 
was  not  scaled  in  the 
original  diagram  and 
should  be  omitted,  as 
constituting  over-run 
by  this  log  rule.  In 
ordinary  scaling  prac- 
tice this  distinction 
would  probably  be 
overlooked  as  too 
great  a  refinement. 


INTERIOR  DEFECTS 


109 


is  scaled  at  that  point  and  its  length  judged  by  experience  gained  in 
the  locality  by  the  butting  off  of  defective  logs;  e.g.,  a  log  20  inches  in 
diameter  at  the  top  end,  16  feet  long,  with  a  center  rot  measuring  3  inches 
at  top  and  15  inches  at  butt,  will  lose  the  equivalent  of  a  15-inch  butt  rot, 
and  not  a  3-inch  piece.     Should  the  log  be  20  feet  long,  the  average 


Fig.  15. — When  the  minimum  length  of  board  i.s  8  feet  this  log  will  scale  one- 
half  of  the  contents  of  a  16-foot  log.  But  with  a  minimum  length  board  of 
10  feet  the  log  according  to  common  practice  will  scale  nothing  and  be  culled. 

dimension  of  this  rot,  or  9  inches,  would  be  taken,  according  to  the 
above  arbitraiy  rule  of  scaling.  But  if  the  rot  is  present  only  in  the 
butt,  the  15-inch  measurement  would  apply  to  that  portion  of  the  log 
which  was  judged  to  be  affected,  provided  the  length  of  the  remaining 
sound  portion  equaled  the  minimum  length  of  board  prescribed. 


Fig.  16.— Center  rot  extending  through  log.     Effect  of  length  of  log  in  determining 
the  diameter  of  the  portion  to  be  culled. 

The  scale  of  this  log,  if  .sound,  would  be  280  board  feet,  Scribner  Decimal  C 
rule.  The  deduction  for  a  rotten  butt  15  inches  in  diameter  and  16  feet  long 
is  228  board  feet,  residue  52  board  feet  or  18.2  per  cent  of  sound  scale.  The 
log  is  a  cull.  The  average  w  dth  of  rim  left  to  be  scaled  after  projecting  the 
area  of  the  rotten  butt  upon  the  top  end,  is  2j  inches,  or  less  than  minimum 
width  of  board,  and  not  the  actual  measurement  of  sound  wood  at  either  the  top 
or  the  butt. 

If  this  log  is  20  feet  long,  i.e.,  longer  than  a  prescribed  maximum  length  of 
16  feet,  the  diameter  of  this  rot  is  averaged  at  9  inches.  The  20-foot  log,  20  inches 
in  diameter  scales  .350  board  feet.  The  9-Lnch  measurement  Is  applied  to  the 
entire  length  of  log,  and  the  deduction  is  111  board  feet.  The  net  scale  is  240 
board  feet,  or  68.6  per  cent  of  total  sound  scale.     Such  a  log  is  merchantable. 


110  THE  SCALING  OF  DEFECTIVE  LOGS 

It  is  evident  that  such  niles  for  deductions  are  arbitrary.  The  16-foot  log 
would  yield  considerable  short  lumber  and  is  under-scaled  by  the  rule.  Where 
short-length  boards  are  commonly  used,  logs  over  12  feet  long  might  be  scaled 
on  the  basis  of  average  diameter  of  rot,  to  correct  this  tendency.  But  it  is  better 
to  adopt  arbitrary  rules  than  to  have  no  methodical  plan  for  scaling  defects. 

The  cull  required  by  the  presence  of  an  unsound  or  hollow  circular  core  is  pro- 
portional to  the  diameter  of  the  core,  and  independent  of  that  of  the  log.  By  the 
diagram  method,  the  deduction  for  center  rot  would  be  found  by  determining  the 
board-foot  contents  of  a  square  with  the  diameter  of  the  rotten  core  and  of  the 
length  indicated  as  above.  This  method  when  checked  against  actual  sawed 
contents  gives  too  smal  a  deduction  for  cores  up  to  9  inches,  and  above  that,  too 
large,  the  relation  varying  from  87  per  cent  for  a  6-inch  core  to  110  per  cent  for 
one  24  inches  in  width.  The  actual  amounts  of  sawed  lumber  lost  for  cores  of 
each  diameter  are  accurately  expressed  by  a  formula  developed  by  H.  D.  Tiemann, 
which  reads, 

L 

Contents  of  core  =  f  (D-l-l)^— , 

i.e.,  add  1  inch  to  diameter  of  core,  square,  and  deduct  -J,  converting  the  remainder 
into  board  feet  by  the  factor 

Length  in  feet 
12  ■ 

This  formula  calls  for  four-fifths  of  the  sawed  board-foot  contents  of  a  square 
1  inch  larger  than  the  core  (0.66Z)2  =  82.5  per  cent  or  f  of  O.SOZ)^)  instead  of  the 
full  sawed  board-foot  contents  of  a  square  of  the  same  size  as  the  core. 

Several  rules  of  thumb  exist  for  determining  the  deduction  for  center  rot,  none 
of  which  are  absolutely  correct,  and  some  very  inaccurate. 

Exam-pie.  In  a  12-foot  log  20  inches  in  diameter  with  a  rotten  center  6  inches 
in  diameter  at  large  end  and  running  through  the  log  and  a  sound  scale  of  210 
board  feet,  the  correct  deduction  is  33  board  feet  which  is  1{T^)\^.  The  following 
rules  of  thumb  can  be  cited,  using  Scribner  Decimal  C  rule. 

1.  Deduct  the  diameter  of  core  from  that  of  log,  and  scale  as  a  log.  This 
gives  a  cull  of  90  board  feet. 

2  Deduct  the  scale  of  a  log  of  same  diameter  as  the  core.  This  gives  a  cull 
of  10  board  feet. 

3.  Scale  out  a  log  with  diameter  3  inches  larger  than  the  core.  This  would  give 
30  board  feet,  but  the  rule  gives  inconsistent  results  for  larger  and  smaller  cores. 

4.  Scale  out  the  contents  of  a  square  timber  whose  side  is  the  diagonal  of  the 
square  of  the  diameter  of  the  core.  This  would  be  lAD'^  and  gives  70  board  feet. 
If  reduced  by  20  per  cent  for  saw  kerf,  and  applied  to  small  end  of  core,  it  would 
come  closer  by  balancing  errors.     None  of  these  rules  is  accurate  or  consistent. 

Butt  Rot,  Termed  also  Ground  or  Stump  Rot.  Butt  rot  enters  the 
butt  log  from  the  ground,  and  usually  extends  but  a  short  distance  into 
the  log.  Its  full  diameter  should  seldom  be  applied  to  the  entire  log, 
even  if  rot  appears  at  the  top  end. 

The  diameter  of  the  rotten  butt  must  first  be  compared  with  the 
scaling  diameter  as  determined  by  the  top  end  of  log  (§81).  If  the  rim 
gf  sound  wood  lying  within  this  inscribed  circle  is  wide  enough  for  boards, 


INTERIOR  DEFECTS  111 

or  if  the  volume  of  the  rotten  core,     '    "    shows  a  smaller  cull  than  the 

15 

sound  scale  of  that  part  of  the  log,  deduction  by  diagram  of  the  squared 

core  is  made  (preferably  by  Tiemann's  formula)  to  a  length  judged  to 

include  the  rotten  portion. 

Example.  A  log  12  feet  long  and  20  inches  in  diameter  at  top  end  has  a  rotten 
butt  6  feet  long,  the  rotten  core  measuring  17  inches  across.  Although  the  butt 
measures  25  inches,  leaving  a  4-inch  rim  of  sound  wood,  the  inscribed  circle  repre- 
senting the  top  of  the  log  is  only  20  inches,  and  the  butt  is  a  cull.  This  observation 
is  borne  out  by  applying  Tiemann's  formula: 

Scale  of  12-foot  log,  210  board  feet, 

Scale  of  6-foot  length,  105  board  feet. 

Cull  for  butt  rot,  §(182)3^  =  108  board  feet, 

or  more  than  the  sound  scale  of  butt.  This  deduction  is  not  applied  to  the  whole 
log  but  only  to  the  butt. 

The  scale  of  the  log  is  then  105  board  feet  on  the  basis  that  the  upper  half  is 
sound. 

If  this  core  should  measure  13  inches, 

Cull  for  butt  rot  §(142)^%- =  65  board  feet. 

The  scale  of  the  log  is  then  210—65  =  145  board  feet. 

But  if  the  minimum  board  length  should  be  over  6  feet,  the  first  log  will  be 
culled  entirely,  and  from  the  second  log,  a  cull  of  f(14'-)J-|^  or  131  board  feet 
Scribner  Decimal  C  is  deducted,  leaving  a  scale  of  but  79  board  feet,  or  37.6  per 
cent  of  the  merchantable  contents. 

Shake.  Shake  is  a  mechanical  defect  caused  by  wind.  The  annual 
rings  have  separated  at  one  or  more  points,  giving  a  circular  or  ring  crack, 
and  the  board  falls  to  pieces  when  sawed.  This  flaw  is  found  at  the  butts 
of  such  species  as  hemlock,  and  is  seldom  more  than  a  few  feet  in  length 
although  entire  logs  may  be  shaky.  Lumber  sawed  from  shaky  por- 
tions of  logs  is  often  worthless. 

A  single  circular  shake  is  scaled  out  in  the  same  manner  as  butt  rot 
except  that  the  contents  of  a  smaller  sound  core  lying  within  the  shake 
may  be  added  or  restored  to  the  scale.  The  diameter  of  this  interior 
core  should  be  measured  at  the  small  end  of  the  culled  section  if  it  extends 
through  the  log,  while  the  diameter  of  the  culled  portion  is  measured 
at  the  butt  or  large  end.  In  short  sections  whose  length  is  guessed  at, 
a  proportionate  reduction  from  butt  diameter  is  made  in  scaling  the 
sound  core.  This  same  method  is  used  to  scale  out  pitch  rings,  where 
this  is  deemed  necessary.  In  most  cases  pitch  is  considered  a  sound 
defect  (§  82).  Where  shake  shows  in  several  rings,  the  entire  shaky 
portion  of  the  log  is  butted,  by  shortening  its  length. 


112 


THE  SCALING  OF  DEFECTIVE  LOGS 


Seams,  Heart  Checks,  Frost  Cracks  or  Pitch  Sea7ns.  Seams  are  cracks 
penetrating  the  log  from  the  surface.  They  have  the  same  effect  as 
shake,  in  causing  boards  to  fall  apart,  and  the  deduction  is  made  by 
enclosing  the  seam  in  a  timber  of  required  dimensions  to  remove  it. 
Twisted  grain,  causing  seams  to  take  a 
spiral  form,  results  in  ruining  either  the 
entire  log  or  a  large  per  cent  of  its  volume. 
The  deduction  must  include  the  entire 
seam  in  a  squared  timber.  The  width  of 
the  plank  deducted  should  not  include  the 
portion  which  would  be  slabbed  in  sawing. 
Method  of  deducting  for  a  twisted  seam 
or  check:  The  wedge  enclosing  the  seam  is 
scaled  as  a  per  cent  of  total  scale  of  cylinder 
proportional  to  areas  of  cross  sections. 
Fig.  17.— Method  of  deduction  g^^  ^^  ^^^^  jogg^  of  i^^ger  diameters,  the 
for  a  seam,  or  a  heart  check.        ,.  ,     ,  •       tt^-        10    •  + 

,     , ,  entire  segment  shown   m   b  ig.    18   is   not 

lost,  if  short  boards  of  scaling  length  can 
be  sawed  from  the  butt  and  top  portions 
of  the  segment  respectively.     This  saving 

will  not  amount  to  more  than  one-third  of  the  total  deduction. 

Worm  Holes.     If  the  size  and  extent  of  worm  holes  is  not  sufficient  to 

cull  the  boards,  their  presence  will  not  cause  a  loss  in  scaling.     It  is 

difficult  to  judge  the  extent  of  damage  from  worm  holes,  except  by  local 

experience  in  observing  the  sawing  of  logs. 


The  width    of    plank 
exchide  both  the  taper  of  log 
and  the  slab,  on  the  small  end. 


Fig.  18. 


-Position  of  twisted  seam  at  butt,  and  at  top  of  same  log,  and  resultant 
sector  deducted  in  scaUng. 


Rot  Entering  from  Knots.  The  most  common  forms  of  rot  enter 
the  tree  through  dead  limbs,  stubs  or  knots,  or  through  wounds  or  abra- 
sions, which  by  penetrating  or  interrupting  the  layer  of  bark  and  live 
sapwood,  expose  the  heartwood  to  infection.  From  these  points  of 
infection  the  fungus  spreads  through  the  heartwood  both  upwards  and 


EXTERIOR  DEFECTS 


113 


downwards.  The  form  which  it  takes  depends  upon  the  species  of 
fungus,  and  of  trees  attacked.  The  unsound  portion  is  surrounded  by 
a  stained  portion  which  is  yet  sound.  The  area  of  the  rot  increases 
with  age  of  tree  and  time  elapsing  since  the  infection  took  place. 

In  deducting  for  rot,  the  amount  of  the  loss  depends  upon  the  location 
of  the  point  of  infection,  usually  a  rotten  knot.  Stain  which  shows  at 
one  end  of  a  log  requires  no  deduction  if  the  rot  of  which  it  is  an  evidence 
lies  in  the  adjoining  log  as  cut  from  the  bole.  On  the  other  hand,  two 
or  more  rotten  knots  in  a  log,  with  stain  showing,  means  a  heavy  dis- 
count and  a  possible  cull.  Sawyers  are  accustomed  to  leave  such  logs 
in  the  woods  and  even  in  the  tree  without  sawing  them.  Rot  from  a 
single  point  of  infection  will  extend 
from  2  feet  to  as  much  as  10  or  1.5 
feet  in  either  direction.  It  is  deepest 
and  most  complete  at  the  point  of  entry, 
tapering  out  with  increasing  distance 
from  this  point.  Rot  of  this  character 
is  so  irregular  that  experience  is  re- 
quired in  observing  such  logs  sawed 
before  proper  deductions  can  be  made 
by  scalers. 

In  deducting  for  interior  rot,  the 
probable  extent  and  shape  of  the  un- 
sound portion  therefore  depends  upon 
the  appearance  of  the  ends  taken  in 
connection  with  unschund  knots.  The 
only  portions  of  the  log  which  can  be 
scaled  are  those  which  will  produce 
sound    boards    having    the    minimum 

length  and  width  prescribed  in  the  rules  for  scaling.  The  deduction 
will  take  the  form  of  a  per  cent  of  the  sound  scale.  Diagrams  are  some- 
times of  assistance,  but  in  logs  containing  rotten  knots  the  extent  of 
rot  is  usually  greater  than  revealed  at  the  cross  section.  The  appa- 
rent cull  must  ordinarily  be  increased,  from  25  to  100  per  cent. 
Since  deduction  of  length  is  equivalent  to  a  percentage  reduction  of 
scale,  this  method  is  frequently  used. 

Peck  in  cypress,  and  the  rot  found  in  Incense  cedar  gives  no 
external  indications,  and  is  not  always  revealed  on  the  cut  ends  of  logs. 
This  condition  tends  to  the  substitution  of  a  straight  percentage  deduc- 
tion from  the  total  scale  instead  of  reducing  the  scale  of  individual 
logs  for  defects. 

92.  Exterior  Defects.  Exterior  defects,  on  the  sides  of  logs,  include 
unsound  sap,  surface  checks,  cat  faces,  fire  scars,  and  scars  caused  by 


Fig.  19. — Log  A  is  infected  at 
the  point  X  and  is  a  cull.  At 
the  lower  end  no  rot  shows, 
but  stain  only.  This  stain 
therefore  shows  at  the  upper 
end  of  log  B,  but  causes  no 
deduction  for  cull. 


114 


THE  SCALING  OF  DEFECTIVE  LOGS 


mechanical  injuries  such  as  lightning  or  falling  timber.  Irregular 
butt  rot,  appearing  as  a  small  patch  on  one  side,  or  rot  from  knots 
which  is  local  in  extent,  can  sometimes  be  scaled  by  the  methods  used 
to  scale  side  defects. 

Exterior  defects,  especially  at  the  butts  of  logs,  may  fall  entirely 
outside  the  inscribed  circle  representing  the  top  or  scaling  diameter,  in 
which  case  they  cause  no  deduction  in  scale.     With  defects  which 

penetrate  deeper  a  further 
portion  is  included  in  the 
slab  allowed  in  sawing, 
within  this  circle. 

Where  the  defect  ex- 
tends })ut  a  few  feet  in 
length,  as  for  instance  a 
fu'e  scar  at  the  butt  of  a 
log,  the  deduction  is  con- 
fined to  that  portion  of  the 
length  of  the  small  c^-linder 
whose  contents  is  scaled, 
which  is  affected  by  the 
defect.  The  amount  to 
subtract  may  be  found  in 
one  of  two  ways;  by  dia- 
gram of  the  slab  affected  by 
the  defect,  or  by  culling  a 
per  cent  of  the  volume  of 
the  log. 

Deductions  by  Slabs. 
The  dimensions  of  the  por- 
tion to  be  deducted  as  a 
slab  are  not  those  of  the 
piece  actually  slabbed  from 
the  butt,  but  only  the  depth  of  the  portion  lying  within  the  inscribed 
circle  of  the  small  end  of  log.  From  this  again  there  is  subtracted  an 
additional  amount  for  slabbing,  shown  in  Fig.  20.  The  remaining 
depth,  multiplied  by  the  average  width  of  the  inscribed  slab,  gives 
the  area  of  the  cross-section  whose  length  will  be  that  of  the  defect, 
a-b-l 
iX" 


Fig.  20. — Effect  of  fire  scar  at  butt,  on  deduc- 
tions from  scale. 


and  volume. 


In  the  above  figure,  the  fire  scar  on  the  butt  log  is  8  inchas  deep,  but  only 
5  inches  of  this  is  within  the  inscribed  scaling  dimensions.  Of  this  1;  inches  is 
slab,  giving  3f  inches  for  lumber.  The  widths  of  the  boards  lost  are  10  inches, 
14  inches  and  18  inches.     The  average  width  of  the  rectangle  is  14  inches.     A 


EXTERIOR  DEFECTS 


115 


diagram  measuring  4  by  14  inches,  whose  length  equals  that  of  the  fire  scar  lying 
within  the  inscribed  cylinder,  gives  the  deductions.  As  the  scar  gets  shallower, 
the  length  lying  within  this  cylinder  is  less  than  its  total  length.  Tables  could 
be  worked  up  by  a  scaler  to  express  the  board-foot  contents  that  could  be  cut  out 
of  sltibs  of  given  thickness  on  circles  (inscribed)  of  given  diameter  for  a  standard 
length  of  log,  allowing  a  minimum  width  of  board  equivalent  to  that  used  by  the 
log  rule  (§  67)      But  ocular  methods  are  almost  equally  efficient  after  practice. 

Deduction  by  Sectors.  Side  defects  extending  deeply  into  the  log 
(Fig.  21)  cannot  be  slabbed  off  and  are  not  easy  to  express  by  diagrams. 
By  enclosing  them  in  V-shaped 
areas  representing  sectors  of  a 
circle,  an  idea  may  be  obtained 
of  their  extent.  This  method 
may  be  used  for  any  defect 
occurring  wholly  on  one  side 
of  the  geometric  center  of  a 
log  and  which  is  more  accu- 
rately enclosed  by  a  sector 
than  a  slab. 


Fig.  21.— Method  of  deducting  from  scale 
by  means  of  sectors  enclosing  defective 
portion  of  log. 


The  cull  per  cent  for  the  portion  of  the  log  affected  is  roughly  equal  to  the 
ratio  between  the  area  of  the  circle  and  of  the  sector.  This  rule  is  exact  for  the 
ratio  I,  and  nearly  so  for  smallei-  or  larger  sectors.  The  error  in  applying  the  rule 
will  average  less  than  3  per  cent  of  the  volume  of  the  log,  and  if  the  defect  is  con- 
fined to  a  short  length,  thi^  error  is  proportionately  less  for  the  whole  log  (from  inves- 
tigations of  H.  D.  Tiemann);  e.g.,  a  sector  equaling  one-fourth  of  a  circle  calls 
for  25  pel  cent  cull.  Cull  tables  may  be  made  for  this  deduction,  but  it  is  equally 
convenient  to  apply  the  percentage  directly  to  the  scale.  This  latter  method 
adjusts  the  cull  factor  to  any  log  rule  (§  89). 

Other  Surface  Defects.  Stained  sap  is  scaled  as  sound.  When 
unsound  or  decayed,  the  scaling  diameter  is  taken  inside  the  sap. 
Surface  checks  caused  by  prolonged  weathering  as  in  the  case  of  dead 
timber,  or  by  neglect  or  exposure  of  logs,  must  be  scaled  out  in  the  same 
manner  as  sap.  Cat  faces,  as  defined  for  cedar  poles  in  the  Lake  States, 
are  defects  on  the  sides  of  logs  caused  by  some  mechanical  injury  to 
the  bark  which  has  caused  a  wound.  A  cat  face  may  be  accompanied 
by  rot,  or  be  merely  a  dry  face,  not  healed  over  and  forming  an  indenta- 
tion in  the  bole.  According  to  its  shape  and  depth,  a  cat  face  is  deducted 
either  as  a  slab  or  a  segment,  of  proper  length.  The  term  cat  face  is 
also  applied  to  a  fire  scar  at  the  butt  of  a  tree,  usually  partly  healed 
over,  which  may  be  sound,  rotten  or  wormy.  Any  surface  defect  partly 
healed  over,  on  the  bole,  caused  by  either  fire  or  mechanical  injury, 
whether  at  the  butt  or  on  the  bole,  may  properly  be  called  a  cat  face. 
Lightning  scars,  even  when  the  tree  is  not  shattered  or  killed,  usually 


116 


THE  SCALING  OF  DEFECTIVE  LOGS 


form  a  dead  streak  causing  a  surface  defect,  sometimes  of  considerable 
proportions. 

Breakage.  The  deduction  for  splits  and  breakage  caused  by  felling 
is  made  either  by  slabbing  or  by  shortening  the  log  length,  to  remove 
the  portion  ruined  by  the  breakage.  Where  this  waste  is  avoidable, 
owners  stipulate  that  it  shall  be  scaled  as  sound,  but  purchasers  of  logs 
insist  on  the  deduction.  In  the  Pacific  Coast  States,  breakage  may 
exceed  25  per  cent  of  the  scale. 

93.  Crook  or  Sweep.  Crook  may  be  defined  as  a  rather  abrupt 
bend  in  the  log  at  a  given  point,  while  sweep  is  a  more  gradual  bend 
extending  over  a  considerable  length.  Crooks  occurring  near  the  ends 
of  a  log  may  be  allowed  for  in  scahng  by  shortening  the  scaling  length. 
With  gradual  sweep  affecting  the  form  of  the  log  as  a  whole,  a  different 
deduction  is  necessary.  The  effect  of  sweep  or  crook  upon  the  scaled 
contents  of  the  log  (§  52)  depends  directly  upon  the  minimum  length 
of  boards  utilized  and  scaled,  or  upon  the  acceptance  of  fixed  minimum 
scahng  lengths  for  the  logs.  If  it  is  assumed  that  the  minimum  board 
governs  the  scale,  deductions  for  crook  or  sweep  will  seldom  be  made, 
since  almost  complete  utilization  can  be  obtained  of  sound  crooked 
logs  by  the  box  factory.  But  if  the  scale  of  a  log  is  based  on  the  output 
of  boards  of  the  standard  scaling  lengths  into  which  the  logs  are  cut, 
and  short  lengths  cannot  be  utilized,  crook  or  sweep  will  cause  deduc- 
tions in  scale  when  it  exceeds  the  normal  minimum  permitted. 

When  logs  crook  in  but  one  plane,  the  loss  in  sawed  kimber  is  proportional 
to  the  relation  which  the  total  deflection  or  crook  bears  to  the  diameter  of  the  log, 
and  does  not  depend  on  the  number  of  inches  of  crook  independent  of  size  of  log; 
e.g.,  for  a  12-inch  log  a  6-inch  crook  is  50  per  cent  of  the  diameter  but  for  a  24-inch 
log,  a  6-inch  crook  is  but  25  per  cent  of  the  diameter,  and  a  50  per  cent  crook 
indicates  a  crook  of  12  inches. 

By  diagram  checks,  and  sawing,  the  per  cent  of  waste  due  to  sweep  for  a  given 
total  number  of  inches  of  crook  per  log  is  found  to  be  independent  of  the  length 
of  log,  and  to  show  the  following  results: 

TABLE  XVIII 

Deductions  for  Crook  and  Sweep 


Sweep  in  terms  of 

diameter  of  log. 

Per  cent 

Waste  in  terms  of 
scale  of  log. 
Scribner  rule 

8i  (or  ,\) 
16!  (or  i) 
25    (ori) 
50    (or^) 

lU 

22i 
66! 

CHECK-SCALING 


117 


From  these  results  a  rule  of  thumb  may  be  suggested  as  follows:  Add  one-third 
to  the  per  cent  of  sweep  as  expressed  in  terms  of  diameter  of  log  to  obtain  the 
per  cent  of  cull;  e.g.,  a  log  16  feet  long  and  16  inches  in  diameter  scales  159  board 
feet.  With  a  sweep  of  4  inches  or  25  per  cent,  deduct  |X25  =  33§  per  cent  or 
53  board  feet;  scale,  106  board  feet.  With  a  sweep  of  8  inches,  deduct  f  X50  =  66f 
per  cent,  or  106  board  feet;  scale  53  board  feet.  With  a  sweep  of  2  inches  no 
deduction  would  be  made,  since  this  is  merely  the  normal  crook. 

Logs  which  crook  in  two  or  more  planes  must  be  culled  far  more  heavily  than 
when  the  axis  lies  in  a  single  plane.  For  a  given  per  cent  of  crook  the  scale  is 
roughly  proportional  to  the  square  of  the  per  cent  scaled  by  the  deductions  set 
forth  above;  e.g.,  a  log  which  scales  50  per  cent  or  one-half  if  crooked  in  one  plane 
will,  if  crooked  in  two  planes,  scale  (l)^  or  25  per  cent  of  its  contents. 

94.  Check-scaling.  By  check-scaling  is  meant  the  re-scahng  of 
selected  logs  or  of  a  portion  of  a  total  run  of  logs,  in  order  to  determine 
the  relative  accuracy  of  the  original  scale,  check  the  methods  used  by 
the  scaler  and  detect  and  correct  errors  in  these  methods.  A  re-scale 
requires  the  remeasurement  of  all  of  the  logs.  The  necessity  for  a 
re-scale  is  usually  revealed  by  a  check-scale. 

Where  a  number  of  scalers  are  employed,  check  scaling  becomes 
necessary  in  order  to  maintain  uniformity  in  scaling  practice.  No 
matter  how  carefully  the  standard  of  scaling  practice  is  set  forth  in 
printed  instructions  which  cover  not  only  the  "  scale  "  with  respect 
to  diameters,  length,  taper  and  trimming  allowance,  but  rules  for  deduc- 
tions for  defects,  individual  scalers  tend  to  vary  from  this  standard 
through  habit  or  carelessness  and  inexperienced  men  are  slow  to  acquire 
accuracy,  especially  in  scaling  defective  logs. 

A  check  scale  should  be  made  by  the  most  ex-perienced  man  available  as  fre- 
quently as  possible,  but  usually  at  from  three  to  six  months'  intervals.  Where 
logs  are  numbered,  the  original  scale  should  show  the  deauctions  made  from  the 
full  scale  of  each  log  ( §  85) .  The  check  scale  can  be  made  at  random  on  as  many 
logs  as  there  is  time  for.  The  total  scale  for  the  logs  checked  is  then  compared 
with  the  original  scale  of  the  identical  logs,  keeping  separate  the  sound  and  the 
defective  logs.  Using  the  check  scale  as  100  per  cent,  the  per  cent  of  error  in 
scaling  is  computed  according  to  the  following  plan: 


Sound  logs 


Scale  by 


No.  of  logs 


Scale  per  cent 
+  or  - 


Defective  logs 


No.  of  logs 


Scale  per  cent 
+  or  — 


Total 


No.  of 
logs 


Scale  per  cent 
+  or  — 


James  Smith 
Check  scale  by 
John  Kipp 


The  standard  of  accuracy  in  the  U.  S.  Forest  Service  for  check  scaling  requires 


118  THE  SCALING  OF  DEFECTIVE  LOGS 

that  the  scale  should  not  vary  from  the  check  scale  by  more  than  the  following 
per  cents: 

For  sound  logs,  within  1  per  cent; 
For  logs  up  to  10  per  cent  defective,  within  2  per  Cent; 
On  logs  11  to  20  per  cent  defective,  within  3  per  cent; 
On  logs  over  20  per  cent  defective,  within  5  per  cent. 

Check  scales  are  made  usually  for  the  purpose  of  correcting  the  scaler,  but  not 
as  a  basis  of  altering  the  scale.  Only  where  the  original  scale  is  shown  to  be 
decidedly  in  error  so  as  to  work  an  injustice  on  the  purchaser  (or  seller)  are  logs 
ever  re-scaled. 

Personnel.  Scalers  should  never  be  reprimanded  in  general  terms  for  scaling 
too  close  or  too  high.  The  result  is  usually  a  worse  error  in  the  opposite  direction. 
Instead,  the  scale  should  be  checked  by  individual  logs  to  discover  the  sources  of 
error  and  the  scaling  practice  corrected  in  detail.  The  fault  may  lie  in  some 
specific  practice  such  as  an  erroneous  method  of  obtaining  diameters  or  in  allowing 
for  certain  common  defects. 

Mill-scale  studies  do  not  furnish  an  adequate  or  satisfactory  check 
on  scaling,  but  serve  merely  to  determine  the  over-run.  The  scale, 
if  in  error,  must  be  corrected  by  re-scaling  the  logs,  not  by  measuring 
the  lumber  (§  74).  Such  studies  do  furnish  an  indication  of  the  scale 
of  defective  logs,  where  the  scaler's  judgment  may  be  in  error,  but  an 
exact  check  is  impossible,  as  it  would  require  the  rejection  of  boards 
sawed  from  the  taper,  which  is  not  practicable. 

95.  Scaling  from  the  Stump.  Where  timber  has  been  cut  in  tres- 
pass and  the  logs  removed,  the  evidence  remaining  is  the  stump,  the 
indentation  on  the  ground  where  the  butt  struck  in  falling,  the  sawdust 
where  the  cuts  were  made  in  sawing  into  log  lengths,  and  the  top, 
giving  the  upper  diameter.  The  length  of  the  tree  can  then  be  meas- 
ured, and  occasionally,  that  of  each  log  sawed.  The  total  difference 
in  diameter  between  top  and  butt  is  distributed  according  to  the  accepted 
local  customs  for  scaling  long  logs.  This  gives  the  scaling  diameter 
and  length  of  each  log  in  the  tree.  Specific  deduction  for  defect  can 
be  made  only  for  stump  rot,  since  this  is  revealed  by  the  stump  and 
the  average  deduction  for  rot  having  the  character  and  extent  of  that 
shown  can  be  made  from  the  butt  log.  Further  deductions  if  made 
must  be  based  on  the  average  per  cent  of  cull  for  timber  of  the  given 
species  and  character. 

When  tops  are  removed,  burned  or  otherwise  rendered  indistinguish- 
able, neither  the  top  diameter  nor  the  length  of  the  tree  can  be  judged. 
Merchantable  length  must  then  be  based  upon  the  heights  of  trees  in 
the  vicinity,  and  volumes  taken  from  volume  tables  (§121)  for  trees 
of  given  diameter  and  height.  A  table  of  stump  tapers  (§  168)  must 
be  used  to  express  the  diameter  of  the  stump  in  terms  of  diameter  4| 
feet  from  ground  (§  134). 


THE  SCALER  119 

96.  The  Scaler.  A  scaler  with  no  other  duties  can  number  and  scale  500  logs 
per  day,  running  10  logs  per  1000'  board  feet  or  .50,000  board  feet  at  a  cost  of  about 
10  cents  per  1000  board  feet,  based  on  wages  and  subsistence  of  $12.5.00  per  month. 
This  average  can  be  exceeded  but  is  apt  to  be  reduced  in  quantity  by  time  lost  in 
travel  to  and  from  the  logs,  scaling  in  the  woods,  or  an  insufficient  number  of  logs 
on  hand  daily  to  occupy  the  full  time  of  the  scaler.  Often  these  logs  must  be 
scaled  daily  and  cannot  accumulate,  because  of  insufficient  room  on  the  skids, 
thus  keeping  a  scaler  in  constant  attendance.  A  scaler  thus  employed  is  often 
given  other  duties  such  as  inspecting  the  work  of  the  saw  crews.  National  Forest 
Scalers  supervise  the  disposal  of  brush,  closeness  of  utihzation  and  the  marking 
of  timber  for  felling.  This  reduces  the  average  cost  of  scahng  to  approximately 
the  basis  mentioned. 

Commercial  scahng  by  private  companies  is  done  far  more  rapidly  and  cheaply 
because  of  the  elimination  of  numbering,  and  by  careless  or  indifferent  methods 
of  measuring  lengths  and  deducting  for  defects.  A  scale  of  1000  to  1.500  pieces, 
and  100,000  board  feet  per  day  and  a  cost  of  5  cents  per  1000  board  feet  or  less 
is  not  unusual  on  large  operations. 

So  important  is  an  accurate  scale  that  the  scaler  must  be  given  every  facility 
to  obtain  the  measurement  with  the  least  trouble  and  greatest  certainty.  This 
usually  means  providing  a  sufficient  force  of  scalers  so  that  thej^  may  be  on  hand 
at  the  most  favorable  time,  or  constantly.  When  on  accoimt  of  small  or  scattered 
operations  the  logs  must  accumulate  the  scaler  is  handicapped  in  various  ways. 
Large  and  high  rollways  require  two  men,  one  on  each  side,  to  get  the  length,  even 
approximately,  and  to  distinguish  top  from  butt,  of  each  log.  Logs  landed  on  ice 
will  in  time  by  their  weight  cause  cracks  and  flooding,  and  small  logs  are  frozen  in. 
Whole  rollways  may  break  through  the  ice  and  become  partially  submerged. 
Snow  covers  and  buries  the  piles,  and  logs  are  overlooked.  Logs  may  be  rolled 
dowTi  steep  banks  and  lie  in  such  confusion  that  scahng  is  difficult  and  dangerous. 
Steam  skidders  pile  logs  in  huge  heaps  impossible  to  scale  at  all  until  loaded  on 
cars.  The  inabUity  of  the  scaler  to  cover  his  route  at  frequent  mterv^als  encourages 
careless  sawing,  timber  steaUng  and  poor  scaling.  Contracts  should  specify  that 
logs  must  be  piled  or  skidded  in  such  a  manner  that  accurate  scaling  is  possible. 

Legal  Status  of  Scaler.  "A  scaler  whose  services  are  agreed  upon  by  both  parties 
to  a  contract  or  sale,  is  the  sole  arbiter  between  these  parties  in  determining  the 
amount  of  the  scale.  But  if  one  party  furnishes  the  scaler  without  the  ex-pressed 
consent  or  agreement  of  the  other,  his  scale  may  be  appealed  from."  Frisco 
Lumber  Co.  vs.  Hodge,  U.  S.  Circuit  Court  of  Appeals,  218  Fed.  Rep.  778. 

"A  scaler  furnished  by  the  defendant  and  boarded  by  plaintiff  would  be  one 
mutually  agreed  upon,  and- they  must  abide  by  his  decisions."  Connecticut  Valley 
Lumber  Co.  vs.  Stone,  U.  S.  Circuit  Court  of  Appeals,  212  Fed.  Rep.  713. 

"Binding  in  the  absence  of  fraud  or  mathematical  mistakes."  Hutchins  vs. 
Merrill,  Supreme  Court  Maine,  84  Atlantic  412. 

"Scale  made  by  scaler  appointed  by  defendant  not  binding  in  absence  of  some 
stipulation  to  that  effect  in  contract."  Owen  vs.  J.  Neils  Lumber  Co.,  Supreme 
Court  of  Minnesota,  145  Northwestern  402  (1914). 

"Scaler  who  performed  his  duty  fairly  and  honestly,  though  neghgently,  could- 
not  be  held  liable  for  dlscrepancj^  between  the  amount  he  scaled  and  the  amount 
of  logs  delivered,  as  permitting  such  action  would  destroy  independence  of  arbitra- 
tion."    Hutchins  vs.  Merrill,  Supreme  Court  Maine,  84  Atlantic  412. 


120  THE  SCALING  OF  DEFECTIVE  LOGS 


References 

Instructions  for  the  Scaling  and  Measurement  of  National  Forest  Timber,  U.  S. 

Dept.  Agr.,  Forest  Service,  1916. 
Checking  Check  Scalers,  T.  S.  Woolsey,  Jr.,  Proc.  Soc.  Am.  Foresters,  Vol.  XI, 

1916,  p.  245. 
Methods  of  ScaUng  Logs,  Henry  S.  Graves,  Forestry  Quarterly,  Vol.  Ill,   1905, 

p.  245.     Cull  tables  by  Tiemann. 
Methods  of  Making  Discounts  for  Defects  in  Scaling  Logs,  H.  D.  Tiemann,  Forestry 

Quarterly,  Vol.  Ill,  1905,  p.  354. 


CHAPTER  IX 
STACKED  OR  CORD  MEASURE 

97.  Stacked  Measure  as  a  Substitute  for  Cubic  Measure.  Stacked 
or  cord  measure  is  the  cubic  space  occupied  by  stacked  wood  when 
the  exterior  dimensions  of  the  stacks  are  measured.  This  is  expressed 
in  terms  of  standard  units  termed  cords.  Wood  in  the  form  of  round 
bolts  or  spht  bolts,  which  are  termed  billets  (§9)  is  usually  intended 
either  for  use  as  bulk  products  such  as  firewood,  pulpwood  or  acid  wood, 
or  for  manufactured  articles  whose  dimensions  conform  to  those  of 
the  bolts  or  billets. 

For  the  former  uses,  the  total  cubic  contents  of  the  wood,  or  of  wood 
and  bark,  is  desired.  This  could  be  obtained  as  with  logs,  by  measuring 
the  dimensions  of  each  separate  bolt  and  totaling  their  contents.  On 
account  of  the  smaller  sizes,  greater  number,  and  irregularity  of  form, 
especially  of  billets,  such  a  method  would  be  time  consuming,  inaccu- 
rate and  impossible  to  check  as  to  results  without  complete  measure- 
ment. Yet  it  is  quite  extensively  employed  to  obtain  actual  cubic 
contents  of  logs  and  bolts  for  commercial  purposes,  when  the  material 
is  fairly  large  and  of  regular  shape  (§  29). 

Where  the  pieces  are  short,  small,  split,  or  irregular  in  form,  the 
more  convenient  and  simple  method  is  to  stack  the  wood  in  ranks  and 
measure  the  surface  dimensions  to  get  stacked  cubic  contents  including 
both  solid  wood  and  air  space. 

98.  The  Standard  Cord  versus  Short  Cords  and  Long  Cords.  A 
standard  stacked  cord  is  a  pile,  4  feet  high,  8  feet  long,  of  pieces  4 
feet  long,  and  contains  128  stacked  cubic  feet.  For  bulk  products,  the 
net  cubic  contents  of  wood,  either  with  or  without  bark  is  desired.  The 
use  of  wood  with  bark  for  fuel  for  domestic  purposes  utilizes  by  far  the 
greater  portion  of  all  wood  sold  in  bulk.  For  this  purpose  the  stand- 
ard cord  is  the  basis  of  delivery  in  the  rough,  to  wood  dealers. 

But  the  domestic  consumer  seldom  burns  4-foot  wood,  and  usually 
requires  short  wood  of  varying  sizes  commonly  between  12  and  24 
inches  in  length  and  making  4,  3  or  2  cuts  to  a  4-foot  stick.  Other 
special  lengths  may  be  specified  when  the  wood  is  cut  direct  from  the 
tree.  This  demand  gives  rise  to  the  short  cord.  A  short  cord  is  a  pile 
measuring  4  by  8  feet  on  the  side  or  face  and  one  rank  deep.  The  depth 
and  cubic  contents  depends  on  the  length  of  the  pieces.     Since  this 

121 


122  STACKED  OR  CORD  MEASURE 

substitution  of  surface  measure  reduces  the  cubic  volume  of  short 
cords,  either  the  price  must  be  reduced,  or  the  full  cubic  contents  of 
a  standard  cord  secm-ed  by  requu'ing  the  cord  to  be  two,  three  or  four 
ranks  deep,  or  to  have  an  additional  length  sufficient  to  make  up  128 
stacked  cubic  feet.  A  standard  cord  of  4-foot  wood  when  cut  into 
stove  lengths  is  considered  a  full  cord,  although  in  repiling  it  shrinks 
from  8  to  13  per  cent  in  stacked  volume  (§  108).  When  the  cord  of 
short  wood  is  measured  on  this  basis,  the  full  dimensions  of  a  standard 
cord  cannot  be  required  on  repiling. 

Wood  is  also  cut  longer  than  4  feet.  The  term  long  cord  usually 
refers  to  a  cord  4  by  8  feet  in  surface  by  5  feet  in  depth  and  containing 
160  cubic  feet.  The  standard  length  of  stick  for  hardwoods  for  dis- 
tillation or  acid  wood  is  50  inches,  giving  a  cubic  contents  of  133^ 
cubic  feet.  Unless  long  cords  are  accepted  by  custom,  stacks  measur- 
ing more  than  4  feet  in  length  of  stack  are  reduced  to  their  equivalent 
volume  in  standard  cords.  When  pulp  wood  bolts,  ordinarily  cut  4 
feet  long,  are  cut  8,  12  or  16  feet  long,  the}^  are  measured  as  standard 
cords,  a  stack  4  by  8  by  8  feet  containing  2  cords. 

99.  Measurement  of  Stacked  "Wood  Cut  for  Special  Purposes.  Stacked  cubic 
measure  is  commonly  employed  in  measuring  bolts  or  split  billets  intended  for  man- 
ufacture into  spokes,  handles,  staves  for  slack  and  tight  cooperage,  shingles  and 
shnilar  piece  products.  Bolts  measuring  over  12  inches  in  diameter  are  usually 
scaled  in  board  feet.  Billets,  if  spUt  or  rived  into  pieces  each  of  which  is  to  be 
shaped  into  one  finished  article  such  a  split  staves,  may  be  counted. 

Bolts  intended  for  sawing  are  usually  measured  by  stacked  contents.  The 
lengths  of  the  bolts  sawed  from  the  tree  must  correspond  to  the  required  length 
of  the  product  plus  a  small  margin  for  trimming,  or  must  be  a  multiple  of  this 
length,  to  avoid  waste.  For  spokes,  30  inches  is  a  common  length.  Handles 
require  lengths  of  from  12  to  60  inches.  Common  lengths  for  staves  for  tight 
cooperage  are  19  inches  and  38  inches.  The  demands  of  the  market  or  purchaser 
determine  the  length  in  every  case. 

The  measurement  of  shingle  bolts  is  frequently  by  double  cords,  in  lengths  of 
8  feet.  On  the  West  Coast,  the  bolts  are  cut  in  lengths  equal  to  3  shingles.  For 
16-inch  shingles  the  cord  is  4  feet  4  inches  in  depth,  while  for  18-inch  shingles, 
the  length  of  bolt  required  is  4  feet  8  or  10  inches.  Shingle  bolts  illustrate  the 
tendency  to  simplify  and  standardize  measurements  of  products  to  save  expense. 
The  bolts  are  not  uniform  in  size,  and  one  cord  may  contain  from  16  to  40  bolts. 
But  it  is  common  practice  to  first  determine  the  average  number  of  bolts  in  a  cord, 
and  then  measure  the  remainder  by  counting  the  bolts  to  avoid  stacking.  The. 
number  agreed  upon  is  used  as  a  divisor  to  obtain  the  quantity  in  cords. 

Stacks  measuring  more  or  less  than  4  feet  in  length  of  stick  can  thus  be  measured 
in  either  of  the  two  ways  described  above  ( §  98) .  Surface  feet  or  32  square  feet 
equivalent  to  4  by  8  feet  may  be  taken  as  a  short  cord.  But  stacked  contents 
based  on  the  standard  cord  of  128  cubic  feet  is  just  as  commonly  employed.  For 
instance,  in  cooperage  it  is  a  common  custom  to  measure  36-inch  stave  bolts  in 
ranks  4  by  11  feet  for  one  cord,  giving  132  cubic  feet  or  approximately  a  standard 
cord. 


EFFECT  OF  SEASONING  ON  VOLUME  OF  STACKED  WOOD      123 

100.  Effect  of  Seasoning  on  Volume  of  Stacked  Wood.  Green 
hardwoods  shrink  on  seasoning,  decreasing  from  9  to  14  per  cent  in 
volume.  Conifers  shrink  from  9  to  10  per  cent.  Contractors  some- 
times stipulate  an  extra  height  of  3  to  4  inches  on  the  stack  to  offset 
this  loss.  Where  such  extra  allowance  for  shrinkage,  or  for  any  other 
reason,  is  required,  it  must  be  specified  by  contract  unless  generally 
accepted  in  the  locality. 

101.  Methods  of  Measurement  of  Cordwood.  Stacked  cordwood 
is  measured  by  a  stick  usually  8  feet  long,  marked  off  in  feet  and  tenths. 
Choppers  prefer  to  pile  each  cord  separately,  since  the  division  into 
a  number  of  smaller  piles  reduces  the  cubic  contents  required  for  one 
cord  (§  103).  When  surface  measure,  32  square  feet,  is  accepted  for 
short  or  long  cords,  their  measurement  is  identical  with  that  of  standard 
cords,  the  length  of  piece  being  measured  only  to  insure  conformity 
with  specifications.  Stacks  piled  to  more  or  less  than  standard  height 
and  length  are  reduced  to  cords  by  dividing  the  surface  feet  by  32; 
e.g.,  a  stack  measuring  12.7  feet  by  6.4  feet  contains  81.28  surface  feet, 
or  2.54  cords. 

When  standard  stacked  contents  is  used  as  a  basis,  the  length  of 
piece  is  also  measured,  the  cubic  contents  of  stacked  wood  obtained 
and  divided  by  128;  e.g.,  a  stack  of  30-inch  bolts  with  the  above  surface 

203  2 

dimensions  gives  81.28  by  2.5  =  203.2  stacked  cubic  feet;  -—-^  =  1.5875 

128 

standard  cords,  while  a  similar  stack  of  5-foot  wood  gives  81.28  by  5 

406.4 
=  406.4  stacked  cubic  feet.  '   =3.175  standard  cords,  instead  of 

128 

the  2.54  cords  based  on  surface  standard. 

A  cord  foot  is  a  pile  measuring  1  by  4  by  4  feet  or  containing  one- 
eighth  of  a  standard  cord.  It  is  also  termed  a  foot  of  cordwood,  being 
equal  to  1  foot  in  length  in  a  stack  of  cordwood  of  standard  dimensions. 
The  unit  applies  to  short  or  long  cords  when  surface  only  is  measured 
and  not  cubic  contents. 

The  chopper  is  required  to  pile  the  rank  to  an  even  height,  pref- 
erably the  standard  of  4  feet.  Unless  otherwise  specified,  the  height 
of  the  pile  is  to  be  the  average  height  of  the  tops  of  the  sticks  in  the  top 
layer.  With  uneven,  crooked  or  poorly  piled  stacks  a  point  1  or  2 
inches  below  this  is  taken.  From  this  height  is  subtracted  whatever 
allowance  is  required  for  shrinkage,  when  so  specified. 

If  the  ends  of  the  stacks  are  not  vertical  the  length  is  measured  at 
one-half  the  height  of  the  pile.  If  wood  is  piled  in  irregular  stacks 
the  average  of  both  height  and  length  is  obtained,  if  necessary  from 
several  equally  spaced  measurements. 

Wood  piled  on  inclined  surfaces  is  measured  incorrectly  if  the  length 


124 


STACKED  OR  CORD  MEASURE 


of  the  pile  is  taken  parallel  with  the  surface  of  the  ground  or  top  of 
stack,  while  height  is  taken  vertically.  The  true  contents  of  a  stack 
with  the  dimensions  shown  in  Fig.  22  is  87.5  per  cent  of  a  cord.     The 

correct  measurement  is  secured  if 
length  and  height  are  taken  at 
right  angles  whether  or  not  the 
length  is  taken  horizontally  or 
along  the  surface. 

102.  Solid  Cubic  Contents  of 
Stacked  Wood.  The  stacked  cord 
is  a  measuie  purely  of  convenience. 
The  purchaser  is  interested  not  in 
the  cord,  but  in  its  solid  cubic 
contents  of  wood.  Stacked  round 
bolts  can  never  give  128  cubic  feet 
of  wood  to  a  cord.  The  highest 
possible  contents  would  be  ob- 
tained from  bolts  which  were  per- 
fectly cylindrical  and  of  uniform 
diameter.  These,  if  stacked  in 
hexagonal  formation,  or  alternat- 
ing, and  with  one  end  bolt  in  each 
tier  split  in  half  to  fill  out  the  tier,  would  give  116.07  cubic  feet,  or 
90.68  per  cent  of  128  cubic  feet,  which  is  the  relation  of  the  area  of  an 
inscribed  circle  to  that  of  a  hexagon.  Thi^  relation  hold>i  true  for  bolts 
of  any  length  or  diameter. 


Fig.  22. — In  the  example  given,  the  ver- 
tical height  of  the  pile  must  be  4. .57 
feet  to  give  128  cubic  feet.  The  actual 
pile  measures  112  cubic  feet  by  either 
method. 


Fig.  2.3. — Hexagonal  piling — 116.07  cubic  feet  per  cord  or  90.68  per  cent  sohd  wood. 
Square  piling — 100.53  cubic  feet  per  cord  or  78.54  per  cent  solid  wood.  It 
is  evident  that  neither  the  diameter  nor  the  length  of  sticks  would  in  any 
way  influence  the  sohd  cubic  contents  of  a  cord  unless  taken  in  conjunction 
with  some  other  factor  whose  effect  varies  with  the  dimensions  of  the  piece. 

When  these  cylinders  are  piled  directh^  above  one  another  in  square 
formation,  the  cubic  contents  of  a  cord  becomes  100.53  cubic  feet,  or 
78.54  per  cent  of  128  cubic  feet,  which  is  the  relation  of  the  area  of 
an  inscribed  circle  to  that  of  square. 

103.  Effect  of  Irregular  Piling  on  Solid  Contents.  In  actual  prac- 
tice, the  solid  contents  of  a  cord  seldom  exceeds  1 00  cubic  feet.     Straight 


EFFECT  OF  IRREGULAR  PILING  ON  SOLID  CONTENTS         125 

smooth  sticks  of  uniform  sizes,  carefully  piled,  may  yield  from  105 
to  107  cubic  feet,  but  never  as  much  as  the  116  cubic  feet  theoretically 
possible.  This  loss  is  due  first  to  irregular  pihng,  and  second,  to  vari- 
ation of  the  bolts  or  sticks  from  uniform  cylindrical  form. 

Piling  exercises  an  enormous  influence,  which  increases  in  direct 
proportion  to  the  irregularities  of  form.  When  to  extreme  crooked- 
ness and  surface  irregularities  is  added  dishonest  piling,  including  the 
laying  of  sticks  at  angles  with  each  other,  or  even  piling  over  stumps 
and  other  trade  practices,  the  purchaser  may  incur  a  loss  of  from  20 
to  30  per  cent  from  piling  alone.  Choppers  are  always  paid  by  stacked 
measure  and  close  supervision  is  required  to  secure  a  full  cord.  The 
factor  of  piling  may  cause  more  variation  in  the  solid  contents  of  a  cord 
than  that  of  form  of  sticks.  Since  this  factor  depends  upon  the  laborer, 
the  contents  of  a  cord  of  wood,  as  a  commercial  standard,  is  based  on 
what  can  be  expected  of  choppers  rather  than  a  theoretical  maximum. 
Conversion  factors  for  obtaining  cubic  contents  of  wood  are  based  on 
average  conditions  of  piling.  The  cord  can  never  be  satisfactorily  used 
as  a  basis  of  scientific  measurements  of  volume  produced  by  trees  and 
stands,  or  of  growth,  though  for  convenience,  cubic  contents  is  often 
converted  into  cords  to  express  the  results  of  these  investigations. 

104.  Effect  of  Variation  in  Form  of  Sticks  on  Solid  Contents. 
Variation  in  the  form  of  sticks  is  caused  by  taper,  eccentric  cross  sections, 
crook,  and  irregularities  or  roughness  of  surface.  All  departures  from 
cylindrical  form  increase  the  air  space  in  a  stacked  cord. 

The  effect  of  taper  can  be  partially  overcome  by  piling  bolts  with 
large  and  small  ends  alternating.  But  this  is  never  done  in  practice. 
Sticks  split  from  bolts  which  include  stump  taper  are  apt  to  be  some- 
what curved  as  well  as  tapering.  Sticks  with  eccentric  cross-sections 
do  not  pack  as  closely  as  round  sticks  and  give  a  smaller  per  cent  of  solid 
contents. 

Crook  is  one  of  the  most  important  factors  in  reducing  the  cubic 
contents  of  a  cord.  The  slightest  departm-e  from  a  straight  axis  exerts 
a  corresponding  influence  in  increasing  the  air  space  in  stacking.  Very 
crooked  sticks  may  reduce  the  contents  of  a  cord  by  50  per  cent. 

Irregularities  of  surface  in  round  sticks  are  caused  by  bark,  knots, 
stubs  and  swellings.  Every  such  protuberance,  by  contact  with  adjoin- 
ing sticks,  decreases  the  solid  contents  of  the  stack.  Split  sticks  are 
irregular  in  both  form  and  surface  and  always  take  up  more  room  than 
the  round  bolts  from  which  they  were  split  or  round  bolts  of  equal 
diameter  and  straightness. 

Since  sticks  with  the  smoothest  surface  and  least  taper  will  pack 
the  closest,  and  the  removal  of  bark  affects  both  factors  favorably,  the 
cubic  contents  of  a  cord  of  peeled  wood  is  always  greater  than  the  cubic 


126  STACKED  OR  CORD  MEASURE 

contents  of  a  cord  of  wood  with  bark,  for  the  same  species  and  sizes  of 
sticks.  The  shrinkage  in  stacked  contents  after  peehng  exceeds  that 
caused  by  loss  of  Ijark  because  of  this  closer  piling.  Bark  is  a  waste 
product  for  pulpwood  or  excelsior  and  purchasers  prefer  to  buy  peeled 
wood. 

The  thinner  the  bark  on  a  tree  the  smoother  it  is  apt  to  be.  Species 
with  smooth  bark  yield  appreciably  more  solid  contents  in  stacks  than 
thick-barked  trees,  because  in  the  latter  case  the  bark  is  usually  irregular 
and  fissured.  Hence  conifers  such  as  spruce  and  balsam,  and  hard- 
woods like  white  birch  and  poplar  give  the  highest  contents  per  cord, 
while  hardwoods  such  as  oak  and  maple  yield  considerably  less  per 
cord  than  conifers. 

The  same  difference  holds  for  branch  wood  as  contrasted  with  l^ody 
wood,  open-grown  and  limby  trees  compared  with  those  grown  free 
from  branches  in  close  stands,  and  split  wood  with  twisted  grain  com- 
pared to  straight  grain. 

While  the  splitting  of  sticks  decreases  the  solid  contents,  by  increasing 
the  irregularities  of  surface  and  the  effect  of  crook  through  reduced 
diameters,  split  corclwood  is  usually  cut  from  much  larger  bolts  than 
round  sticks,  and  hence  a  cord  of  split  wood  may  contain  a  greater 
solid  content  than  one  of  round  sticks,  especially  if  the  round  pieces 
are  below  3  inches  and  cut  from  limbs. 

105.  Effect  of  Dimensions  of  Stick  on  Solid  Contents.  The  effect 
of  a  given  amount  or  rate  of  crook,  or  of  given  irregularities  of  surface, 
in  diminishing  the  solid  contents  of  a  stack,  increases  with  increased 
length  of  stick,  but  this  effect  is  more  nearly  proportional  to  the  square 
of  the  length  than  to  the  length.  Hence  the  longer  the  sticks  in  a 
stacked  cord,  the  less  its  net  cubic  contents,  other  factors  being  equal. 

This  explains  the  shrinkage  in  cubic  volume  when  4-foot  wood  is 
cut  into  shorter  lengths  and  restacked.  In  sticks  longer  than  6  feet 
this  becomes  a  serious  factor  and  pulpwood  from  fairly  straight  logs 
when  sold  in  from  8-  to  12-foot  lengths  gives  about  12  per  cent  less  cubic 
contents  than  for  4-foot  bolts  (Table  XXI,  p.  130). 

Conversely,  the  cubic  volume  of  sticks  increases  as  their  cross- 
sectional  area,  which  is  as  the  square  of  the  diameter,  while  the  effect 
of  both  crook  and  surface  irregularities  increases  in  porportion  to  the 
'surface  of  the  stick,  which  is  directly  in  proportion  to  diameter  and 
consequently  less  than  cross-sectional  area  or  volume.  A  crook  of 
2  inches  in  a  stick  with  3-inch  diameter  has  twice  the  effect  that  a 
2-inch  crook  would  have  on  a  6-inch  stick.  Due  to  these  relations,  the 
solid  contents  of  a  cord  of  wood  always  increases  with  the  increased 
average  diameter  of  the  sticks,  but  diminishes  with  increased 
length. 


THE  BASIS  FOR  CORDWOOD  CONVERTING  FACTORS 


127 


106.  The  Basis  for  Cordwood  Converting  Factors.  The  value  of 
stacked  wood  depends  upon  the  quantity  of  wood  contained  in  the 
stacked  cord  as  well  as  upon  its  quality.  It  is  just  as  consistent  to 
require  a  knowledge  of  the  solid  cubic  contents  of  stacked  cords  as  it 
is  to  measure  sawlogs  for  board-foot  contents  by  a  log  rule.  For  this 
purpose,  converting  factors  are  required,  and  these  factors  are  deter- 
mined by  actual  measurement  of  the  solid  wood  in  cords  composed  of 
sticks  of  different  diameters  and  degrees  of  straightness. 

Since  a  cord  contains  128  cubic  feet  of  space,  the  solid  contents  in 
cubic  feet  may  be  expressed  in  terms  of  per  cent;  e.g.,  a  cord  containing 
90  cubic  feet  of  wood  gives  70  per  cent  of  stacked  contents  in  wood. 
A  cord  of  theoretically  perfect  cylindrical  sticks  piled  square  gives 
100.5  cubic  feet,  or  79  per  cent  (§  102).  This  in  actual  practice  is  about 
the  maximum  contents  of  stacked  cord,  no  matter  how  the  piling  is 
done,  for  losses  caused  by  taper,  crook  and  surface  compensate  for  any 
gain  by  hexagonal  over  square  arrangement  of  sticks.  Smooth  pine 
or  white  birch  may  give  102  to  107  cubic  feet  for  large  sticks,  but  the 
attainable  maximum  solid  cubic  contents  of  cords  can  for  commercial 
purposes  be  set  at  100  cubic  feet. 

TABLE  XIX 
Solid  Contents  of  Stacked  Wood  * 


Cubic  feet  solid  wood 

Per  cent 

in  one  cord  or  per 

Class  of  product 

solid  contents 

cent  of  standard 

in  stack 

contents  of  100  cubic 
feet  per  cord 

Large  smooth  logs  or  bolts. . . 

75-80 

96  0-102  4 

60-75 

76  8-  96  0 

50-65 

64  0-  83  2 

Fagot  naaterial  (small  branches  a 

nd  twigs)  .... 

30-45 

38.4-  57.6 

30-40 

28  4-  51  2 

*  Adolph   R.   von   Guttenberg, 
Chap.  XII,  p.  179,  Tubingen. 


in   Lorey's    Handbuch   der   Forstwisscnschaft,    Vol.    Ill,    1903, 


There  is  thus  a  choice  of  two  methods  of  expressing  converting 
factors  for  indicating  the  solid  or  cubic  contents  of  wood  in  a  cord; 
first,  the  number  of  feet  of  solid  wood  in  a  cord  of  128  stacked  feet; 
second,  the  per  cent  of  a  stacked  cord  which  this  cubic  contents  repre- 
sents. Of  the  two,  the  former  is  preferable  for  two  reasons;  first,  it 
is  directly  applicable  to  cubic  contents  of  trees  as  a  divisor  or  con- 
verting factor  to  obtain  cords;    second,  it  indicates  the  comparative 


128  STACKED  OR  CORD  MEASURE 

solid  volume  in  cords  of  different  cubic  contents  on  a  basis  which  prac- 
tically amounts  to  a  100  per  cent  commercial  standard.  For  if  100 
cubic  feet,  as  indicated  above,  is  the  practical  maximum  solid  cubic 
contents  of  a  cord  of  stacked  wood,  a  cord  containing  70  solid  cubic 
feet  bears  a  70  per  cent  relation  to  this  maximum,  regardless  of  the  fact 
that  70  feet  is  but  54  per  cent  of  the  space  in  a  stacked  cord  of  128  feet. 
This  accidental  relation  holds  good  only  for  standard  cords.  To  apply 
this  same  basis  of  comparison,  instead  of  the  per  cent  of  stacked  con- 
tents, to  long  or  short  cords,  the  solid  contents  would  have  to  be  com- 
pared to  78.12  per  cent  or  Iff  of  the  stacked  contents.  Average  cord- 
wood  worked  up  from  hardwoods,  either  split  or  round,  is  often  reckoned 
at  90  cubic  feet  or  90  per  cent  of  a  maximum  cord,  which  is  70  per  cent 
of  stacked  contents. 

107.  Standard  Cordwood  Converting  Factors.  The  cubic  contents 
of  stacked  wood  has  been  thoroughly  investigated  by  European  author- 
ities on  the  basis  of  the  stacked  cubic  meter,  of  length  equal  to  39.37 
inches  or  8.63  inches  short  of  a  4-foot  standard.  According  to  the  per 
cents  given  in  Table  XXI  (p.  130)  these  results  should  give  about  1  per 
cent  more  than  the  contents  of  similar  sticks  4  feet  long. 

The  following  Table  XX  is  adopted  from  the  results  of  an  investi- 
gation conducted  by  Prof.  F.  Baur,  and  published  in  a  pamphlet  entitled 
"  Untersuchungen  liber  die  Festgeholt  und  das  Gewicht  des  Schicht- 
holzes  und  der  Rinde,"  Augsburg  1879,  pp.  97-99.  These  factors 
may  be  regarded  as  standard  for  4-foot  lengths,  after  subtracting  1  per 
cent. 

The  difference  in  per  cents  between  hardwoods  and  conifers  in  this 
table  is  seen  to  fall  largely  in  the  smaller  sizes.  Where  branch  wood 
is  mixed  in  the  cord  the  per  cent  of  difference  between  hardwood  and 
conifers,  usually  about  6  per  cent,  may  be  increased  to  12  or  15  per 
cent,  since  many  conifers  lack  mei'chantable  branches,  while  hardwood 
branches  are  usually  crooked. 

108.  Converting  Factors  for  Sticks  of  Different  Lengths.  The 
influence  of  length  on  per  cent  of  solid  contents  is  fairly  constant  for 
sticks  of  all  diameters,  but  differs  tremendously  according  to  the  amount 
of  crook  in  the  average  stick.  Table  XXII  gives  average  results 
for  conifers,  which  as  a  rule  are  much  straighter  than  hardwoods.  It 
is  seen  in  the  table  that  the  per  cents  when  standardized  for  sticks  of 
the  same  diameter  do  not  differ  much,  whether  the  sticks  average  over 
5.5  inches  or  are  between  1  inch  and  2.5  inches  in  diameter. 

The  differences  in  contents  caused  by  crook  and  surface  irregularities  is  well 
shown  in  Table  XXIII,  prepared  for  hardwoods  by  Konig,  p.  131.  In  this  table 
the  values  for  straight  sticks  4  feet  long  slightly  exceed  the  values  in  Table 
XXI  since  these  sticks  are  selected.     But  for  other  lengths  even  in  this  class  the 


CONVERTING    FACTORS   STICKS   OF    DIFFERENT  -  LENGTHS      129 


percentages  increase  more  rapidly  than  for  conifers;  while  for  crooked  and  knotty 
sticks  the  differences  caused  by  length  are  excessive,  when  added  to  those  caused 
by  diameter. 

TABLE  XX 
Standard  Converting  Factors  for  Cordwood 


Cubic  feet 

solid  wood  in 

Per  cent 

a  cord  or 

Species 

Diam- 
eter 

Class  of 
material 

Character  of 
piece 

solid  wood 
in  a 
cord 

per  cent  of 

standard 

contents  of 

100  cubic  feet 

per  cord 

Conifers 

Large 

Round  logs 

Straight 

80 

102.4 

Medium 

Split  firewood 

Straight,  smooth 

75 

96.0 

Medium 

Split  firewood 

Crooked,  knotty 

70 

89.6 

Small 

Firewood 

Round  bolts 

70 

89.6 

Small 

Firewood 

Top  wood 

60 

76.8 

Small 

Strips 

Hewn  from  bole 

50 

64.0 

Small 

Chips 

Hewn  from  bole 

45 

57.6 

Hardwoods 

Large 

Sawlogs 

Straight 

80 

102.4 

Medium 

Split  firewood 

Straight,  smooth 

70 

89.6 

Large 

Split  firewood 

Ivnotty,  crooked 

65 

83.2 

Small 

Firewood 

Round  bolts 

65 

83.2 

Small 

Firewood 

Knotty,  crooked 

55 

70.4 

Small 

Firewood 

Top  wood 

55 

70.4 

Small 

Firewood 

Branch  wood 

45 

57.6 

Small 

Strips 

Hewn  from  bole 

35 

44.8 

Small 

Chips 

Hewn  from  bole 

25 

32.0 

Small 

Brush 

Long  branches 

15 

19.2 

109.  Converting  Factors  for  Sticks  of  Different  Diameters.     The 

figures  in  table  XXIV  indicate  the  influence  of  diameter  of  stick  upon 
sohd  contents  of  stacked  cords,  for  various  species.  The  differences  in 
contents  for  Species  is  due  entirely  to  differences  in  form  and  smooth- 
ness of  sticks. 

Second-growth  white  pine  and  Norway  or  red  pine  give  results  approximating 
white  birch.  Old  growth,  knotty  twisted  grain  and  limby  northern  hardwoods 
give  60  cubic  feet  per  cord,  as  against  90  cubic  feet  for  tall  slender  straight  clear 
second-growth.  A  cord  of  average  hardwoods  does  not  contain  more  than  70 
cubic  feet.  A  cord  of  second-growth  hickory  spoke  bolts  contains  95  cubic  feet. 
Chestnut  acid  wood  on  the  Pisgah  National  Forest,  N.  C,  is  scaled  as  110  cubic 
feet  of  wood  per  cord  of  160  stacked  cubic  feet,  or  87  cubic  feet  per  standard 
cord.  In  California,  a  cord  of  red  and  white  fir,  averaging  60  sticks,  contains  81 
cubic  feet.  Western  juniper  in  Arizona  averages  62  cubic  feet  of  sohd  wood 
per  cord. 


130 


STACKED  OR  CORD  MEASURE 


TABLE  XXI 

Conifers  * 
Influence  of  Length  of  Stick  upon  the  SoUd  Cubic  Contents  of  a  Cord 


Sohd  contents 

Solid  contents 

Sohd  contents 

Length 
of 

per  cord. 
Sticks  over 

Per  cent 
in  terms 

per  cord. 
Sticks  from  2.5 

Per  cent 

per  cord. 
Sticks  from  1 

Per  cent 

5.5  inches  in 

to  5.5  inches  in 

to  2.5  inches  in 

stick. 

diameter  at 
small  end. 

of  4-foot 
sticks 

diameter  at 
small  end. 

of  4-foot 
sticks 

diameter  at 
small  end. 

of  4-foot 
sticks 

Feet 

Cubic  feet 

Cubic  feet 

Cubic  feet 

1 

91.80 

+  3.2 

85.25 

+  3.4 

65.69 

+  3.2 

2 

90.90 

+  2.2 

84.35 

+  2.3 

65.32 

+  2.7 

3 

89.98 

+   1.2 

83.40 

+  1.6 

64.60 

+  1.5 

4 

88.92 

0 

82.42 

0 

63.62 

0 

5 

87.75 

-  1.3 

81.30 

-   1.3 

62.60 

-   1.6 

6 

86.45 

-  2.8 

80.00 

-  3.0 

61.60 

-  3.2 

8 

83 .  75 

-  5.8 

77.20 

-  6.3 

59.40 

-  6.6 

10 

81.00 

-  8.9 

74.30 

-  9.9 

56  90 

-10.5 

12 

78.05 

-12.2 

71.20 

-13.6 

54.25 

-14.7 

14 

74.85 

-15.8 

67.95 

-17.5 

51.50 

-19.0 

*  Raphael  Zon,  Forestry  Quarterly,  Vol  I,  1903,  p.  132. 

These  results  were  verified  by  test  on  balsam  fir  in  the  Adirondack  region  of  New 
York 


TABLE  XXII 

Influence  of  Length  of  Stick  on  Solid  Cubic  Contents  of  a  Standard  Cord, 
Balsam  Fir 


Volume 

Length. 
Feet 

Diameter  of  sticks, 
small  end,  7  inches 

and  over. 

Cubic  feet 

Loss  in  long 
sticks. 

Per  cent 

Diameter  of  sticks, 

small  end,  4  to  7 

inches. 

Cubic  feet 

Loss  in  long 
sticks. 

Per  cent 

4 
8 
12 
16 

96.7 
91.6 

86.2 
80.2 

-  5.3 
-10.8 
-17.1 

92.4 
87.4 
81.6 
75.5 

-  5.4 
-11.6 
-18.3 

This  table  was  based  on  56  cords  by  R.  Zon,  Bui.  55,  U.  S.  Dept.  of  Agriculture, 
p.  52. 


CONVERTING    FACTORS    STICKS    OF    DIFFERENT    DIAMETERS    131 


TABLE  XXIII 

Interdependence  of  the  Stick  Length  and  the  Volume  of  Solid   Wood  per 

Cord* 


Length 
of 

Straight  Sticks 

1 
Crooked  Sticks      |       Knotty  Sticks 

stick. 
Feet 

Volume. 
Cubic  feet 

Difference. 
Per  cent 

Volume. 
Cubic  feet 

Difference. 
Per  cent 

Volume. 
Cubic  feet 

Difference. 
Per  cent 

1 
2 
3 

4 
5 
6 

99.81 
97.28 
94.72 
92.16 
89.60 
87.04 

+8.3 
+5.5 
+2.8 
0.0 
-2.8 
-5.5 

93.47 
89.60 
85.76 
81.92 
78.08 
74.24 

+14.1 

+  9.4 

+  4.7 

0.0 

-  4.7 

-  9.4 

89.60 
84.48 
79.36 
74.24 
69.12 
64.00 

+20.7 
+13.8 
+  6.9 
0.0 
-  6.9 
-13.8 

'  Cited   in   Dr.    MuUer's   Lehrbuch   der   Holzmesskunde,    Graves    Mensuration,   p.    104. 

TABLE  XXIV 

Solid  Contents  of  a  Standard  Cord  Based  on  Diameter  of  Stick 

Average,  4-foot  wood 


Average 

Mixed 

diameter  at 

Paper      Ba 

sam 

Red 

hard- 

middle 

birch.*        fi 

r.t 

Spruce. t  Aspen. § 

1 

Beech 

•^     maple.  II 

woods.! 

of  sticks. 

1 

Inches 

Cu.  ft.      Cu 

I 

.ft. 

Cu.  ft.      Cu.  ft. 

Cu.  f 

t.       Cu.  ft. 

Cu.  ft. 

3 

64 

7Q 

75 

49 

67 

60 

4 

72 

12 

80 

57 

69 

65 

5 

82 

B6 

84 

64 

54 

70 

69 

6 

87 

58 

86 

71 

62 

72 

73 

7 

91 

30 

88 

77 

70 

74 

77 

•8 

96 

n 

90 

83 

77 

77 

80 

9- 

100 

32 

91 

88 

83 

80 

83 

10 

103             < 

33 

92 

92 

88 

84 

85 

11 

105             < 

34 

92 

96 

93 

87 

88 

12 

105 

93 

90 

90 

13 

105 

94 

92 

92 

14 

95 

93 

95 

15 

96 

95 

97 

16 

96 

96 

99 

17 

97 

. 

96 

18 

97 

t  R.  Zon. 


t  H.  L.  Churchill. 
I[  E.  E.  Carter. 


E.  H.  Frothingham. 


132  STACKED  OR  CORD  MEASURE 

110.  The  Measurement  of  Solid  Contents  of  Stacked  Cords — 
Xylometers.  The  sohd  or  cubic  contents  of  stacked  cords  must  be 
actually  measured  in  order  to  determine  the  converting  factors  for 
wood  as  influenced  by  any  of  the  above  conditions.  The  purpose  may 
be  to  obtain  either  an  average  factor  for  commercial  use,  or  to  further 
test  the  effect  of  crook,  diameter  or  length  of  sticks  specialh'  selected. 

Two  methods  of  measurement  are  available,  actual  calipering  or 
stereometric  ^  calculation,  and  xylometric  -  measurement.  By  the  first 
method,  the  diameter  of  each  bolt  is  measured  in  the  middle  (Ruber's 
method)  taking  two  measurements  at  right  angles  to  obtain  the  average. 
The  length  is  measured  if  necessary,  but  the  sticks  are  usually  cut  to 
a  standard  length.  Split  billets  cannot  be  measured  by  this  means, 
and  in  this  case,  the  round  bolt  must  first  be  measured  before  splitting. 
The  measured  wood  is  piled  and  the  contents  of  the  sticks  required  to 
make  a  stacked  cord  are  totaled  for  as  many  cords  as  possible,  to  obtain 
average  factors. 

Wood  after  splitting,  or  very  small  crooked  or  irregular  pieces  such 
as  branches  or  root  wood,  is  best  measured  by  a  xylometer.^  The  dis- 
placement of  water  when  wood  is  submerged  in  a  tank  is  exactly  equal 
to  the  cubic  volume  of  the  wood.  The  only  question  is  the  fo  m  of  the 
tank  and  method  of  measuring  the  cubic  volume  of  water  displaced. 

One  plan  (invented  by  Karl  Heyer,  Giessen,  1846)  is  to  have  an 
overflow  spout  flush  with  the  water  level  and  to  catch  and  measure 
water  which  overflows. 

But  this  is  found  to  take  seven  times  as  long  as  Reisig's  method 
(Darmstadt,  1837)  which  employes  a  tank  about  5^  feet  high  and  about 
twice  as  wide  as  the  diameters  of  the  largest  sticks.  The  cross-section 
must  be  uniform  at  all  points.  The  scale  is  worked  out  for  cubic  feet 
and  decimals,  corresponding  to  the  inch  scale  in  height  of  water  in  the 
tank  and  is  either  marked  on  the  inside  of  the  tank,  or  better  on  a  stand 
pipe  of  glass  outside  the  tank,  with  proper  connection,  and  carefully 
plumbed.  This  gives  instant  readings  when  a  piece  is  submerged. 
The  endwise  position  favors  complete  submersion. 

111.  Cordwood  Log  Rules.  The  Humphrey  Caliper  Rule,  1882.  Cord- 
wood  log  rules  are  in  use  in  Southern  New  Hampshire  and  in  Massa- 
chusetts for  measuring  the  cubic  contents  of  white  pine  logs  in  terms 
of  stacked  cords  and  stacked  cubic  feet.  These  rules  are  based  upon 
the  principle  of  the  circle  inscribed  in  a  square  (§  102).  It  is  assumed 
that  a  cord,  no  matter  what  the  diameter,  length  or  character  of  the 
timber,  contains  100.5  cubic  feet  of  solid  wood.  The  diameter  is  cali- 
pered  in  the  middle  of  the  log  outside  the  bark,  but  the  rule  could  be 

1  Stereometry,  the  art  of  measuring  solid  bodies.     Stereos  (Gr.)  =solid. 
^Xylos  (Gr.)^  water. 


DISCOUNTING  FOR  DEFECT  IN  CORD  MEASURE  133 

applied  to  peeled  wood  by  subtracting  diameter  of  bark.  The  old 
Partridge  rule  used  at  Winchendon,  Mass.,  computes  the  stacked  volume 

of  the  log  as  (-D-)—  with  Z)  =  diameter  in  feet.     Each  "cubic  foot" 

by  this  rule  is  yfg  cord.  The  rule  is  thus  based  on  stacked  contents, 
and  fractional  cords  are  reduced  to  decimals  by  the  divisor  128;  e.g., 
64  "  feet  "  would  give  .5  cord. 

To  simplify  this  process  the  cordwood  caliper  rule  known  as  the 
Humphrey  Caliper  ^  Rule,  was  divided  into  -ywo  of  a  cord;  i.e.,  instead 
of  measuring  a  stacked  cubic  foot  the  unit  or  y^  cord  equaled  1.28 
stacked  cubic  feet.  The  scale  stick  for  this  rule  was  not  marked  off 
in  inches,  but  for  each  standard  length  of  stick  the  graduations  repre- 
senting diameter  were  placed  at  the  points  which  gave  logs  measuring 
a  certain  even  volume  (§80).  Hence  no  fractional  stacked  feet  were 
shown. 

Since  oy  either  rule,  the  cubic  contents  of  a  cord  is  given  as  100.5 
cubic  feet,  the  Humphrey  Rule  by  using  the  decimal  system  expressed 

the  contents  as  -    ^^^ —  within  an  error  of  but  0.5  per  cent.     The  values 
100 

of  the  rule  thus  correspond  with  those  given  for  cubic  contents  of  cyhn- 

ders,  but  pointed  off  for  two  decimals. 

If  we  accept  the  standard  of  100  solid  cubic  feet  of  wood  as  the 
maximum  contents  of  a  cord,  the  Humphrey  Caliper  Rule  measures 
wood  of  any  character  or  degree  of  straightness,  surface,  roughness, 
length  or  diameter  not  only  by  a  uniform  standard  of  cubic  contents 
(as  does  the  Partridge  Rule)  but  directly  in  cubic  feet,  or  in  standard 
cubic  contents. 

This  rule  therefore  offers  a  double  advantage.  It  is  not  only  a  cubic- 
foot  standard,  which  is  desirable  for  all  scientific  measurements  of  volume 
and  growth,  but  it  serves  to  standardize  cord  measure  as  well,  on  the 
basis  of  solid  rather  than  stacked  contents.  The  limitations  in  the 
use  of  the  rule  are  the  same  as  those  of  all  caliper  rules  (§  84).  It  can- 
not be  appHed  to  wood  in  the  stack  but  only  to  pieces  measured  singly. 
Scale  sticks  made  up  for  these  values  would  enable  measurements  of 
cubic  contents  to  be  made  directly  for  logs  or  trees  to  be  used  for  vol- 
ume tables  or  other  scientific  purposes  and  would  do  away  with  cal- 
culation of  cubic  contents.  This  rule  is  used  as  the  principal  com- 
mercial standard  in  the  vicinitj^  of  Keene,  New  Hampshire.  It  can  be 
made  up  by  anyone  on  the  basis  of  diameter  by  applying  the  cubic 
contents  of  cylinders  given  in  Table  LXXVII,  Appendix  C. 

112.  Discounting  for  Defect  in  Cord  Measure.     Pulpwood  must  be  sound  and 
free  from  rot  or  defective  knots.     Where  logs  of  8,  12  or  16  feet  are  measured  by 
'  Invented  by  John  Humphrey,  Keene,  N.  H. 


134 


STACKED  OR  CORD  MEASURE 


the  cord,  defective  portions  may  be  culled  by  subtracting  from  the  total  stacked 
volume,  a  piece  whose  volume  is  the  square  of  the  diameter  in  feet  multiplied  by 
length  in  feet.  This  deduction  coincides  with  the  basis  of  a  standard  cord  of 
100.5  solid  cubic  feet  and  is  based  on  Y^-g  cord  for  each  cubic  foot  subtracted. 
This  method  is  the  basis  of  the  following  table:  • 

TABLE  XXV* 

Measurements   of   4-foot    Round    Spruce    Pulpwood — with    Cull    Factors 
Based  on  Solid  Cubic  Contents 


Average 

diameter  of 

stick. 

Solid  contents  of 
cord. 

Sticks  per  cord. 

Volume  to  be  deducted 
for  each  stick  culled. 

Inches 

Cubic  feet 

Number 

Cubic  feet 

3 

75.0 

375 

0.34 

4 

79.8 

228 

.56 

5 

83.6 

152 

.84 

6 

86.1 

109 

1.16 

7 

87.7 

82 

1.56 

8 

89.6 

64 

2.00 

9 

90.3 

51 

2.51 

10 

91.6 

42 

3.08 

11 

92.4 

35 

3.66 

12 

93.3 

29.7 

4.27 

13 

94.1 

25  5 

5.02 

14 

95.0 

22.1 

5.87 

15 

95.8 

19  6 

6.67 

16 

96.5 

17.1 

7.71 

17 

97.0 

15.4 

8.59 

18 

97.4 

13.7 

9.70 

19 

97.9 

12.4 

10.76 

20 

98.3 

11.3 

12.06 

Prepared  by  H.  L.  Churchill  for  spruce  in  the  Adirondack  region,  New  York. 


Where  the  contents  of  the  cord  are  expressed  directly  in  soHd  cubic 
feet,  special  tables  can  be  worked  up  for  deducting  the  actual  cubic 
contents  for  sticks  of  given  diameters. 

The  Humphrey  Caliper  Rule  will  serve  to  make  deductions  based 
on  solid  measure,  by  scaling  the  contents  of.  the  defective  portion  as 
a  stick  of  a  given  length  and  diameter. 

113.  The  Measurement  of  Bark.  Bark,  when  used  for  tannin,  is  stripped  off 
in  sheets  and  piled  in  cords.  At  the  factory  a  cord  is  measured  by  weight.  Eastern 
hemlock  bark  must  weigh  2240  pounds  per  cord,  when  dry. 

The  bark  peelers  are  paid  by  the  stacked  cord  measure,  which  is  in  some 
localities  4  by  4  by  8  feet  but  more  often  is  required  to  be  full  in  one  or  more 
dimensions,  according  to  local  specifications.     In  New  York,  the  dimensions  are 


CONVERTING  STACKED  CORDS  TO  BOARD  FEET 


135 


4  by  4  by  8  feet.  In  Upper  Michigan,  4^  by  4^  by  8|  feet  is  sometimes  recjuired, 
in  order  that  the  cord  shall  check  out  in  weight.  Others  stipulate  45  by  4-3  by  8 
feet.  In  the  West,  hemlock  bark  is  usually  bought  and  .sold  by  the  standard  cord, 
although  weight  per  cord  (2240  pounds)  is  sometimes  used.  Tan-bark  oak  is  sold 
by  weight.' 

Bark  forms  the  largest  per  cent  of  total  volume  in  young,  small  and  rapidly 
growing  trees,  exposed  to  light  and  growing  on  dry  exposed  sites.  It  gives  the 
smallest  per  cent  of  total  volume  on  old^  large  trees,  grown  in  dense  stands,  and 
on  slow  growing  or  suppressed  trees. 


Measurement  of  bark 
following  species,  show: 


per  cent  of  total  volume  of  tree  with  bark,  for    the 


Species 

Character 

Per  cent  bark 

Southern  yellow  pine  species 

2-inch  trees 

Diminishing  with  increased 

diameter 

12-inch  trees 

Diminishing  with  increased 

diameter 
Diminishing  with  increased 

diameter 
Diminishing  with  increased 

diameter 

Dimmishing  with  increased 

diameter 

All  dianjeters 

All  diameters 

All  diameters 
All  diameters 
All  diameters 

40 

30  to  15 

24 

24  to  12 
15  to  12 

Ash 

22.4  to  10.3 

Hickory           

22  to  12 

Cottonwood 

Average  22 
Average  11  to  12  f 

Spruce,   balsam,    white  pine,  white 
birch 

15  to  19 

The  manufacturers  of  pulp,  excelsior  and  products  requiring  peeled  wood, 
when  forced  to  purchase  their  raw  material  with  bark  on,  soon  determine  the 
reduction  factor  required  for  their  species  and  locality.  The  large  and  variable 
per  cent  of  bark  on  loblolly  pine  in  the  South  forces  the  purchaser  of  pulpwood 
stock  to  insist  on  peeling. 

114.  Factors  for  Converting  Stacked  Cords  to  Board  Feet.  WTiere  the  output 
of  wood  in  a  given  region,  or  for  a  given  tract  or  ownership  is  in  the  form  of  both 
cordwood  and  sawlogs,  it  is  often  desirable  to  reduce  cordwood  to  terms  of  its 
equivalent  in  board  feet,  in  order  to  express  the  total  production  in  terms  of  a 
single  standard.  Less  often,  this  conversion  is  desired  as  the  basis  of  sale  or 
contracts  for  logging.  It  is  not  the  purpose  of  such  conversion  to  determine  the 
actual  quantity  of  lumber  which  can  be  sawed  from  sticks  of  cordwood  sizes  and 
shapes. 

»  The  standard  cord  in  Oregon  is  2300  pounds.  The  standard  cord  in  California 
is  2400  pounds. 


136  STACKED  OR  CORD  MEASURE 

The  board-foot  contents  of  a  stacked  cord  depends  first  on  the  solid  cubic  con- 
tents of  the  cord  rather  than  its  stacked  measure,  and  second,  on  the  diameter 
of  the  sticks  which  it  contains  (§  54).  Since  soUd  contents  also  depends  on  diam- 
eter of  stick,  the  ratio  of  board  feet  to  stacked  contents  increases  with  diameter 
from  both  sources,  or  much  faster  for  stacked  than  for  cubic  volume. 

The  diameter  of  the  average  stick  is  the  determining  factor  in  this  ratio.  The 
ratio  itself  will  thus  vary  over  a  wide  range  depending  on  the  class  of  wood  handled. 
Crook  and  other  irregularities  of  form  have  the  same  double  effect  as  diameter, 
in  reducing  first  the  soUd  contents,  and  next,  the  board-foot  contents  per  cubic 
foot  of  wood.  The  latter  ratio  can  be  determined  for  straight  sticks  by  Table  III 
(§  41),  Tiemann  log  rule,  based  on  middle  diameters,  outside  bark.  For  crooked 
sticks,  a  further  reduction  in  ratio  is  required. 

To  obtain  the  true  ratio  for  a  given  cord  of  straight  wood,  it  is  necessary  to 
determine  first,  the  converting  factor  for  sohd  cubic  contents,  and  second,  the 
average  diameter  of  the  sticks,  at  middle  point  outside  bark.  By  use  of  Table  III 
the  converting  factor  from  cubic  to  board  feet  is  found  for  logs  or  bolts  of  this 
average  size,  and  this  multiplied  by  solid  cubic  contents  gives  contents  of  the 
stacked  cord  in  board  feet. 

But  commercial  log  rules  are  based  on  diameter  at  small  end  and  do  not  usually 
give  actual  sawed  contents.  For  such  rules  the  ratio  can  be  approximated  directly 
by  determining  the  average  diameter  and  number  of  sticks  in  a  cord,  and  scaling 
their  contents  with  a  log  rule. 

The  ratio  for  actual  board-foot  contents  of  cordwood  diminishes  to  zero  for 
sticks  averaging  from  3  to  4  inches  in  diameter,  which  is  a  common  size  for  cord- 
wood.  If  so  determined,  the  converting  factor  is  not  an  indication  of  the  real 
volume  or  utility  of  the  contents  of  a  cord  of  wood.  For  a  given  species  and  class 
of  cordwood  an  arbitrary  converting  factor  can  be  obtained,  based  first  on  the 
per  cent  of  solid  cubic  contents  of  a  cord  of  sticks  of  average  diameter  and  second, 
on  an  average  or  fair  ratio  between  board  feet  and  cubic  feet,  and  not  on  the  ratio 
for  the  actual  small  or  irregular  sizes.  For  instance,  western  juniper  cordwood 
gives  about  60  cubic  feet  per  cord.  Adopting  a  fairly  low  ratio  of  46  per  cent  or 
5.55  board  feet  per  cubic  foot  of  total  solid  contents,  the  board-foot  converting  factor 
is  60  times  5.55  or  333  board  feet  per  cord,  or  8  cords  per  1000  board  feet.  For 
white  pine,  100  cubic  feet  per  cord,  with  nearly  the  same  ratio,  5.5  board  feet  per 
cubic  foot,  gives  550  board  feet  per  cord.  The  ratio  of  500  board  feet  per  cord 
adopted  by  the  U.  S.  Forest  Service  for  pulpwood  gives  5.55  board  feet  per  cubic 
foot  for  wood  yielding  90  cubic  feet  per  cord,  which  is  a  fair  average  for  well-shaped 
sticks. 

It  would  appear  then  that  the  factor  5.55  has  some  merits  as  a  universal  con- 
verting factor  and  that  the  variation  of  board-foot  converting  factors  for  entire 
cords  should  be  based  on  the  difference  in  cubic  contents  of  the  cord  rather  than  by 
the  adoption  of  variable  ratios  between  board  feet  and  cubic  feet.  This  practice 
is  sound.  The  factor  5.55  corresponds  to  the  actual  sawed  contents  of  a  log 
between  7  and  8  inches  in  diameter  at  middle  of  stick  inside  bark.  The  basis 
of  this  ratio  is  comparison  between  total  cubic  contents  including  taper,  and  actual 
sawed  contents.  Commercial  log  rules  deal  with  reduced  values  for  both  cubic  and 
sawed  output,  using  the  contents  of  the  small  cylinder  for  the  one,  and  neglecting 
over-run  in  the  other.  These  two  reductions  may  not  be  of  equal  weight,  but  tend 
to  give  approximately  equal  ratios  to  those  stated. 

If  the  average  diameter  of  logs  exceed  7^  inches  at  middle,  inside  bark,  the  actual 
ratio  is  correspondingly  larger.      Only  in  this  way  can  ratios  as  high  as  575  board 


WEIGHT  AS  A  MEASURE  OF  CORDWOOD  137 

feet  per  cord,  used  on  the  Pacific  Coast,  be  obtained.     The  ratio  in  New  England 
for  pulp  wood  is  5G0  board  feet.' 

115.  Weight  as  a  Measure  of  Cordwood.  For  fuel,  weight  is  a 
better  measure  of  the  value  of  cordwood  than  solid  cubic  volume,  and 
of  still  greater  utility  for  the  measurement  of  stacked  volume.  Its 
merits  increase  with  the  increasing  irregularity  of  form  in  sticks  which 
render  the  determination  of  solid  contents  of  stacks  so  uncertain.  But 
one  factor  operates  against  the  substitution  of  weight  for  stacked 
measure,  for  fuel  wood,  and  that  is  the  unfamiliarity  of  the  public  with 
the  proper  standard  weights  which  should  constitute  a  cord.  This 
is  due  first  to  the  great  variation  in  weight  between  wood  of  different 
species,  a  variation  which  would  be  equalized  as  to  'price  if  equal  weights 
regardless  of  bulk  commanded  approximately  the  same  price,  and  second, 
to  the  gi-eat  difference  in  weight  between  green  and  air-dried  wood. 
If  sold  by  weight,  dealers  would  endeavor  to  sell  the  wood  as  green  as 
possible.  Green  wood  has  less  net  fuel  value  per  pound,  not  only 
because  the  purchaser  pays  for  water  instead  of  net  dry  weight,  but  also 
because  each  pound  of  dry  wood  has  to  generate  heat  enough  to  vaporize 
all  the  water  in  the  wood  and  only  the  surplus  heat  is  given  off. 

But  for  dead  dry  juniper  or  pinon  or  mesquite  roots  or  for  well- 
seasoned  woods  difficult  to  measure  in  bulk,  weight  is  practically  the 
universal  standard.  Dealers  customarily  deliver  from  200  to  400 
pounds  less  of  weight  per  cord  than  the  actual  weight  of  an  average 
cord  of  such  wood.  For  instance,  pinon  should  weigh  3000  pounds 
per  cord,  but  it  is  often  sold  at  2000  pounds  per  cord.  It  would  be 
better  to  substitute  weight  altogether  and  not  maintain  the  pretense 
of  delivering  a  cord  by  measure.  This  would  place  the  dry  wood 
on  the  same  basis  as  coal. 

Air-dried  wood  still  contains  from  15  to  20  per  cent  moisture.  The 
variation  in  per  cent  of  water  in  green  wood  compared  with  dry  wood 
is  extreme,  as  illustrated  by  Table  LXXXIII  (Appendix  C). 

References 

Factors  Influencing  the  Volume  of  Solid  Wood  in  the  Cord,  Raphael  Zon,  Forestry- 
Quarterly,  Vol.  I,  1903,  p.  126. 

Untcrsuchungen  liber  die  Festgehalt  und  das  Gewicht  des  Schichtholzes  und  der 
Rinde,  F.  Baur,  Augsburg,  1879. 

Mitteilungen  aus  dcm  Forstlichen  Versuchswcsen  Oesterreiches,  1877-1881,  Report 
by  Von  Seckendorff. 

Paper  Birch  in  the  Northeast,  S.  T.  Dana,  U.  S.  Forest  Service  Circular  163,  1909, 
pp.  34-35. 

1  In  Forest  Mensuration  of  White  Pine  in  Ma.ssachusetts,  p.  45,  ratios  for  white 
pine  1-inch  lumber  are  given,  running  from  488  board  feet  for  5-inch  logs  to  730 
board  feet  for  24-inch  logs,  measured  at  middle  of  log  outside  bark. 


138  STACKED  OR  CORD  iMEASURE 

Second  Growth  Hardwoods  in  Connecticut,   E.   H.   Frothingham,   U.   S.   Forest 

Service  Bui.  96,  1912,  pp.  63-64. 
The  Northern  Hardwood   Forest,  E.  H.  Frothingham,  Bui.  285,  U.  S.  Dept.  Agr., 

1915,  p.  62. 
Balsam  Fu-,  Bui.  55,  U.  S.  Dept.  Agr.,  1914,  p.  52. 
Measuring  Cordwood  in  Short  Lengths,  R.  C.  Hawley,  Journal  of  Forestry,  Vol. 

XVn.  1919,  p.  312. 
A  Practical  Xylometer  for  Cross-ties,  F.  Dunlap,  Forestry  Quarterly,  Vol.  Ill,  1905, 

p.  335. 
A  Practical  Xylometer,  J.  S.  Illick,  Journal  of  Forestry,  Vol.  XV,  1917,  p  859. 


PART  II 
THE  MEASUREMENT  OF  STANDING  TIMBER 


CHAPTER  X 
UNITS  OF  MEASUREMENT  FOR  STANDING  TIMBER 

116.  Board  Feet — Basis  of  Application.  The  value  of  standing 
timber  must  be  determined  as  a  basis  for  sale  either  of  the  timber  alone, 
or  of  the  land  and  the  timber.  This  value  depends  upon  the  quantity 
of  wood  which  may  be  cut  from  the  tract,  but  still  more  upon  its  value 
per  unit  of  volume.  As  set  forth  in  Part  I,  the  contents  of  logs  and 
trees  in  North  America  are  expressed,  whenever  possible,  in  terms  of 
the  final  products  instead  of  by  cubic  volume  as  in  Europe.  Standing 
timber,  therefore,  is  commonly  measured  in  terms  of  board  feet,  cords, 
or  pieces  such  as  poles,  piles  or  railroad  ties  and  is  rarely  expressed  as 
cubic  feet,  since  it  is  seldom  sold  on  that  basis.  If  estimated  by  cubic 
feet,  the  contents  are  usually  converted  into  their  equivalent  in  cords. 

When  the  board-foot  unit  is  used  in  timber  estimating,  the  basis 
of  determining  the  contents  of  the  standing  timber  must  be  identical 
with  that  on  which  the  timber  is  to  be  sold  when  cut. 

If  manufactured  on  the  tract  by  small  portable  mills,  the  actual 
sawed  output  in  lumber,  the  mUl  cut,  furnishes  this  basis.  When 
round-edged  lumber  is  sawed  and  small  trees  utilized  to  a  small  top 
diameter  (§  21)  the  yield  in  board  measure  maj^  be  100  per  cent  greater 
than  when  the  "  sawlog  "-sized  timber  only  is  merchantable,  as  in 
large  logging  operations. 

When  scaled  and  sold  in  the  log,  the  estimated  contents  of  the  stand, 
before  cutting,  should  coincide,  not  with  the  sawed  output,  but  with 
the  log  scale.  Since  different  log  rules  give  different  scaled  contents 
for  the  same  logs,  the  estimate  must  be  based  upon  the  log  rule  which 
will  be  used  to  scale  the  logs.  Hence  an  estimate  made  on  the  basis 
of  the  Doyle  rule  will  differ  from  one  based  on  the  Scribner  rule  or  the 
International  rule.  In  aU  large  logging  operations  where  the  logs 
are  transported  some  distance  to  the  mill,  timber  is  estimated  solely 
on  the  basis  of  the  standard  log  rule  in  use. 

139 


140  UNITS  OF  MEASUREMENT  FOR  STANDING  TIMBER 

Local  log  rules  based  on  mill  tallies  may  be  substituted  for  the  sawed 
product  as  the  basis  of  estimating  timber  on  small  tracts. 

No  such  difficulties  affect  the  estimating  of  timber  in  terms  of  cubic 
units  or  cords,  which  include  the  entire  contents  of  all  trees  within  the 
merchantable  limits  of  size,  up  to  the  merchantable  limit  in  the  tops. 

117.  The  Piece.  Poles  or  piling  usually  comprise  the  entire  mer- 
chantable portion  of  the  trees  which  produce  them,  but  can  only  be 
cut  from  trees  having  the  specified  dimensions.  Familiarity  with  these 
specifications  enables  the  cruiser  to  count  the  number  of  pieces  in  the 
stand,  and  to  tally  them  in  separate  classes.  The  same  method  *may 
be  used  in  estimating  standard  railroad  ties,  but  in  this  case  the  number 
of  ties  in  each  tree  must  be  counted  separately  in  accordance  with  the 
five  standard  grades  (Appendix  B,  §  369).  Where  the  tree  is  large 
enough  to  produce  more  than  one  standard  tie  from  a  single  8-  or  8|- 
foot  length,  the  cruiser  must  rely  either  on  his  knowledge  of  the  contents 
of  the  bolt  in  ties,  or  refer  to  a  volume  table  for  piece  products  (§  162). 
He  gets  the  total  tie  count  for  the  tree  by  adding  the  contents  of  each 
separate  bolt,  up  to  a  point  where  the  diameter  is  too  small  to  produce 
another  standard  tie.  Posts  are  counted  in  the  same  way  but,  owing 
to  their  smaller  value  and  greater  number,  the  count  is  usually  more 
or  less  of  an  approximation.  The  same  system  may  be  used,  if  required, 
in  estimating  the  quantity  of  mine  timbers  and  mine  ties  in  a  stand. 
Products  such  as  stave  bolts,  which  demand  a  high  quality  of  timber 
practically  free  from  knots  and  all  forms  of  defect,  and  are  of  small 
size,  introduce  two  features  common  to  estimating  in  board  feet,  namely, 
a  table  of  volumes,  and  discounts  for  cull.  Stave  timber  for  staves 
of  given  sizes  may  be  estimated  by  knowing  how  many  staves  may 
be  cut  from  bolts  of  given  dimensions.  The  number  and  size  of  the 
cuts  in  each  tree  will  give  their  sound  contents,  from  which  are  deducted 
all  visible  defects.  A  liberal  allowance  is  also  rnade  for  invisible  defects 
in  the  interior  of  the  tree. 

Since  only  a  portion  of  a  stand  is  converted  into  these  forms  of 
product,  the  estimating  of  piece  products  may  be  only  a  part  of  a 
general  estimate  in  which  the  remainder  of  the  stand  is  measured 
either  for  logs  or  for  cord  wood. 

118.  Choice  of  Units  in  Estimating  Timber.  Methods  of  timber 
estimating  are  determined  by  the  cruiser's  choice  as  to  whether  he  will 
deal  directly  with  one  of  four  units,  namely,  the  stand  as  a  whole,  the 
individual  tree,  the  individual  log,  or  the  piece  (§  117).  Any  one  of 
the  first  three  methods  may  be  used  when  the  volume  of  the  stand 
is  expressed  in  terms  of  cubic  units,  or  in  board  feet.  If  the  tree  or 
log  is  not  used,  the  stand  is  considered  as  a  whole  and  a  direct  guess 
or  estimate  is  made  of  its  total  contents  (§  206).     If  the  tree  or  the  log 


THE  LOG  AS  THE  UNIT  IN  ESTIMATING  141 

is  used,  the  method  requires  a  count  and  tally  by  different  sizes,  and 
gives  rise  to  many  systems  of  estimating,  depending  on  whether  the 
entire  area  or  only  a  portion  of  it  is  to  be  counted. 

119.  The  Log  as  the  Unit  in  Estimating.  When  the  product  to 
be  estimated  in  board  feet  is  lumber,  the  log  becomes  a  convenient 
and  much  used  unit  for  estimating.  Lumber  is  measured  or  scaled 
in  the  log  bj^  a  given  log  rule.  The  contents  is  given  for  logs  according 
to  their  diameter  inside  bark  at  small  end,  and  length.  Hence  a  tally 
of  the  top  diameter  inside  bark  and  the  length  of  each  log  in  a  tree, 
and  the  use  of  a  log  rule,  will  give  the  board-foot  contents  of  the  tree. 
If  every  log  is  so  tallied  the  stand  is  measured  by  merely  totaling  the 
contents  of  the  logs,  without  computing  the  volume  of  separate  trees. 

No  further  volume  basis  is  needed  in  this  method  than  the  log 
rule  or  scale  stick.  But  the  cruiser  must  know  the  amount  of  taper 
in  each  log,  the  thickness  of  bark  to  be  deducted,  and  the  log  length 
to  use  in  estimating. 

Log  lengths  as  actually  cut  are  determined  by  the  crooks  and  other 
peculiarities  of  each  tree.  But  in  estimating  timber,  these  variable 
log  lengths  are  disregarded  and  a  uniform  or  standard  length  is  adopted 
which  conforms  within  reasonable  limits  to  the  average  log  length  most 
frequently  used.  For  eastern  conifers  this  is  16  feet,  while  hardwoods 
may  require  12  feet.  On  the  Pacific  Coast,  32  feet  is  used  by  many 
cruisers.  If  logs  when  cut  average  shorter  than  the  standard,  the 
scaled  contents  of  the  logs  will  over-run  the  estimate,  while  if  longer 
logs  are  cut,  the  scale  will  fall  short  (§  83). 

The  method  of  tallying  the  logs  in  a  tree  is  as  follows: 

1.  Estimate  or  measure  the  diameter  of  the  butt  log  either  at  the 
stump,  at  4|  feet  from  the  ground,  or  at  1  foot  above  the  butt  swell, 
choosing  one  of  these  methods  to  the  exclusion  of  the  others.  Foresters 
use  4^  feet  as  the  accepted  standard. 

2.  Deduct  the  double  thickness  of  bark  to  obtain  the  diameter, 
inside  bark,  at  this  point. 

3.  Estimate  the  number  of  inches  to  deduct  from  this  diameter  for 
taper,  to  obtain  the  diameter  at  the  top  of  the  first  log  of  standard 
length.     This  and  all  upper  estimates  of  diameter  are  inside  the  bark. 

4.  Estimate  by  eye  the  number  of  standard  logs  in  the  tree,  to  the 
limit  of  merchantable  size.  The  top  diameter  at  this  point  should 
be  known  or  estimated,  inside  bark. 

5.  From  the  diameter  of  the  top  of  the  first  log,  inside  bark,  deduct 
successively  the  estimated  taper,  in  inches,  to  obtain  the  diameter 
of  each  remaining  log. 

An  alternate  plan  frequently  used  is  to  measure  the  diameter  out- 
side bark  at  the  butt,  or  at  4^  feet,  subtract  the  taper  outside  bark 


142  UNITS  OF  MEASUREMENT  FOR  STANDING  TIMBER 

for  the  first  log,  and  then  subtract  the  estimated  thickness  of  bark  at 
this  point,  or  at  the  top  of  the  first  log  instead  of  at  the  butt. 

A  third  plan  is  to  estimate  directly  the  diameter,  minus  bark,  at 
the  top  of  the  first  log,  without  measuring  the  butt.  Or,  a  table  may 
be  prepared  showing  diameter,  inside  bark,  at  the  top  of  the  first  log, 
for  trees  of  different  diameters  at  4^  feet. 

Each  of  these  plans  aims  to  secure  the  diameter,  inside  bark,  at 
the  top  of  the  butt  log  as  the  basis  from  which  to  figure  the  top  diam- 
eters of  the  remaining  logs. 

The  eye  may  be  trained  to  estimate  log  lengths  and  taper  by  the  use  of  a  pole 
with  a  cross-piece  at  the  top,  marked  off  in  inches.  The  length  of  pole  (about 
12  feet)  permits  holding  the  cross-piece  at  the  height  of  the  top  of  the  first  log 
plus  an  allowance  for  height  of  stump.  By  comparison  with  this  measured  length, 
the  number  of  logs  in  the  upper  bole  may  be  estimated  by  eye.  By  measuring 
the  tree  at  4^  feet,  and  reading  the  cross-arm,  the  taper,  in  inches,  for  the  butt 
log  is  shown.  Bark  thickness  is  then  subtracted  as  determined  for  the  species 
by  observation  on  felled  trees  or  logs.  This  varies  for  the  top  of  the  butt  log, 
from  2  inches  to  1  inch  for  most  species.  The  total  number  of  logs,  to  the  limit 
of  merchantable  diameter,  gives  the  total  taper  to  that  point.  If  6  inches  is  the 
merchantable  limit,  this  diameter,  subtracted  from  that  of  the  top  of  the  butt 
log  inside  bark,  indicates  the  taper  to  be  distributed  between  the  upper  logs. 
Bearing  in  mind  the  tendency  to  more  rapid  taper  in  the  crown,  the  actual  taper 
of  each  log  can  be  approximated  with  reasonable  accuracy  and  its  diameter  inside 
bark  recorded.  Two  men  usually  work  together  in  this  practice,  or  in  training. 
One  man  may  use  the  method  if  the  pole  is  made  long  enough  to  be  leaned  against 
the  tree  (17  to  18  feet),  while  he  gets  far  enough  off  to  judge  its  height. 

This  method  assumes  that  the  eye  can  be  trained  to  judge  diameters 
to  an  inch,  at  varying  distances  and  heights  above  ground.  But  in 
timber  estimating  only  the  general  character  of  the  tree  is  noted,  and 
its  total  height,  or  the  number  of  standard-length  logs.  The  taper 
of  the  successive  logs  is  obtained  from  measuring  the  diameters  of 
felled  or  wind-thrown  trees  of  the  same  character  as  the  standing  timber. 
The  taper  for  a  16-foot  log  may  vary  from  1  to  10  inches  or  even  more, 
depending  on  site,  density  of  stand,  butt  diameter,  and  position  of  the 
log  in  the  tree. 

Many  cruisers  assume  that  once  the  difference  in  diameter  between 
the  top  of  the  second  and  the  first  log  is  ascertained  or  assumed,  each 
successive  upper  log  will  have  an  equal  taper,  giving  to  the  tree  a  uniform 
taper  per  log  of  2,  3  or  more  inches.  They  know  that  the  butt  log 
will  taper  more  rapidly  than  the  second  log,  but  the  above  practice 
ignores  the  taper  of  the  butt  log. 

They  also  know  that  as  soon  as  the  green  crown  is  encountered, 
the  taper  per  log  again  increases.  But  in  regions  where  rough  logs 
in  the  crown  are  seldom  utilized,  this  assumption  of  a  uniform  taper 
for  the  second  and  higher  logs  in  the  bole  is  approximately  correct. 


LOG  RUN  OR  AVERAGE  LOG  METHOD  143 

Where  greater  accuracy  is  sought,  and  especially,  where  the  diameter 
of  the  tree  is  measured  at  4J  feet  rather  than  guessed  at,  tables  may 
be  compiled  from  the  actual  measurement  of  the  upper  diameters  of 
felled  trees  which  show  the  average  taper  for  each  log,  for  trees  of  given 
diameter  and  height,  and  with  the  width  of  bark  actually  measured 
and  deducted  for  the  top  of  the  butt  log.  These  tables  will  enable 
the  cruiser  to  tally  the  sizes  of  his  logs  without  relying  on  his  eye  for 
more  than  the  determination  of  total  height  or  number  of  logs. 

Log  grades  (§87),  when  used  in  timber  estimating,  require  the  tally 
of  the  top  diameter  of  the  logs,  separated  into  grades.  This  permits 
of  the  separate  totaling  of  volume  in  each  log  grade  on  the  tract. 

120.  Log  Run  or  Average  Log  Method.  The  tallying  of  the  actual 
size  of  every  log  on  a  tract  is  so  slow  and  expensive  that  it  is  possible 
only  when  the  timber  is  large  and  scattered.  Woodsmen,  who  use  the 
log  as  the  unit  of  estimating,  do  not  usually  tally  any  sizes  but  obtain 
the  total  number  of  logs  on  the  area  by  five  steps,  namely: 

1.  A  count  of  the  trees. 

2.  Decision  as  to  the  average  number  of  logs  per  tree.  This  may 
be  in  halves  or  even  quarters,  as  3j  logs  per  tree,  referring  of  course 
to  the  standard  length  adopted  for  estimating. 

3.  The  board-foot  contents  of  an  average  log. 

The  last  point  is  based  on  familiarity  with  the  results  of  scaling  logs 
cut  from  similar  timber,  and  the  cruiser  expresses  it  in  terms  of  "  log 
run  "  or  number  of  logs  required  to  scale  1000  board-feet  of  lumber, 
as  illustrated  by  the  following  figures : 

Log  Run.  Contents  of  Average  Log. 

2  per  1000  board  feet.  500  board  feet. 

5  per  1000  board  feet.  200  board  feet. 

10  per  1000  board  feet.  100  board  feet. 

20  per  1000  board  feet.  50  board  feet. 

40  per  1000  board  feet.  25  board  feet. 

The  "  log  run  "  increases  as  the  average  log  content  diminishes. 
Knowing  the  log  run,  or  guessing  at  it,  the  estimate  in  board  feet  is 
obtained  by: 

4.  Multiplying  the  total  number  of  trees  by  the  number  of  logs  per 
tree. 

5.  Dividing  the  total  number  of  logs  by  the  log  run  or  number  of 
logs  in  1000  board  feet  of  lumber. 

This  method  was  used  by  many  old-time  cruisers  in  the  Lake  States 
region  to  the  exclusion  of  all  others.  When  old  and  young,  or  large 
and  small  timber  is  found  on  the  same  tract,  separate  classes  are  usually 
made  in  the  count. 


144  UNITS  OF  MEASUREMENT  FOR  STANDING  TIMBER 

121.  The  Tree  as  a  Unit  in  Estimating.     Volume  Tables.     The 

necessity  for  combined  speed  and  accurac}'  to  reduce  the  cost  and 
increase  the  reliability  of  timber  estimates  has  led  to  the  almost  uni- 
versal substitution  of  the  tree  unit  for  the  log  unit.  Instead  of  entering 
the  size  of  each  log  separately,  the  dimensions  of  the  entire  tree  are 
noted. 

This  requires  that  the  volume  of  entire  trees  of  the  sizes  tallied  be 
previously  known.  The  sum  of  the  volume  of  the  logs  which  they  con- 
tain gives  this  information.  A  table,  in  which  the  average  volume 
of  trees  of  given  sizes  is  shown,  is  termed  a  volume  table,  in  contrast 
to  a  log  rule  or  log  table,  which  gives  only  the  contents  of  single  logs 
and  never  that  of  entire  trees. 

To  avoid  confusion  in  these  terms,  it  should  be  noted  that  the  stand- 
ard definitions  are: 

For  a  log-volume  table — the  term,  Log  Rule. 

For  a  tree-volume  table — the  term.  Volume  Table. 

The  latter  term  should  never  be  used  by  foresters  to  mean  the 
contents  of  logs,  although  the  term  log  table  may  be  used.  The  term 
"  volume  table  "  always  refers  to  the  volume  of  trees,  being  substituted 
for  the  longer  descriptive  term.  Tree-volume  Table. 

Timber  cruisers  were  slow  to  see  the  advantage  of  thus  tabulating 
or  summing  up  the  total  volumes  of  trees  in  systematic  form.  They 
either  adhered  to  the  log  basis,  or  in  the  instances  when  they  used  the 
tree  volume  as  a  unit,  merely  calculated  this  for  "  average  "  trees  by 
mentally  summing  up  the  contents  of  the  logs  in  individual  trees,  and 
from,  the  general  knowledge  thus  obtained,  assuming  that  trees  in  a 
given  stand  averaged  or  "  ran  "  a  certain  volume  per  tree.  This  method 
was  universally  used  in  the  South,  where  the  Doyle  rule  readily  lent 
itself  to  quick  mental  computations  of  the  contents  of  16-foot  logs 
(subtract  4  inches  from  the  diameter  inside  bark,  and  square  the 
remainder  for  board-foot  contents  of  log,  §  65) .  The  total  count  of 
trees,  multiplied  by  the  average  contents  per  tree,  gave  the  estimate. 

122.  Volume  Tables  Based  on  Standard  Tapers  per  Log.  **  Uni- 
versal "  Volume  Tables.  In  the  Pacific  Northwest,  the  great  height 
of  the  trees  and  consequent  large  number  of  logs  in  each  tree,  and 
the  relatively  few  trees  per  acre,  each  with  a  large  volume,  soon  brought 
a  realization  of  the  need  for  substituting  the  tree  unit  for  the  log.  The 
difficulty  of  mentally  computing  the  contents  of  trees  varying  so  widely 
in  volume  forced  the  use  of  the  volume  table,  in  which  was  recorded 
the  total  volumes  of  trees  of  all  sizes.  These  cruisers'  volume  tables, 
of  which  several  have  been  constructed,  are,  in  most  instances,  based 
on  the  principle  of  uniform  taper  per  log,  varying  fi'om  2  to  10  inches. 
The  contents  of  successive  logs,  as  scaled  by  the  accepted  log  rule, 


VOLUME  TABLES  BASED  ON  STANDARD  TAPERS   PER  LOG      145 

diminishing  in  top  diameter  by  the  indicated  taper,  are  totaled,  and 
the  sum  taken  as  the  vokime  of  the  tree.  These  computations  do  not 
require  the  measurement  of  the  tree  but  are  performed  in  the  office 
from  the  log  rule. 

The  volumes  in  such  a  table  are  the  scaled  contents  of  logs  by  a  given  log  rule, 
and  will  apply  only  to  regions  where  this  same  log  rule  is  used.  But  it  is  a  simple 
matter  to  compute  a  new  table  for  any  other  log  rule,  by  the  same  method,  since 
no  field  work  is  required.  Wherever  the  log  rule  is  the  standard,  such  a  table  is 
applied  to  all  species,  types  and  character  of  trees,  and  in  this  sense  is  universal. 
The  assumption  underlying  such  a  table  is  that  the  merchantable  portion  of  all 
trees  have  the  shape  of  the  frustums  of  cones,  hence  the  determination  of  the  three 
factors,  average  taper  per  log,  diameter  at  top  of  first  log,  and  number  of  logs  in 
the  tree,  determine  the  scaled  contents  of  the  tree  as  given  in  the  table.  As  shown 
below,  the  assumption  is  not  correct. 

In  applying  this  table,  these  cruisers  seldom  attempt  to  tally  the  dimensions 
of  each  tree.  The  trees  are  counted,  separately  by  species,  and  also  by  classes, 
as  large,  medium  or  small.  Then  the  average  diameter,  average  number  of  logs  per 
tree,  and  average  taper  per  log  is  decided  on  usually  by  guess  or  by  judgment. 
The  volume  table  merely  serves  to  give  the  assumed  volume  of  a  tree  of  this 
diameter,  height  and  taper.  The  estimate  or  total  for  the  species  is  obtained  by 
multiplying  this  volume  by  the  tree  count. 

The  advantages  of  obtaining  a  universal  and  elastic  volume  table,  applicable  to 
any  species,  region  and  character  of  timbers  are  self-evident.  The  defects  in 
uniform  or  universal  volume  tables  based  on  the  frustums  of  cones  are: 

1.  The  form  of  the  average  tree  of  any  species,  when  the  merchantable  portion 
only  is  considered,  resembles  more  nearly  the  frustum  of  a  paraboloid  than  that  of 
a  cone  (§  26).  While  the  merchantable  portion  may  be  treated  as  the  frustum  of 
a  cone,  yet  investigation  shows  that  the  average  volume  of  trees  of  different  species 
and  diameters  is  usually  either  less  or  greater  than  that  assumed  by  the  table. 
This  possible  error  is  consistently  neglected. 

2.  For  accurate  application,  the  universal  table  requires  the  determination  of 
three  dimensions  for  every  tree  whose  volume  is  to  be  ascertained,  namely,  diam- 
eter, height  and  taper.  A  tally  of  every  tree  by  diameter  and  height  is  possible, 
but  the  separation  of  a  third  factor,  tree  by  tree,  makes  the  tally  too  complicated, 
and  requires  the  substitution  of  average  tapers  for  a  species,  or  for  groups  of 
diameters  as  indicated  above.  But  the  trees  in  any  given  stand  or  area  never  taper 
uniformly.  The  larger  trees  have  the  greater  taper.  Those  growing  in  dense 
stands  have  the  least.  No  average  can  be  found  which  will  apply  even  to  the 
trees  of  one  diameter  class,  much  less  to  trees  of  all  classes.  The  assumption  of  a 
definite  taper  for  the  trees  on  a  plot  will  tend  to  over-estimate  the  volume  of  trees 
larger  than  the  selected  average  tree,  and  under-estimate  those  of  small  diameter. 
Whether  these  errors  balance  depends  more  on  luck  than  on  skill. 

3.  The  use  of  such  a  table  presupposes  the  system' of  counting  rather  than  of 
tallying  each  tree,  and  assumes  the  risk  of  error  in  selecting,  largely  by  eye,  an 
average  tree  which,  when  multiplied  by  the  count,  will  give  the  approximate 
estimate.  It  does  not  lend  itself  to  an  accurate  inventory  of  the  timber,  tree 
by  tree,  in  which  the  diameter  and  merchantable  length  of  each  tree  is 
recorded. 

4.  Since  such  tables  assume  that  upper  diameters  differ  by  gradations  of  1  inch 
per  log,  a  4-log  tree  will  show  top  diameters  in  the  table  differing  by  4-inch  classes. 


146 


UNITS  OF  MEASUREMENT  FOR  STANDING  TIMBER 


while  the  average  taper  may  be  somewhere  between  these  Umits  and  the  volume 
be  given  incorrectly  by  either  the  upper  or  lower  class.  A  tree  20  inches  at  the  top 
of  the  first  log  will  be  classed  as  having  a  taper  per  log  of  1  inch,  2  inches  or  3  inches. 
At  the  top  of  the  fourth  log,  the  first  tree  will  measure  17  inches,  the  second  tree, 
14  inches,  and  the  third,  11  inches.  The  actual  average  top  diameter  may  fall  at 
12  inches  or  at  15  inches. 

123.  Substitution  of  Mill  Factor  for  Log  Rules  in  Universal  Tables.  In  the 
above  tables,  the  contents  of  the  logs  are  determined  by  the  standard  log  rule 
used  in  scaling.  Dr.  C.  A.  Schenck  substituted  what  is  termed  the  mill  factor 
for  the  log  rule,  thus  basing  the  volume  of  the  tree  upon  the  sawed  output  (§  116). 
Assuming,  as  a  basis,  that  the  cubic  contents  of  the  cyhnder  measured  at  the  small 
end  of  the  log,  when  multiplied  by  12,  gives  the  maximum  board-foot  contents 
(§  12),  the  waste  for  slabbing,  edging  and  saw  kerf,  independent  of  taper,  which  is 
not  considered,  will  reduce  this  output  to  from  8  to  5  board  feet  per  cubic  foot. 
The  per  cents  of  cubic  contents  of  the  cylinder  based  on  small  end  of  log,  which 
these  mill  factors  represent  are; 


Scaled  contents  of 

Cubic 

nearest  equivalent 

Mill  factor 

contents. 

log  rule 
(Table  II,  §38). 

Per  cent 

Per  cent 

8 

661 

Vermont  (63.4) 

7 

m 

Calcasieu  (57.8) 

6 

50 

Orange  River  (50.9) 

5 

41f 

Delaware  (42.4) 

An  example  of  these  mill-factor  tables  is  given  on  page  147,  for  logs  16  feet  long: 

To  determine  these  values  the  volume  in  cubic  feet  of  the  cylinder  was  mul- 
tiplied by  5,  6,  7  and  8  respectively.  These  tables  give  the  cruiser  the  oppor- 
tunity to  substitute  a  fixed  per  cent  of  utilization,  as  indicated  above,  for  a  log 
rule.  The  other  three  variables  remain  the  same,  namely,  diameter,  number  of 
logs  and  rate  of  taper  per  log. 

It  is  assumed  that  the  mill  factor  can  be  chosen  to  suit  the  local  conditions  of 
milling,  the  factor  8  or  665  per  cent  representing  the  use  of  band  saws  in  large  mills, 
while  the  factor  5  approximates  the  conditions  in  small  local  circular-saw  hard- 
wood mills,  thus  making  the  cruiser  independent  of  log  rules.  This  apparent 
advantage  is  nulhfied  by  two  serious  defects:  First,  the  taper  of  the  log  is  neglected, 
and  this  frequently  produces  a  mill  factor  of  10  for  large  logs.  Second,  the  board- 
foot  contents  is  assumed  to  vary  directly  as  the  cubic  contents,  so  that  the  tables 
force  the  use  of  log  rules  based  on  cubic  rather  than  sawed  products  and  introduce 
the  errors  of  this  method.  Mill  factors  increase  directly  with  the  average  diameter 
of  the  log  independent  of  mill  practice.  It  is  not  sufficient  merely  to  know  the 
general  character  of  the  milling,  but  the  sizes  of  the  timber  must  also  be  known. 
An  average  mill  factor  based  on  both  of  these  variables  may  be  seriously  in  error 
and  the  use  of  different  mill  factors  for  logs  or  trees  of  different  sizes  is  apparently 
necessary  to  secure  accuracy.  The  use  of  these  tables  is  therefore  not  as  satis- 
factory as  their  apparent  simplicity  seems  to  indicate. 


VOLUME  TABLES  BASED  ON  ACTUAL  VOLUMES  OF  TREES   147 

TABLE  XXVI 

A  Portion  of  a  Volume  Table  Based  on  Mill  Factors 
Trees  measuring  9  inches  at  top  of  first  16-foot  log,  inside  bark 


Mill  factor 

Taper  per  Log 

16-foot 

1  inch 

2  inches 

3  inches 

4  inches 

logs 

Board  feet 

5 

31 

31 

31 

31 

1 

6 

37 

37 

37 

37 

7 

43 

43 

43 

43 

8 

57 

57 

57 

57 

5 

55 

49 

45 

40 

2 

6 

66 

59 

54 

48 

7 

77 

69 

62 

57 

8 

89 

79 

71 

65 

5 

74 

59 

3 

6 

89 

71 

7 

104 

83 

8 

118 

95 

•• 

124.  Volume  Tables  Based  on  Actual  Volumes  of  Trees.  Volume 
tables  as  used  by  foresters  arc  based  on  the  measurement  of  the  actual 
contents  of  entire  trees,  and  not  upon  assumed  regular  taper  or  conical 
form.     The  tree  contents  or  volume  table  may  give, 

Entire  cubic  contents  of  stem,  with  bark,  or  without  bark. 
Merchantable,  cubic   contents  of  stem,   or  of  stem  and  larger 

branches,  with  or  without  bark. 
Merchanta])le  contents  of  stem  in  terms  of 
Board  feet 

By  a  given  log  rule. 

By  mill  tally,  under  given  conditions  of  sawing. 
Other  units,  such  as 
Standard  cross  ties. 
Poles,  or  posts. 
Staves  or  headings. 
Cords,  usually  converted  from  cubic  feet. 


148  UNITS  OF  MEASUREMENT  FOR  STANDING  TIMBER 

Combination  Volume  Tables  giving  the  merchantable  volume  in 
Ties,  and  residual  cords. 

Board  feet,  and  residual  cords  and  other  combinations. 
Graded  Volume  Tables,  giving  the  volume  in 
Board  feet,  by  lumber  grades. 
Logs,  by  log  grades. 

The  use  of  the  last-named  tj'pe  has  not  yet  been  attempted. 

Volume  tables  of  this  character  make  possible  the  tallying  of  every 
tree,  eliminate  the  risk  of  averaging  the  dimensions  or  volume  of  trees 
counted,  and  require  of  the  cruiser  only  the  recording  of  diameters 
and  of  heights,  and  discounts  for  defect. 

Since  trees  vary  so  widely  in  form,  height  and  taper,  and  the  table 
is  implicitly  relied  on  to  give  correctly  the  variable  volumes  caused 
by  these  factors,  without  measuring  the  taper,  the  use  of  such  tables 
and  their  reliability  or  accuracy  must  be  thoroughly  understood,  or 
it  may  easily  lead  to  errors  of  greater  magnitude  than  those  incurred 
by  an  experienced  cruiser  using  the  universal  "  taper  "  table  for  volumes 
(§  149). 

The  greatest  drawback  in  the  use  of  specific  volume  tables  is  the 
number  of  tables  required,  and  the  cost  of  their  preparation.  Species 
may  differ  from  each  other  in  form  or  bark  thickness,  so  as  to  require 
separate  volume  tables.  Substitution  of  a  table  made  for  one  species 
for  use  with  a  different  species  is  justifiable  only  when  research  has 
shown  the  two  species  to  possess  the  same  bark  thickness  and  average 
form. 

Tables  made  for  one  unit  of  measure,  or  even  for  a  given  log  rule 
are  not  serviceable  for  a  different  unit  or  log  rule.  Tables  of  merchant- 
able volume,  accurate  for  a  given  standard  of  tree  utilization,  become 
obsolete  when  a  closer  standard  is  adopted.  For  these  reasons,  and 
owing  to  the  great  number  of  species,  range  of  conditions,  difference  in 
log  rules,  and  variety  of  products,  the  cruiser  entering  a  new  region 
is  usually  confronted  with  a  lack  of  tables,  and  is  driven  to  adopt 
either  the  universal  taper  system,  or  the  log,  as  his  means  of  estimating 
volumes.  The  adoption  of  a  universal  cubic-foot  basis  for  volume 
would  greatly  simplify  the  problem  of  volume  tables. 

125.  The  Point  of  Measurement  of  Diameters  in  Volume  Tables. 
Either  of  the  above  types  of  volume  table  shows  volumes  for  trees  of 
given  diameters  and  heights.  The  diameter  must  be  measured  near 
the  base  of  the  tree,  where  it  can  be  reached  with  calipers  or  tape. 
But  there  is  no  regularity  about  the  flare  of  the  butts  of  trees,  for  this 
is  determined  by  exposure  to  wind  strain,  by  the  size  of  the  bole,  the 
site  and  the  species.  Butt  swelling  increases  more  rapidly  with  age 
than  does  the  diameter  of  the  bole,  so  that  the  older  and  larger  the  tree, 


DIAMETERS  IN  VOLUME  TABLES 


149 


the  more  pronounced  this  swelling,  and  the  further  it  extends  up  the 
trunk.  Tree  volumes  must  be  averaged  on  the  basis  of  their  diameter 
in  inches.  If  this  diameter  is  taken  at  some  point  on  the  butt  swelling, 
a  tree  with  a  rapid  butt  swelhng  will  have  a  far  smaller  volume  than 
one  of  the  same  stump  diameter  and  a  gradual  swelling,  as  is  illus- 
trated in  Fig.  24  by  trees  A  and  B.  But  if  these  diameters  were  taken 
at  a  point  above  the  butt  swelhng  the  two  trees  would  properly  fall 
into  different  classes.  Since  it  is  necessary  to  put  in  a  single  class 
trees  whose  volumes  are  as  nearly  similar  as  possible  (trees  A  and  C), 
the  practice  of  classifying  these  trees  by  their  diameter  on  the  stump 
is  inaccurate.     The  height  of  stump  itself  is  also  a  variable.     Tables 


^ 


A  B  C 

Fig.  24. — Comparison  of  stump  height  and  breast  height  as  points  of  measurement 
to  determine  the  diameter  of  standing  trees. 


based  upon  "  diameter  at  the  stump,"  which  do  not  indicate  at  what 
height  this  diameter  is  measured,  are  difficult  to  apply  and  unreliable. 
For  very  large  trees  with  excessive  butt  swelling  such  as  cypress, 
or  many  West  Coast  species,  the  diameter  classes  should  be  based 
upon  measurements  taken  above  this  swelling.  A  standard  form  of 
universal  table  used  on  the  Pacific  Coast  is  based  on  a  butt  measure- 
ment to  be  taken  1  foot  above  the  point  where  the  butt  swelling  ceases. 
The  disadvantage  of  measuring  at  a  variable  height  is  considered  as 
offset  by  the  merit  of  avoiding  this  variable  factor  of  butt  swelling. 
In  cypress,  one  tj^pical  table  was  based  on  diameter  at  20  feet  from' 
the  ground  and  cruisers  customarily  estimate  cypress  trees  from  the 
diameter  obtained  above  the  butt  swelling. 


150  UNITS  OF  MEASUREMENT  FOR  STANDING  TIMBER 

For  most  species,  the  point  4^  feet  above  ground  has  been  accepted 
by  foresters  for  measurement  of  diameter  as  it  falls  above  the  swell- 
ing and  at  a  convenient  height  for  use  of  calipers.  This  height  is  also 
used  in  England  and  India.  In  Continental  Europe,  1.3  meters,  or 
4.3  feet,  is  the  standard  height. 

This  measurement  at  4|  feet  is  termed  diameter  breast  high,  and 
is  abbreviated  both  in  speech  and  record  to  D.B.H.  Measurement 
outside  bark  is  always  indicated  by  the  abbreviation. 

In  the  Philippines  and  other  tropical  countries  it  will  be  impossible 
to  use  a  similar  height  for  many  species  owing  to  the  development 
of  buttresses  on  the  trunks.  Such  species  will  probably  have  to  be 
measured  either  above  the  flare,  or  at  a  height  of  16  to  20  feet,  by 
eye,  using  the  4|  foot  standard  point  only  for  species  and  types  which 
permit  it. 

Where  D.B.H.  is  adhered  to  for  species  like  Western  larch,  red 
cedar  or  Douglas  fir  on  the  Pacific  Coast,  butt  swelling  greatly  inter- 
feres with  the  uniformity  of  the  volumes  for  these  specias  for  trees  of 
given  diameters  when  compared  with  other  species  like  western  yellow 
pine  whose  swelling  seldom  reaches  this  height.  This  apparent  dif- 
ference in  volume  may  be  from  20  to  40  per  cent  in  favor  of  the  pine. 

126.  Bark  as  Afifecting  Diameter  in  Volume  Tables.  For  species 
whose  bark  is  of  uniform  thickness  for  trees  of  the  same  D.B.H.,  the 
diameter  taken  outside  the  bark  is  preferable  as  a  standard  of  classi- 
fication to  diameter  inside  the  bark.  The  cruiser  has  no  time  to  measure 
bark  thickness  except  on  occasional  test  trees.  The  width  of  bark, 
however,  is  seldom  uniform.  For  trees  of  the  same  diameter,  it  is  thick- 
est on  exposed  and  on  rapidly  growing  trees,  and  thinnest  on  sheltered, 
crowded  and  slow-growing  or  suppressed  trees  (§  113).  The  larger 
the  trees,  the  greater  the  actual  thickness  of  bark,  and  the  wider  the 
possible  variation  in  thickness.  This  thickness  may  range  from  2 
to  5  inches  and  over,  on  West  Coast  species.  Volume  tables  based 
on  diameter  inside  bark,  therefore,  are  more  consistent  and  accurate 
as  tables,  than  those  based  on  outside  bark  measurement. 

But  this  would  require  the  tallyman  to  throw  ofT  the  double  width 
of  bark  from  every  tree  tallied.  The  experienced  cruiser,  who  deals 
with  single  average  trees  only,  can  from  his  experience  throw  off  the 
proper  average  width  of  bark  for  the  selected  tree,  increasing  the  deduc- 
tion for  open  and  exposed  situations  and  vice  versa.  There  is  no 
such  choice  in  the  tally  of  every  tree.  The  mistakes  made  in  mental 
arithmetic  and  the  errors  in  guessing  the  proper  width  of  bark  to  allow 
would  be  more  serious  than  discrepancies  in  the  table.  In  practice, 
then,  D.B.H.  would  have  to  be  recorded  and  average  bark  thickness 
afterwards  deducted  previous  to  computing  the  volume. 


CLASSIFICATION  OF  TREES  BY  DIAMETER  151 

Species  with  thick  bark  will  show  a  smaller  volume  for  the  same 
diameters  than  those  with  thin  bark,  because  of  taking  the  diameter 
on  the  bark  surface  and  not  on  the  wood.  Individual  trees  with  thick 
bark  will  give  correspondingly  less  volume  than  the  average  for  the 
diameter  class  shown  in  the  table.  Timber  on  exposed  sites  will  be 
over-estimated  by  tables  based  on  diameter  outside  bark  unless  con- 
structed locally  for  the  same  sites.  Width  of  bark,  therefore,  is  a  cause 
of  variation  in  the  attempted  standardization  of  volume  by  diameter 
classes,  which  is  eliminated  in  the  universal  tables  when  these  are  based 
on  diameter  inside  bark,  at  either  top  of  log,  D.B.H.,  or  stump. 

127.  Classification  of  Trees  by  Diameter.  Standard  volume  tables 
are  commonly  based  on  D.B.H.  outside  bark.  The  actual  diameter 
of  trees  can  be  measured  as  closely  as  the  nearest  ^inch.  The  aver- 
age of  two  measurements  taken  at  right  angles  is  considered  the  diam- 
eter of  the  tree. 

For  felled  trees  whose  volume  is  to  be  measured  in  the  construction 
of  volume  tables,  the  diameters  are  recorded  to  the  nearest  actual 
xVinch.  But  these  volumes  are  classified  later  by  1-inch,  or  2-inch 
classes.  One-inch  classes  have  been  adopted  as  standard  for  Eastern 
species,  while  in  the  West,  owing  to  the  greater  range  of  diameters 
encountered,  2-inch  classes  are  deemed  sufficient.  Each  1-inch  class 
includes  all  trees  whose  average  D.B.H.  is  above  .5  in  the  inch  below, 
and  .5  and  under  in  the  given  inch  class;  e.g.,  the  9-inch  class  includes 
trees  measuring  8.6  to  9.5  inches.  In  2-inch  classes,  the  even  inch  is 
used.  A  10-inch  class  would  include  trees  measuring  9.1  to  11.0 
inches. 

128.  Classification  of  Trees  by  Height.  Height  is  never  used  as 
the  sole  basis  of  tree  classes;  diameter  is  the  fundamental  basis  of 
classification.  But  height  exerts  an  enormous  influence  on  the  volumes 
of  trees  of  the  same  D.B.H.,  the  extreme  difference  in  volumes  for  dif- 
ferent heights  being  more  than  100  per  cent.  These  differences  in  height 
and  volume  for  trees  of  the  same  diameters  occur  in  stands  of  different 
density,  growing  on  different  qualities  of  site,  or  at  different  altitudes. 
They  correspond  with  differences  in  the  average  taper  per  log,  as  dis- 
tinguished in  universal  volume  tables. 

It  follows  that  the  separation  of  trees  of  a  given  diameter  class  into 
several  height  classes  previous  to  averaging  their  volumes  is  another 
way  of  distinguishing  between  trees  of  gradual  and  of  rapid  taper, 
and  that  if  enough  of  these  height  classes  are  made,  the  differences  in 
volume  due  to  more  or  less  rapid  taper  are  distinguished  even  more 
accurately  than  by  introducing  taper  as  a  factor  in  the  table.  The 
height,  rather  than  any  arbitrary  amount  of  taper,  is  the  real  basis  of 
classification,  and  the  actual  average  volume,  rather  than  an  assumed 


152  UNITS  OF  MEASUREMENT  FOR  STANDING  TIMBER 

volume,  is  then  expressed  in  the  table.  The  rate  of  taper  for  trees  in 
different  height  classes  within  any  diameter  class,  as  20  inches  D.B.H., 
need  not  be  shown  in  such  tables.  If  measured,  it  will  be  found  to  differ 
by  arbitrary  fractions  of  inches  instead  of  by  exact  1-inch  classes  per 
standard  log. 

Height  classes  may  be  based  on  total  height,  or  on  the  length  of  the 
merchantable  bole.  In  the  former  case,  height  classes  are  based  on 
either  5-  or  10-foot  gradations,  using  the  same  system  of  rounding 
off.  as  for  diameters,  e.g.,  the  70-foot  height  class  with  10-foot  gradations 
includes  all  trees  66  to  75  feet  in  height.  With  5-foot  gradations,  it 
includes  trees  68  to  72  feet  in  height.  When  merchantable  heights 
are  used,  these  lengths  are  commonly  standardized  to  conform  to  a 
common  log  length  such  as  16  feet  and  expressed  as  1,  2,  3  or  more  log 
trees.  The  log  length  used  is  alwaj^s  stated.  Half-log  lengths  may  be 
differentiated.  With  valuable  hardwoods  of  variable  merchantable 
length,  there  is  some  need  for  closer  classification  of  merchantable 
lengths,  but  volume  tables  are  seldom  constructed  for  intervals  of  less 
than  8  feet. 

129.  Diameter  Alone,  Versus  Diameter  and  Height,  as  Basis  of 
Volume  Tables.  To  separate  or  classify  the  volumes  of  trees  of  each 
given  diameter  class  into  from  4  to  10  height  classes  requires  the  measure- 
ment of  from  250  to  1000  trees,  in  order  that  the  average  volume  in 
each  of  these  numerous  classes  may  be  found  with  some  accuracy 
(§  137).  This  makes  it  impossible  to  take  the  time  to  construct  such 
tables  for  local  or  immediate  use.  Hence  many  volume  tables  have 
been  based  on  diameter  alone,  averaging  together  trees  of  all  heights. 
Sometimes  the  average  heights  of  the  trees  of  each  diameter  class  are 
shown,  often  they  are  omitted. 

For  timber  of  uniform  age  and  density  of  stand  and  growing  on  the 
same  quality  of  site,  individual  trees  of  the  same  diameter  will  still 
differ  considerably  in  height  and  volume;  yet  an  average  height  for 
each  diameter  may  be  found,  which  will  indicate  quite  closely  the 
average  volume  for  that  particular  stand  or  type  and  age  class.  But 
such  a  volume  table  is  quite  worthless  for  application  to  any  other 
stand,  age  class  or  type,  unless  it  can  first  be  shown  that  the  average 
heights  based  on  diameter  are  the  same  in  both  cases.  Lacking, 
first,  the  knowledge  of  the  average  heights  used  in  the  table,  and  second, 
the  demonstration  that  these  coincide  with  those  of  the  stand  to  be 
estimated,  the  only  possible  procedure  is  the  preparation  of  an  entirely 
new  volume  table. 

But  with  a  table  based  on  a  classification  of  heights  and  correspond- 
ing volumes  under  each  diameter  class,  stands  of  any  degree  of  density 
or  age,  and  growing  on  any  site,  may  be  estimated  by  use  of  this  table, 


STANDARD  VERSUS  LOCAL  VOLUME  TABLES  153 

if  the  volumes  taken  from  the  table  are  those  for  heights  correspond- 
ing to  the  trees  in  the  stand. 

130.  Standard  Versus  Local  Volume  Tables.  Volume  Tables  based 
on  both  diameter  and  height  classes,  in  whose  construction  from  500 
to  several  thousand  trees  have  been  used,  selected  from  as  wide  a  range 
of  sites  and  locations  as  possible,  are  termed  Standard  VolufJie  Tables, 
while  those  based  on  diameter,  either  alone  or  with  the  average  height 
of  trees  of  each  diameter  class  stated,  and  applicable  only  to  a  given 
stand  or  site,  are  known  as  Local  Volume  Tables. 

It  follows  that  local  volume  tables  applicable  to  any  stand,  age 
or  site  can  be  derived  from  the  values  given  in  a  standard  volume  table 
and  can  be  expressed  on  the  basis  of  diameter  alone  by  first  determin- 
ing, for  the  stand,  the  average  height  to  use  for  each  diameter  class. 

Classification  by  both  diameter  and  by  height  is  not  sufficient  to 
secure  complete  accuracy  in  volume  tables  because  of  differences  in 
average  form  (§  166).  But  such  tables,  well  constructed,  are  vastly 
more  accurate  than  any  universal  table  based  on  uniform  tapers,  or 
frustums  of  cones,  and  are  known  to  apply  with  almost  the  same  degree 
of  accuracy  throughout  the  entire  range  of  a  species.  Greater  vari- 
ation in  form  and  volume  of  stand  is  caused  by  differences  in  soil,  expo- 
sure and  density  in  a  restricted  locality  than  by  a  thousand  miles  dif- 
ference in  location. 


CHAPTER  XI 

THE  CONSTRUCTION  OF  STANDARD  VOLUME  TABLES  FOR 
TOTAL  CUBIC  CONTENTS 

131.  Steps  in  Construction  of  a  Standard  Volume  Table.  The 
steps  in  the  construction  of  a  standard  volume  table,  whether  for  total 
cubic  contents,  or  for  any  form  of  product,  are  practically  the  same. 
They  are : 

1.  Selection  of  felled  trees  in  sufficient  number,  and  representing 
the  complete  range  of  diameter  and  height  classes  of  the  species  or 
locality. 

2.  Measurement  of  each  tree  to  secure  all  the  data  needed  for  the 
construction  of  the  volume  table. 

3.  Computation  of  volume  of  each  tree. 

4.  Classification  of  tree  volumes  according  to  diameter  and  height 
classes. 

5.  Averaging  the  volumes  of  trees  of  each  separate  diameter  and 
height  class. 

6.  Elimination  of  iri-egularities  in  final  table  by  graphic  plotting 
and  curves. 

132.  Selection  of  Trees  for  Measurement.  As  only  felled  trees 
can  be  measured  with  the  accuracy  needed  for  construction  of  volume 
tables,  the  choice  is  presented  of  utilizing  timber  already  felled,  either 
by  wind,  or  by  loggers,  or  of  felling  the  trees  for  measurement.  Wind- 
fallen  trees  are  usually  of  the  larger  sizes,  and  scattered  individually 
or  in  groups,  and  are  measured  more  as  a  check  on  rough  methods 
of  estimating  than  in  the  systematic  construction  of  tables.  A  logging 
job  presents  the  opportunity  to  secure  trees  of  all  diameters  except 
those  below  merchantable  size.  The  operation  may  be  too  local  in 
extent  to  embrace  the  extreme  forms  desired,  and  a  standard  table 
covering  the  extremes  of  diameters  and  complete  range  of  heights 
should  be  based  on  trees  cut  from  several  different  operations  covering 
the  range  of  altitude  and  soil  qualities  for  the  species  or  type. 

The  influence  of  soil,  altitude,  age  and  other  factors  upon  the  form 
of  trees  of  the  same  diameter  and  height  class  is  discussed  in  Chapter 
XVI.  When  it  can  be  shown  that  differences  in  volume  can  be  cor- 
related with  age,  or  site,  separate  standard  tables  may  be  constructed 
for  trees  of  the  specified  classes  or  sites.     In  this  case,  the  same  principle 

154 


THE  TREE  RECORD  155 

of  securing  as  wide  a  range  of  diameter  and  height  classes  as  possible, 
by  distributing  the  selection  of  the  trees,  applies  within  the  limits  of 
the  predetermined  region,  type  or  age  class. 

The  number  of  trees  necessary  to  secure  a  good  basis  for  a  volume 
table  increases  with  the  range  of  diameter  and  height.  Ten  trees  in 
each  separate  diameter  and  height  class  will  suffice,  and  only  in  a  few 
standard  tables  has  this  number  been  secured.  This  would  call  for  a 
total  of  500  to  2500  trees.  Ordinarily,  a  sufficient  number  of  trees 
is  easily  obtained  for  the  smaller  and  more  common  diameter  and  height 
groups,  but  the  material  becomes  scarce  as  the  larger  sizes  are  reached. 
The  graphic  methods  of  averaging  are  chiefly  useful  in  overcoming  this 
deficiency  (§  138).  The  use  of  form  factors  also  facilitates  the  con- 
struction of  tables  from  fewer  trees  (§  175).  Standard  tables,  com- 
puted by  averaging  the  volumes  of  trees  by  the  method  given  in  this 
chapter  should  be  based  on  at  least  300  trees,  and  if  used  as  a  general 
reference  table  should  never  have  less  than  500  and  preferably  over 
1000  trees.  Local  tables  based  on  diameter  alone  can  be  made  from 
10  to  50  trees.  It  is  desirable  to  tabulate  the  number  of  trees  measured 
in  each  diameter  and  height  class  in  the  field  as  the  work  progresses, 
and  to  make  a  special  effort  to  find  trees  of  the  less  numerous  sizes  to 
fill  out  the  table.  On  the  other  hand,  the  more  common  sizes  should 
be  represented  by  somewhat  greater  numbers  of  trees  in  the  table 
than  odd  sizes,  as  errors  in  the  table  affect  the  results  of  estimating 
in  proportion  to  the  per  cent  of  volume  of  the  stand  which  falls  in 
the  specified  classes. 

To  secure  trees  of  smaller  sizes  than  are  considered  merchantable 
by  loggers,  in  order  to  show  total  cubic  contents  for  these  classes,  or 
contents  in  terms  of  smaller  products  not  being  utilized  in  that  locality, 
the  trees  may  be  felled  by  the  mensuration  crew.  This  must  be  done 
for  all  sizes  in  absence  of  logging,  but  it  adds  greatly  to  the  time  and 
cost  of  the  work. 

133.  The  Tree  Record.  The  data  for  each  tree  must  be  entered 
on  a  separate  blank,  or  printed  form,  and  headed  by  the  items. 

Species, 

Locality, 

Date, 

Name  of  investigator, 

Number  of  analysis. 

Records  should  be  carefully  filled  in  with  legible  figures,  using  a 

4H  or  6H  pencil.     They  constitute  permanent  records    of    tree  form 

and  may  be  available  for  use  in  compiling  data  many  years  afterward. 

Description  of  site  factors  are  useful  in  determining  their  influence, 

if  any,  on  the  form  and  volume  of  trees  of  the  same  diameter  and  height. 


156  CONSTRUCTION  OF  STANDARD  VOLUME  TABLES 

These  are, 

Soil,  origin,  whether  sedimentary  or  residual. 

Depth,  rock,  physical  character,  sand,  etc. 

Exposure  and  slope. 

Altitude. 

Forest  type. 

Character  and  density  of  stand. 
These  items  involve  considerable  repetition  and  are  often  omitted, 
or  may  be  written  up  for  groups  of  trees.  But  if  the  material  is  to  be 
used  for  investigations,  to  determine  the  effect  of  site  factors  on  form, 
each  tree  analysis  should  be  associated  with  a  complete  description 
covering  the  points  enumerated. 

134.  Measurements  of  the  Tree  Required  for  Classification.  The 
measurements  of  the  felled  tree  must  be  taken  before  the  logs  are 
removed  by  skidding.  These  may  be  divided  according  to  their  pur- 
pose into  those  needed  to 

1.  Classify  the  tree  by  dimensions  and  character. 

2.  Obtain  the  volume  of  the  stem  and  branches. 

The  first  class  of  measurements  consists  of  D.B.H,,  height  of  stump, 
total  height,  crown  and  bole.  The  D.B.H.  (§  125)  is  the  most  important 
measurement  taken.  This  point  must  be  located  on  the  butt  log  of 
felled  trees,  unless  the  D.B.H.  has  been  taken  in  advance  of  felling 
the  tree.  To  the  stump  height  is  added  the  additional  height  needed 
to  equal  4^  feet,  which  is  measured  upon  the  butt  log.  If  the  butt  cut 
is  slanting,  care  is  taken  to  measure  from  the  same  point  on  the  log  as 
on  the  stump,  thus  reproducing  the  measurement  which  would  be  taken 
on  the  standing  tree — otherwise  a  slight  error  is  incurred.  The  D.B.H. 
and  all  other  measurements  of  diameter  are  taken  in  two  directions, 
at  right  angles.  This  is  always  possible  on  the  felled  trees  as  shown 
in  Fig.  25. 

The  average  of  these  two  diameters  is  obtained  and  recorded  to 
the  nearest  yVinch,  and  is  never  rounded  off  to  the  nearest  inch. 

The  height  of  stump  is  taken  not  only  to  obtain  D.B.H.  on  felled 
trees,  but  as  a  basis  from  which  merchantable  length  and  contents 
is  figured  (Chapter  XII).  It  is  recorded  in  feet  and  tenths,  or  in  feet 
and  inches.  Stump  height  is  measured  vertically  from  the  root  collar 
or  point  of  contact  with  the  ground,  and  at  the  average  height  of  this 
collar.  On  side  hills,  this  point  occurs  half  way  between  the  upper 
and  lower  sides  of  the  stump. 

The  total  height  of  every  tree  measured  for  volume  should  be  recorded, 
whether  or  not  it  is  to  be  used  as  a  basis  of  height  classification  (§  137). 
The  most  accurate  method  is  to  stretch  a  steel  tape  from  the  butt  to 
tip  of  crown,  along  the  stem,  although  a  pole  graduated  in  feet  is  some- 


MEASUREMENTS  OF  TREE  REQUIRED  FOR  CLASSIFICATION      157 

times  substituted.  To  this  height  the  stump  height  is  added,  and  the 
total  recorded  to  the  nearest  foot.  The  height  of  a  rounded  or  irregular 
crown  is  measured  to  a  line  drawn  at  right  angles  to  the  bole,  and  tan- 
gent to  the  highest  point  of  crown.  Height  may  also  be  obtained  by 
adding  together  the  lengths  of  the  separate  sections  of  the  bole,  plus 
the  distance  from  the  top  of  last  section  to  tip  of  trees. 

Character  of  crown  may  or  may  not  be  required.  It  is  useful  in 
hardwoods  where  separate  tree  classes  may  be  desired,  and  in  any 
species  where  growth  is  being  investigated  and  as  the  index  of 
form,  as  indicated  in  Chapter  XVI.  On  felled  trees,  two  measure- 
ments are  taken.  Width  of  crown  is  measured  as  the  tree  lies,  at 
widest  point,  at  right  angles  to  stem.     Length  of  crown  is  the  dis- 


FiG.  25. — Method  of  measuring  a  log  twice  at  right  angles  to  obtain  the  average 
diameter. 

tance  from  tip  to  the  point  where  the  lowest  vigorous  and  well-shaped 
green  branch  joins  the  bole,  or  better  still,  at  a  point  on  the  bole,  oppo- 
site the  lower  limit  of  the  green  crown  or  foliage.  Some  judgment  is 
required  in  excluding  from  crown-length  small,  feeble  or  straggling 
single  live  branches  which  may  have  survived  by  accident  on  one  side 
but  do  not  form  part  of  the  main  crown  of  the  tree.  Dead  branches 
or  knots  form  no  part  of  the  crown. 

The  position  or  class  of  the  crown  in  the  stand  may  also  be  described, 
as  open-grown,  dominant,  co-dominant,  intermediate,  or  overtopped. 
This  is  best  judged  before  felling. 

The  following  definitions  have  been  adopted  as  standard  by  the  Society  of 
American  Foresters. 

Crown  Class.  All  trees  in  a  stand  occupying  a  similar  position  in  the  crown 
cover.     The  crown  classes  usually  distinguished  are: 


158  CONSTRUCTION  OF  STANDARD  VOLUME  TABLES 

Dominant.  Trees  with  crowns  extending  above  the  general  level  of  the  forest 
canopy  and  receiving  full  light  from  above  and  partly  from  the  side;  larger  than 
the  average  trees  in  the  stand,  and  with  crowns  well  developed  but  possibly  some- 
what crowded  on  the  sides. 

Co-dominant.  Trees  with  crowns  forming  the  general  level  of  the  forest  canopy 
and  receiving  full  light  from  above  but  comparatively  little  from  the  sides;  usually 
with  medium-sized  crowns  more  or  less  crowded  on  the  sides. 

Intermediate.  Trees  with  crowns  below,  but  still  extending  into  the  general 
level  of  the  forest  canopy,  receiving  a  little  direct  light  from  above,  but 
none  from  the  sides;  usually  with  small  crowns  considerably  crowded  on  the 
sides. 

Overtopped.  Trees  with  crowns  entirely  below  the  general  forest  canopy  and 
receiving  no  direct  light  either  from  above  or  from  the  sides.  These  may  be 
further  divided  into  oppressed,  usually  with  small,  poorly  developed  crowns,  still 
alive,  and  possibly  able  to  recover;  and  suppressed  or  dying  and  dead. 

As  currently  used,  overtopped  trees  are  now  classed  as  suppressed;  and  an 
additional  class,  open-grown,  is  added,  consisting  of  trees  standing  alone  with 
crown  free  on  all  sides. 

The  hole  is  not  described  unless  there  is  some  marked  pecuharity 
which  may  explain  an  abnormal  shape  or  volume  and  enable  the  investi- 
gator later  to  decide  whether  to  use  or  reject  it  in  his  tables.  Such 
peculiarities  include  forks,  dead  tops,  abnormal  or  swollen  butts,  especi- 
ally if  the  D.B.H.  is  affected,  or  other  deformities  in  shape.  The  pres- 
ence of  rot,  shake,  or  other  internal  defects  may  be  noted,  but  does 
not  influence  the  subsequent  measurements  (§156)  or  volume  of  the 
tree,  unless  its  form  is  affected  abnormally,  as  sometimes  happens 
when  rot  at  the  butt  causes  abnormal  butt  swelling  extending  beyond 
D.B.H. 

135.  Measurements  Required  to  Obtain  the  Volume  of  the  Tree. 
Systems  Used.  While  the  object  of  measurements  of  the  stem  is  to 
obtain  its  volume,  these  also  serve  to  record  the  form  of  the  bole.  The 
diameter  is  taken  (§  29)  at  definite  points,  dividing  the  bole  into  lengths 
which  are  recorded  consecutively.  The  cubic  volume  of  round  logs 
of  any  length  is  easily  computed  from  the  end  diameters  (Smalian 
formula)  if  the  proper  precautions  are  taken  to  guard  against  the  influ- 
ence of  butt  swelHng  (§29).  But  if  the  recorded  diameters  or  form 
of  the  trees  are  to  be  used  to  get  average  form  or  taper  (§166)  as  well 
as  merely  for  volume,  these  measurements  should  be  taken  at  the  same 
heights  or  intervals  on  all  trees. 

For  cubic  volume,  the  log  lengths  into  which  the  bole  is  cut  by  the 
loggers  may  be  disregarded.  This  factor  would  exert  no  appreciable 
influence  on  the  tree  contents  when  the  full  volume  of  each  log  is  accu- 
rately obtained. 

There  are  three  systems  of  taking  these  upper  diameter  or  taper 
measurements,  as  follows  (Fig.  30,  §  155) : 


VOLUME  OF  THE  TREE.     SYSTEMS  USED  159 

System  A.  Disregard  stump  height.  Take  diameter  at  every 
10  feet  from  ground  to  tip.  Record  length  of  tip  above  last  10-foot 
taper. 

This  method  permits  of  accurate  averaging  of  these  diameters  on 
different  trees  to  obtain  average  form,  and  also  gives  the  total  cubic 
volume  of  the  tree.  But  it  is  unsafe  to  rely  solely  upon  these  measure- 
ments for  the  volume  of  the  first  10-foot  log,  which  should  be  supple- 
mented by  stump  taper  measurements,  taken  at  1,  2,  3,  4  and  4|  feet 
from  the  ground.  This  gives  a  complete  record  of  form  and  an  accu- 
rate basis  for  total  volume. 

By  means  of  form  or  taper  tables  (§  167)  based  on  these  measure- 
ments, the  diameters  at  any  other  points  may  be  obtained  from  dia- 
grams, and  the  volume  of  the  tree  can  then  be  calculated  for  any  unit 
of  product. 

System  B.  This  method  is  a  compromise  between  measurements 
intended  solely  to  secure  form  or  total  cubic  volume,  and  those  required 
for  merchantable  volume  (§  145).  The  height  of  stump  is  first  recorded 
and  the  height  of  upper  diameters  is  then  taken  from  the  stump  as  a 
base.  As  stump  height  tends  to  increase  with  diameter  of  tree,  the 
upper  measurements  of  larger  trees  fall  at  higher  points  on  the  bole, 
by  just  the  difference  in  stump  heights.  This  inaccuracy  is  usually 
accepted  and  the  diameters  which  fall  at  equal  height  above  the  stump 
are  averaged  together. 

The  length  of  log  or  interval  adopted  for  upper  diameter  or  taper 
measurements  by  this  method  is  a  multiple  of  4  feet.  Four-foot  inter- 
vals give  closest  results,  and  correspond  to  cordwood  lengths.  A  more 
common  interval  is  8  feet,  corresponding  with  the  standard  length  of 
cross-ties.  Greater  lengths  give  less  accurate  permanent  data.  If 
only  the  16-foot  tapers  are  required  for  the  immediate  purpose  of  the 
table,  it  is  comparatively  little  extra  work  to  take  the  8-foot  points 
as  well,  for  future  use  if  needed. 

System  C.  By  this  method  the  logs  as  cut  by  the  sawyers  are 
measured  as  they  lie,  for  diameter  and  length.  As  these  commercial 
lengths  vary,  the  taper  measurements  for  different  trees  will  fall  at 
several  different  points  even  for  the  first  log,  and  require  tabulation 
at  2-foot  intervals.  Except  when  measured  for  total  cubic  feet,  the 
resultant  volumes  will  vary  according  to  the  lengths  cut  (§43),  and 
not  solely  according  to  the  dimensions  of  the  tree  as  by  Systems  A 
and  B.  No  advantage  is  gained  by  the  securing  of  volume  correspond- 
ing to  the  used  lengths  of  the  tree  measured,  since  in  every  logging 
job,  the  average  of  lengths  used  will  differ.  This  method  is  therefore 
inadvisable.  But  a  record  can  be  made  on  the  analysis  blank  of  the 
log  lengths  actually  cut,  and  their  scaled  contents,  to  determine  the 


160 


CONSTRUCTION  OF  STANDARD  VOLUME  TABLES 


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COMPUTATION  OF  VOLUME  OF  THE  TREE  161 

difference  between  volumes  as  cut  and  scaled,  and  volumes  from  regular 
tapers. 

In  case  the  study  of  the  growth  of  trees  at  upper  sections  is  required 
(§  289)  either  the  trees  will  have  to  be  felled  and  bucked  into  sections 
of  even  lengths  by  System  A  or  System  B,  or  else  the  logs  as  cut  by 
System  C  must  be  accepted  as  the  basis  of  this  growth  study. 

For  total  cubic  volume,  the  taper  measurements  are  continued 
to  the  tip  in  either  system.  With  slight  additional  cost,  these  extra 
measurements  taken  above  the  merchantable  top  diameter  limit  com- 
plete a  permanent  record  of  tree  form  available  for  future  computa- 
tion of  volume  for  any  unit  or  limit  of  merchantable  sizes. 

A  further  modification  is  the  addition  of  trirmning  lengths,  usually 
standardized  as  i^feet  in  16  feet,  so  that  the  points  marked  fall  at 
8.15  feet,  16.3  feet,  24.45  feet,  etc.  If  this  is  done  the  fact  should  be 
be  noted  on  the  analysis.  Total  cubic  volume  is  obtained  as  accurately 
by  this  method  as  by  System  A,  and  in  addition,  the  data  can  be  used 
directly  to  determine  the  volume  in  board  feet.  It  is  therefore  pref- 
erable for  most  objects  to  System  A. 

The  width,  single,  of  bark  is  measured  at  each  diameter  (§29),  and 
recorded  as  read.  This  width  is  then  doubled  and  subtracted  to 
obtain  diameter  inside  bark.  ^ 

If  the  volume  of  sapwood  is  desired,  this  will  require  the  sectioning 
of  the  tree,  and  measurement  of  width  of  sap.  Sapwood  volume  is 
therefore  most  easily  obtained  by  System  C. 

The  measurements  are  entered  on  a  blank,  of  which  an  example 
is  shown  on  p.  160. 

This  completes  the  field  record.  The  remainder  of  the  work  is 
performed  at  any  time  in  the  office. 

The  crew  for  field  measurements  of  volume,  when  the  trees  are 
already  felled,  should  consist  of  two  to  three  men,  one  of  whom  records 
the  data  while  the  others  measure  the  tree. 

136.  Computation  of  Volume  of  the  Tree.  For  total  cubic  volume, 
each  section  is  usually  computed  by  the  Smalian  or  mean  end  fornmla 
in  which 

5  =  area  of  large  end  of  section  in  square  feet; 

6  =  area  of  small  end  of  section  in  square  feet; 

?  =  length  of  section  in  feet; 
F  =  cubic  volume. 

*  Abbreviations  are  used,  as  follows: 

Diameter  outside  bark,  D.O.B. 
Diameter  inside  bark,     D.I.B. 


162  CONSTRUCTION  OF  STANDARD  VOLUME  TABLES 

Then 

For  the  sum  of  the  volumes  of  the  sections  each  end  area  except 
the  first  and  last  is  evidently  used  twice.  A  series  of  three  such  sec- 
tions would  total 


H'^H^hd^y 


When,  as  in  systems  A  and  B,  equal  lengths  of  section  (I)  are  used, 
the  formula  can  be  expressed 

i.e.,  average  the  first  and  last  basal  areas,  and  add  the  remaining  areas. 
Then  multiply  by  length  of  one  section  to  obtain  the  sum  of  volumes 
of  the  sections. 

The  areas  in  square  feet,  corresponding  to  the  diameters  of  each 
section  are  found  in  Table  LXXVIII,  Appendix  C,  p.  490. 

Sections  different  in  length  from  the  standard  must  be  computed 
separately. 

The  tip,  beyond  the  last  taper,  is  computed  as  a  paraboloid,  by  the 
same  formula, 

The  volume  of  stump,  needed  to  complete  the  tree  when  system  B 
is  used,  is  standardized  by  custom  as  a  cylinder,  whose  diameter  is  that 
of  the  stump  section,  thus  neglecting  the  variable  factor  of  stump 
taper.     Its  volume  is  therefore 

V=Bl. 

System  A  permits  the  volume  of  the  section  up  to  4  or  4|  feet  to  be 
computed  accurately  if  desired. 

Owing  to  the  serious  error  incurred  by  measuring  the  butt  section 
by  the  Smalian  method,  the  use  of  Huber's  formula  for  the  first  8-  or 
16-foot  log  may  give  more  consistent  results.  In  this  case,  for  a  16- 
foot  log  (0  the  basal  area  at  8  feet  (6')  gives  the  log  volume,  or 

V  =  b'l. 

A  check  should  be  made  by  this  method  against  the  Smalian  method 
for  the  butt  section  (§29). 

The  total  cubic  volume  of  branches  and  twigs  is  practically  never 


CLASSIFICATION  AND  AVERAGING  OF  TREE  VOLUMES       163 

computed.     The  measurement  of  merchantable  voknne  of  hmbs  and 
branches  is  discussed  in  §  146. 

For  obtaining  the  total  volume  of  the  tree  bole  exclusive  of  branches 
by  regarding  the  bole  as  a  complete  paraboloid,  the  so-called  Schiffel's 
Formula  may  be  applied.  For  this  purpose  the  area  of  the  cross 
section  at  D.B.H.,  and  one  at  one-half  height  above  stump  is  obtained 
and  applied,  thus: 

V=(.16B+Mh^)h     (§177). 

Volume  of.  Bark.  The  volume  of  the  tree  may  be  computed  from 
D.O.B.  to  give  total  cubic  contents  with  bark.  It  is  then  computed, 
if  necessary,  from  the  D.I.B.,  to  give  the  peeled  contents  or  wood 
without  bark.  The  volume  of  bark  is  obtained  by  subtraction  of  the 
second  from  the  first  result. 

Volume  tables  give  the  volume  with  bark,  or  without  bark,  accord- 
ing to  the  use  to  which  wood  is  put  and  the  form  in  which  it  is  sold. 
When  the  peeled  volumes  are  given,  the  per  cent  of  bark  in  terms  of 
peeled  volume  may  be  shown  for  each  diameter. 

137.  Classification  and  Averaging  of  Tree  Volumes  According  to 
Diameter  and  Height  Classes.  1.  The  separate  sheets  are  now  sorted 
first  into  diameter  classes  (§127). 

2.  The  height  classes,  for  tables  giving  total  cubic  volume,  are  based 
on  total  height  of  tree.  Whether  10-foot,  or  5-foot  classes  are  used 
depends  on  the  total  height  of  the  species.  For  second-growth  hard- 
woods or  small  timber,  5-foot  classes  are  preferred,  while  in  the  extremely 
tall  timber  of  the  West  Coast,  20-foot  classes  are  sometimes  sufficient. 
For  either  standard,  trees  are  placed  nearest  their  actual  height.  The 
trees  of  each  diameter  class  are  now  sorted  into  their  respective  height 
classes.  The  trees  in  each  separate  diameter  and  height  class  are  then 
checked  to  see  that  no  mistakes  of  classification  have  been  made. 

3.  The  average  volume  is  found  for  the  trees  of  each  separate  group 
or  class  comprising  all  trees  falling  in  the  same  diameter  and  height 
class. 

If  trees  having  the  same  diameter  and  height  had  similar  forms, 
the  volumes  of  all  trees  in  any  one  diameter  and  height  class  would 
be  equal,  except  for  the  differences  due  to  the  fact  that  the  actual 
diameter,  or  height,  though  falling  within  the  size  Imiits  required,  may 
be  larger  or  smaller  than  the  exact  standard  size  of  the  class. 

But  variation  in  the  form  of  the  bole  is  a  third  factor  which  causes 
considerable  variation  in  volume  for  trees  of  the  same  total  height 
and  diameter  (§  166).  Trees  whose  form  is  full,  lying  between  the 
paraboloid  and  the  cylinder,  have  a  correspondingly  greater  volume 
than  trees  with  a  form  lying  between  the  paraboloid  and  cone,  or  neiloid 


164 


CONSTRUCTION  OF  STANDARD  VOLUME  TABLES 


(§  26).  The  extreme  range  of  volume  caused  by  differences  of  form 
alone  for  trees  of  the  same  height  and  D.B.H.  is  as  much  as  40  per  cent. 
Even  the  average  volume  of  trees  of  the  same  ages  or  sites  may  differ 
by  more  than  20  per  cent. 

The  volume  of  single  trees  follow  the  general  law  of  averages. 
Those  which  depart  most  widely  from  this  law  are  few  in  number, 
while  a  range  of  5  per  cent  above  or  below  the  average  would  probably 
include  by  far  the  larger  number  of  trees  in  fairly  uniform  stands. 

When  the  exact  volume  of  a  specific  tree  is  wanted  it  is  unsafe  to 
assume  that  this  tree  is  an  average  specimen.  It  must  be  measured 
separately.  But  in  estimating  standing  timber,  the  object  sought  is  the 
total  volume  of  the  stand,  or  the  sum  of  all  trees.  If  the  average  vol.- 
ume  of  trees  of  each  size  class  is  correctly  given  in  a  volume  table, 
the  cruiser  can  assume  that  every  tree  tallied  is  an  average  tree,  and 
the  result  or  total  will  be  the  same  as  if  the  true  volume  of  each  sepa- 
rate tree  were  measured. 

This  averaging  of  the  variable  individual  volumes  of  trees  of  each 
class  to  obtain  a  reliable  average  volume  is  the  principal  service  rendered 
by  volume  tables.  The  timber  cruiser  stretches  this  same  principle 
much  farther  when  he  attempts  to  average  the  volumes  of  trees  of  totally 
different  diameters  and  heights,  and  the  chances  for  error  are  much 
greater,  especially  as  this  is  usually  a  mental  process  or  guess,  while 
the  averaging  of  trees  in  a  volume  table  is  a  calculation  based  on  exact 
measurements. 

The  method  of  obtaining  the  average  volume  of  trees  for  a  given 
size  is  as  follows.  Enter  on  a  sheet,  labeled  with  the  diameter  and  height 
class,  the  data  for  each  tree,  according  to  the  illustration  given  below 
for  four  trees.     Place  at  top  of  sheet  the  tree  class,  e.g., 


13  Inches— 60  Feet 

Diameter. 

Height. 

Volume  with  bark. 

Inches 

Feet 

Cubic  feet 

12.7 

56 

59.0 

13.1 

58 

63.2 

13.4 

61 

66.0 

13.4 

62 

68.2 

4)52.6 

257 

256.4 

13.15 

59.25 

64.1 

CLASSIFICATION  AND  AVERAGING  OF  TREE  VOLUMES       165 


T.ABLE  XXVII 

Preliminary  Averages  for  Pitch  Pine.     Volume  Table  Based  on 

Diameter  and  Total  Height.     139  Trees 

Height  Classes — Feet 


D.B.H. 

Inches 

7 

50 

55 

60 

65 

70 

75 

80 

7.5          1 
6.96 
52.6 

8 

8.0          1 
8.73 
52.0 

9 

9.0        1 
14.28 
63.0 

10 

10.2        1 
12.51 
50.0 

9.75       4 

14.88 
53.4 

10.0       1 
17.37 
58.1 

10.5       2 
19.05 

65.8 

11 

11.5        1 
17.78 
50.0 

10.9       6 
17.67 
55.6 

11.1       3 
19.78 
59.35 

11. 1       2 
23.35 
63.2 

12 

12.3        1 
17.93 
52.0 

12.3       6 
24.18 
55.1 

12.2       8 
24.27 
59.6 

12.0        1 
26.09 
63.0 

. 

Legend 

13 

12.9       4 
23.4 
49.6 

13.1      11 
26.23 
54.2 

13.15     4 
27.53 
59.25 

13.4       2 
34.27 
65.0 

D.B.H.           No. 
Inches           Trees 

14 

13.9       6 
31.8 
56.6 

14.0       9 
31.61 
60.3 

14.1        5 
34.05 
64.1 

14.1       2 
42.32 
68.5 

13.6        1 
38.92 
73.4 

14.3       1 
46.1 
78.0 

Cubic 
feet 

15 

14.7       2 
32.9 
51.5 

15.1        1 
36.1 
57.0 

15.1       3 
39.44 
60.2 

15.2       4 
39.96 
64.2 

15.1       2 
45.3 

15.0        1 
43.55 
77.0 

Total 

Height 

Feet 

16 

16.3       2 
37.15 
54.5 

16.1       7 
43.71 
59.8 

15.9       3 
44.69 
64.9 

16.1        5 
49.21 
69.3 

17 

18 

16.9       3 
44.67 
54.8 

16.7       2 
47.26 
60.0 

16.8       2 
47.82 
64.8 

17.1        1 
51.3 
68.0 

17.1       2 
55.57 
73.45 

17.0       1 
65.14 
78.0 

18.0        1 
54.82 
60.0 

18.0       4 
61.57 
64.25 

18.3       2 
59.25 
68.1 

19 

18.6        1 
60.45 
66.0 

19.1        3 
65.27 
70.2 

19.0       2 
71.82 
74.0 

20 

20.0        1 
69.56 
67.8 

166  CONSTRUCTION  OF  STANDARD  VOLUME  TABLES 

The  quotients  represent  respectively  the  actual  average  diameter, 
height  and  volume  for  the  class.  These  data,  together  with  the  number 
of  trees  measured  in  each  class,  are  entered  on  a  large  sheet  in  the  form 
shown  in  Table  XXVII,  p.  165,  and  constitute  the  basic  or  rough  table 
which  is  the  first  step  in  preparing  a  standard  volume  table.  Thus 
64.1  cubic  feet  is  not  the  average  volume  for  13-inch  trees  60  feet  high 
but  for  trees  averaging  13.15  inches  and  59.25  feet  in  height. 

138.  The  Graphic  Plotting  of  Data — Its  Advantages.  The  volumes  shown  in 
such  a  table  should  increase  with  both  diameter  and  height.  If  sufficient  basic 
data  has  been  obtained,  this  rate  of  increase  in  the  values  of  the  table,  both  verti- 
cally and  horizontally,  will  follow  the  law  of  averages  which  expresses  the  true 
relation  of  the  two  variables;  for  the  vertical  columns,  volume  and  diameter;  for 
the  horizontal,  volume  and  height.  But  where  only  a  few  trees  are  obtained  in  a 
class,  these  trees  may  not  only  be  larger  or  smaller  in  diameter  and  height  than  the 
true  average,  but  may  have  too  full  or  too  slender  a  form,  and  the  average  of  their 
volumes  will  be  correspondingly  higher  or  lower  than  the  regular  progression  to  be 
expected.  The  form  of  this  progression  or  increase  will  be  determined  by  the 
character  of  the  two  variables.  For  cubic  volume  based  on  diameter,  with  trees 
of  the  same  height  and  form,  the  increase  in  volume  will  be  proportional  to  D^. 
If  these  values  are  plotted  on  cross-section  paper,  the  result  will  be  a  curve  showing 
graphically  to  the  eye  the  law  of  increase  in  volume  based  on  diameter. 

The  increase  in  volurne  based  on  height  can  be  shown  in  a  similar  manner  by 
plotting  the  volumes  and  heights.  This  curve  will  differ  in  shape  from  the  first, 
since  volume  tends  to  increase  directly  as  height  for  trees  of  the  same  diameter, 
and  the  curve  showing  this  approaches  a  straight  line.  When  thus  presented  to 
the  eye,  any  irregularities  or  inconsistencies  in  the  average  volumes  obtained  in 
Table  XXVII  become  evident  at  once,  while  to  detect  them  by  mere  examination 
or  checking  of  the  arithmetical  table  would  be  far  from  satisfactory. 

Since  such  irregular  values  do  not  conform  to  the  general  law  of  increase  in 
volume  based  on  diameter  and  height,  they  cannot  be  depended  upon  to  give  the 
true  average  volume  of  all  the  trees  of  a  size  class.  One  of  two  things  must  now 
be  done — either  more  data  must  be  collected  in  the  field  in  order  to  improve  these 
averages,  or  the  averages  obtained  must  be  harmonized,  and  these  irregular  values 
changed  or  corrected.  The  irregular  volumes  plotted  would  be  based  on  sufficient 
field  data  to  bring  out  the  real  tendency  or  character  of  the  law  of  the  relations 
sought.  The  minor  irregularities  in  this  case  are  not  serious  enough  to  prevent  a 
fairly  accurate  approximation  of  this  law  and  a  drawing  of  the  curve  as  indicated 
by  the  data. 

The  principles  of  graphic  plotting  are  treated  in  analytical  geometry,  or  graphic 
algebra.  The  relation  of  the  two  variable  quantities  is  shown  by  a  series  of  plotted 
points  in  which  the  horizontal  and  vertical  lines  each  represent  a  scale  of  values 
corresponding  to  one  of  the  quantities  or  variables.  Both  being  positive  quantities, 
the  lower  left-hand  corner  of  the  chart  is  taken  as  zero,  or  the  origin.  The  hori- 
zontal line  passing  through  this  point  along  the  base  of  the  sheet  is  the  axis  of 
abscissa}  or  horizontal  scale,  and  the  abscissa  or  value  of  each  point  is  measured 
parallel  with  this  axis  or  along  the  scale  thus  indicated.  The  vertical  line  through 
the  origin,  forming  the  left  margin  of  sheet  is  the  axis  of  ordinates  or  vertical  scale. 
The  zero,  or  intersection  of  these  two  axes,  is  usually  located  to  the  right  and  above 
the  extreme  lower  corner  of  the  sheet  to  give  a  margin  for  entering  the  scales.     The 


THE  GRAPHIC  PLOTTING  OF  DATA 


167 


scale  of  diameters,  by  inches,  is  then  placed  along  the  horizontal  scale  while  the 
volume  scale  is  entered  on  the  vertical  scale.  The  whole  forms  a  system  of  rectan- 
gular co-ordinates.  Each  point  on  the  paper  represents  two  quantities,  a  diameter, 
measured  parallel  with  the  base,  and  forming  the  abscissa  of  the  point,  and  a 
volume,  measured  vertically,  and  forming  an  ordinate.  This  is  illustrated  by 
Fig.  26. 

In  this  figure,  the  volumes  of  three  average  trees,  or  the  averages  volimies  of 
three  groups  of  trees  have  been  plotted,  namely,  10-inch,  13.15-inch  and  16.1-inch 
trees.  The  horizontal  and  vertical  values  of  each  point  are  indicated  by  dotted 
lines.  If  the  theoretical 
relation  of  volume,  and 
diameter  for  all  points 
is  as  y  to  px~  we  would 
not  only  expect  y  (vol- 
ume) to  increase  faster 
than  X  (diameter),  but 
this  increase  would  be 
in  the  form  of  a  regular 
curve,  and  once  the 
position  of  this  curve 
is  indicated  by  a  suffi- 
cient number  of  reli- 
able points,  all  other 
values  for  x  and  y, 
representing  the  vol- 
umes for  all  diameters, 
would  fall  on  the  same 
curve.  False  or  ab- 
normal average  vol- 
umes obtained  from 
too  few  trees  will  not 
fall     exactly     on     the 

curve,  but  above  or  below  it.  The  greater  the  number  of  trees  used  in  obtain- 
ing an  average  point,  the  more  closely  will  the  point  representing  this  value  approach 
or  coincide  with  the  curve. 

The  actual  shape  of  the  curve  will  depend  upon  the  relation  arbitrarily  estab- 
lished between  the  two  scales.  Doubling  the  values  on  the  ordinates,  for  instance, 
reduces  the  ordinate  distance  one-half.  The  scale  selected  must  bring  all  values 
within  the  boimdaries  of  the  sheet,  which  is  usually  accomplished  if  the  largest 
ordinate  is  not  less  than  one-half  nor  greater  than  one  and  one-half  times  the 
greatest  abscissa. 

The  value  of  using  this  method  is  that  each  separate  point  or  average  aids  in 
establishing  the  law,  or  fixing  the  values  for  all  the  others.  If  enough  good  or 
well-weighted  points  are  obtained,  they  correct  the  abnormality  of  other  points 
based  on  insufficient  data  and  even  show  up  arithmetical  mistakes  in  obtaining 
these  averages.  The  curve  makes  possible  the  mterpretation  of  missing  data,  but 
it  is  considered  unsafe  to  extend  it  to  cover  values  beyond  the  hmits  of  the  original 
data. 

Although  from  the  standpoint  of  mathematics  it  makes  no  difference  which 
variable  is  plotted  on  the  horizontal  and  which  on  the  vertical  scale,  yet  as  the 
purpose  of  this  plotting  is  to  convey  to  the  eye  the  tendency  or  law  of  increase  in 


1 

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Absci 

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40 

35 

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10       11      12       13 
Axis  of  Abscissae 


14        15       16  Inches  of  D.l 


Fig.  26. — Rectangular  coordinates,  showing  position  of 
a  curve  of  volume  on  diameter  as  determined  by  three 
points   whose   ordinates    and    abscissae  are  known. 


168 


CONSTRUCTION  OF  STANDARD  VOLUME  TABLES 


one  variable  when  based  upon  another  definite  variable,  as  for  instance,  the  increase 
in  volume  due  to  increase  in  diameter  by  1-inch  classes,  it  is  always  preferable  to 
plot  the  independent  variables  on  the  horizontal  scale  and  the  dependent  variables 
on  the  vertical  scale. 

Neglect  of  this  precaution  not  only  conveys  an  ocular  impression  the  reverse  of 
the  actual  law,  but  tends  to  create  the  false  notion  that  the  two  variables  are  inter- 
changeable, whereas  one  must  always  be  an  independent  or  fixed  base,  on  which 


60 


.g  3"5 


2ff 


/ 

/ 

/ 

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1 

A 

/ 

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A 

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,0^^' 

9 

<s 

\y 

< 

y 

A 

1 

-y 

3 

10  11  12  13         14  15  16  17  18  19 

D.B.H.  Inches 

Fig.  27. — Curve  of  volume  based  on  D.B.H.  for  trees  of  a  single  height  class. 


the  required  data  are  collected,  classified  and  arranged.  For  instance,  in  deter- 
mining the  relation  between  D.B.H.  and  age  of  trees,  absolutely  different  results 
are  obtained  if  in  the  first  instance,  the  average  D.B.H.  is  found  for  all  trees  of 
given  age  classes,  and  in  the  second,  the  average  age  is  determined  for  all  trees  of 
given  D.B.H.  classes  (§  275).  The  values  of  these  tables  or  curves  are  not  inter- 
changeable. The  dependent  variable  can  always  be  identified  as  the  one  whose 
values  are  sought;  the  independent,  the  one  whose  values  are  already  known. 

The  use  of  curves,  or  graphic  plotting,  enables  the  investigator  to  obtain  a 
given  degree  of  accuracy  with  a  greatly  reduced  number  of  field  measurements. 


APPLICATION  OF  GRAPHIC  METHOD  169 

This  saving  in  field  work  is  from  100  to  500  per  cent;  in  fact  it  would  be  impractical, 
though  possible,  to  get  the  same  degree  of  accuracy  by  the  averaging  of  field  data 
as  in  Table  XXVII  without  using  the  graphic  method.  The  appHcation  .of  these 
principles  would  have  greatly  improved  the  construction  of  certain  log  rules, 
notably  the  Scribner  rule  (§  68). 

139.  Application  of  Graphic  Method  in  Constructing  Volume  Tables. — In 
applying  this  method  to  the  values  in  Table  XXVII  volume  is  evidently  the  variable 
whose  value  is  sought,  while  diameter  and  height  are  the  two  independent  variables. 
It  is  evident  that  not  more  than  two  values  can  be  plotted  in  a  single  point, 
nor  more  than  two  variables,  as  for  instance,  diameters  and  volumes  in  a  single 
curve.  The  volume  of  trees  varies  with  both  diameter  and  height,  yet  variations 
due  to  height  cannot  be  shown  in  the  same  curve  with  those  due  to  diameter.  But 
if  we  select  from  the  original  table  (XXVII)  the  volume  of  trees,  all  of  which  fall 
in  the  same  height  class,  the  factor  of  height,  for  these  volumes,  becomes  a  constant, 
except  for  deviations  from  the  true  average  height  of  the  class,  which  can  be  ignored 
in  plotting  this  curve.  The  curve  formed  by  the  volumes  of  this  group  of  selected 
trees  will  be  designated  as  the  volume  curve  based  on  diameters,  for  trees  of  the 
specified  height.  Such  a  curve  is  shown  in  Fig.  27,  with  the  original  average  volumes 
plotted. 

In  determining  just  where  the  curve  should  fall,  the  weight  of  each  point  is 
influenced  by  the  number  of  trees  included  in  the  average  column  for  that  diameter; 
the  weight  of  a  point  varies  with  the  square  root  of  the  number  of  entries  and  not 
directly  with  the  number  of  entries.  Thus  an  average  of  a  point  representing  one 
tree  and  a  point  representing  four  trees  would  be  on  a  straight  line  connecting  them 
and  one-third  of  the  way  from  the  "4"  point  to  the  "1"  point.  The  number  of 
trees  in  each  class  should  therefore  be  entered  on  the  sheets  opposite  the  point 
representing  the  volume. 

The  original  volume  for  the  trees  of  a  given  diameter  class  may  represent  a 
diameter  slightly  larger  or  smaller  than  the  exact  inch.  For  instance,  in  Table 
XXVII,  the  average  diameter  for  17-inch  trees,  55  feet  high,  was  16.7  inches.  This 
volume  should  not  be  entered  above  17  inches,  but  above  its  true  average  diameter. 

When  the  curve  is  completed,  the  values  are  read  from  it  for  each  exact  inch  of 
diameter. 

A  comparison  of  the  original  and  harmonized  values  from  the  above  curve  is  given 
in  Table  XXVIII,  p.  171. 

The  averages  for  33  out  of  38  trees  and  6  out  of  9  diameter  classes  fall  within 
2  per  cent  of  the  curve. 

140.  Harmonized  Curves  for  Standard  Volume  Tables  Based  on 
Diameter.  So  far,  the  volumes  of  trees  of  different  diameters  for  but 
one  height  class  have  been  shown.  By  the  same  method,  a  curve  is 
constructed  for  each  separate  height  class,  based  on  the  scale  of  diam- 
eters. If,  instead  of  making  each  of  these  curves  on  separate  sheets, 
they  are  all  placed  on  the  same  sheet,  their  relation  to  each  other  is 
shown. '  All  curves  should  show  the  same  general  trend,  in  harmony 
with  the  law  of  variation  between  diameter  and  volume.     The  set 

1  Where  insufficient  data  are  available  and  height  divisions  are  small,  the  values 
for  different  heights  will  frequently  overlap.  In  such  cases  it  is  better  to  plot 
every  alternate  height  class  first,  and  draw  the  respective  curves  before  plotting  the 
intervening  classes. 


170 


CONSTRUCTION  OF  STANDARD  VOLUME  TABLES 


of  harmonized  cui'ves  of  volume  based  on  diameter  is  shown  in  Fig. 
28  with  height  class  of  the  trees  in  each  curve  indicated. 

From  this  set  of  curves  a  table  can  be  read,  whose  form  is  similar 
to  that  of  Table  XXVII,  but  whose  volumes  increase  regularly  with 


U         15  16 

Diameteivlaclies 

Fig.  28. — Curves  of  Tolume  based  on  diameter  for  separate  height  classes,  plotted 
from  original  averages  in  Table  XXVII. 


diameter,  and  whose  values  are  interpolated  to  even  inch  classes  from 
the  averages  of  the  original  table. 

141.  Harmonized  Curves  Based  on  Heights.  But  this  table  is 
not  necessarily  in  final  form,  for  the  variations  caused  by  height  must 
also  be  harmonized.     The  first  set  of  values  has  been  made  regular 


HARMONIZED  CURVES  BASED  ON  HEIGHTS 


171 


TABLE  XXVIII 

COMPAKISON  OF  ORIGINAL  AND   HARMONIZED  AVERAGE   VOLUMES 


D.  B.H. 

Original 

Harmonized 

volumes. 

volumes. 

Remarks 

Inches 

Cubic  feet 

Cubic  feet 

9 

14.0 

10 

17.38 

16.5 

One  tree  with  full  bole 

11 

19.78 

19.75 

12 

24.27 

23.4 

13 

27.53 

•      27.4 

14 

31.61 

32.1 

15 

39.44 

37.3 

Original  volumes  evidently  too  cylin- 
drical for  average 

16 

43.71 

43.1 

17 

47.26 

49.5 

Original  diameter  16.7  inches,  but  aver- 
age volume 

18 

54.82 

56.2 

One  tree  with  poor  form 

19 



63.6 

TABLE  XXIX 

Volumes  Read  from  Curves  of  Volume  on  Diameter  for  Different  Height 

Classes 


Height  Classes,  Feet 

D.  B.H. 

50 

55 

60 

65 

70 

75 

80 

Inches 

Cubic  Feet 

9 

9.5 

12.2 

13.0 

14.0 

10 

12.9 

15.4 

16.5 

17.6 

11 

16.2 

18.8 

19.9 

21.3 

12 

19.7 

22.4 

23.2 

25.1 

13 

23.5 

26.2 

27.1 

29.4 

14 

27.8 

30.6 

31.8 

34.1 

39.3 

41.0 

45.7 

15 

32.3 

35.0 

37.1 

39.0 

44.0 

46.0 

51.4 

16 

40.0 

43.0 

44.7 

49.0 

51.5 

57.2 

17 

45.0 

49.2 

51.3 

54.4 

57.4 

63.6 

18 

55.5 

58.0 

60.0 

63.8 

70.2 

19 

65.0 

66.0 

70.2 

20 

172  CONSTRUCTION  OF  STANDARD  VOLUME  TABLES 

within  each  height  class  separately,  but  this  does  not  prevent  the  values 
of  all  the  trees  of  a  given  height  class  from  being  too  low  or  too  high. 
In  fact,  if  one  of  the  volume  curves  representing  a  height  class  is  incor- 
rectly drawn  lower  or  higher  than  it  should  be,  this  very  result  is  pro- 
duced.^ 

The  law  of  variation  of  volume  based  on  height  may  be  expressed 
by  the  equation  y  =  px,  since  volume  (y)  increases  approximately  in 
direct  proportion  to  height  (x).  For  trees  of  the  same  diameter,  whose 
volumes  lie  on  the  same  ordinate  in  Fig.  28,  the  curves  of  volumes  for 
regular  gradations  of  height  should  be  spaced  at  about  equal  distances. 
This  interval,  of  course,  increases  with  each  diameter  class.  Since  this 
is  known,  the  first  set  of  curves  based  on  diameter  may  be  harmonized, 
not  only  in  direction  but  in  spacing,  being  placed  at  equal  intervals 
on  each  successive  ordinate.  The  resultant  table  will  then  show  volumes 
increasing  regularly  by  height. 

A  still  better  method  of  securing  this  regularity  is  to  plot,  from  the 
values  obtained  from  the  first  set  of  curves,  a  second  set  in  which 
heights  are  the  determinate  variable,  or  basis  plotted  on  the  horizontal 
scale,  and  volumes  are  plotted  vertically  as  before.  Diameter  must 
now  be  eliminated  as  a  variable,  by  plotting  all  the  volumes  for  trees 
of  a  single  diameter  class  in  the  same  curve.  Beginning  with  the  first 
diameter  class  in  Fig.  28,  which  is  intersected  by  two  or  more  curves 
of  volume  representing  different  height  classes,  these  volumes  at  the 
intersecting  points  are  read,  beginning  with  the  lowest.  The  series 
of  values  thus  obtained  represents  the  volumes  of  successive  height 
classes,  and  as  such  are  plotted  on  the  new  sheet,  and  connected  to 
form  a  new  curve,  which  represents  only  trees  of  the  diameter  class 
so  taken. 

Each  point  so  plotted  should  be  placed  above  the  actual  average 
height  for  the  class,  as  found  in  the  original  averages  shown  in  Table 
XXVII,  e.g.,  for  the  15-inch  curve,  the  55-foot  class  must  be  plotted, 
not  above  55  feet,  but  above  57  feet,  which  is  the  actual  average 
height  for  this  class. 

Separate  new  curves  are  thus  plotted  for  the  trees  in  each  diameter 
class.  Instead  of  plotting  these  values  direct  from  the  first  set  of 
curves,  a  table  may  be  made  from  the  values  read  from  these  curves, 

1  The  tendency  to  error  may  be  greatly  reduced  in  the  original  curves  if  the 
the  square  of  the  diameter  is  made  the  basis  of  the  table,  or  abscissae  scale,  in  which 
case  the  curves  take  the  form  of  straight  lines  characteristic  of  those  based  on 
height.  The  same  result  may  be  obtained  by  plotting  on  logarithmic  cross-section 
paper.  (Logarithmic  Cross-section  Paper  in  Forest  Mensuration,  Donald  Bruce, 
Journal  of  Forestry,  Vol.  XV,  1917,  p.  335.) 


HARMONIZED  CURVES  BASED  ON  HEIGHTS 


173 


and  the  new  values  then  replotted  from  this  table.     In  this  case,  the 
values  from  each  curve  will  be  read  horizontally  from  the  table  instead 
of  from  the  vertical 
column  as  in  the  first       ^ 
instance. 

"Strip"  Method  of 
Replotting.  A  rapid 
method  of  replotting 
direct  from  the  curve  is 
by  means  of  a  strip  of 
paper.  The  zero  or  end 
of  strip  is  placed  on  the 
base  or  abscissa,  and 
held  in  a  vertical  posi- 
tion, so  that  the  edge 
lies  on  the  ordinate  re- 
presenting the  diameter 
class  to  be  transferred; 
a  mark  is  then  made 
where  the  curve  of  vol- 
ume for  each  successive 
height  class  intersects 
the  strip.  These  marks 
may  be  numbered  or 
otherwise  designated, 
but  their  mere  order  is 
a  sufficient  identifica- 
tion. Transferring  this 
paper  to  the  second 
sheet,  the  vertical  or 
ordinate  distance  (which 
represents  volume  in 
each  set  of  curves)  for 
the  first  height  class, 
is  plotted  on  the  ordi- 
nate intersecting  the 
abscissa  representing 
that  height.  The  strip 
is  then  moved  to  the 
right,  to  intersect  the 
next' height  on  the  scale 
and  the  corresponding 
volume  point  transferred 

to  the  sheet.     When  plotted    thus,    these    volumes  indicate  the  position  of  the 
curve  of  volume  for  different  heights,  for  trees  of  the  given  diameter  class. ^ 


6  40 


3  35 


^ 

A 

^■' 

/> 

^9" 

/ 

^ 

^ 

^y 

17" 

^ 

>; 

y\ 

^ 

^ 

^ 

^ 

y 

16" 

^ 

J^ 

^ 

/' 

P^ 

^ 

^ 

14" 

^ 
^ 

^ 

13" 
1^" 

^^ 

^ 

11" 

1 
t 

^ 

he  dott 
^e  ocig 
^he  lack 

;d  lines 
nal  cur 
of  harn 

show 
'es. 
iony  in 

'^ 

'^ 

lo" 

tt)ese  cur 
the  irreg 
new  cur\ 
tdansDose 

ilarity 
es  wher 
d. 

3fthe 
thus 

;^ 

■^ 

9" 

5 

0          5 

5          6 

0          6 

5 

7 

0             T 

5         8 

0 

Height-,  Peefe 

Fig.  29. — Curves  of  volume  based  on  height.  Original 
curves,  dotted,  from  curves  shown  in  Fig.  28,  or 
values  from  Table  XXIX.  Harmonized  curves 
drawn. 


1  This  method  is  described  by  W.  B.  Barrows,  "Reading  and  Replotting  Curves 
by  the  Strip  Method,"  Proc.  Soc.  Am.  Foresters,  Vol.  X,  1915,  p.  65. 


174 


CONSTRUCTION  OF  STANDARD  VOLUME  TABLES 


Irregularities  in  spacing  the  first  set  of  curves  are  now  shown  by 
this  second  set  as  similar  distortions  of  each  curve  where  they  inter- 
sect the  same  ordinate.     This  is  shown  in  Fig.  29.^ 

Volumes  read  from  this  second  and  final  set  of  curves  increase  with 
both  diameter  and  height  according  to  the  true  laws  of  variation  appli- 
cable to  each  dimension.  In  this  way  Standard  Volume  Tables  are 
secured,  which  may  be  applied  to  a  species  throughout  its  range,  unless 
it  is  convincingl}^  shown  that  there  are  consistent  differences  in  form 
and  volume  not  due  to  either  height  or  diameter,  which  can  be  cor- 
related with  age  or  site,  and  call  for  separate  standard  table. 


TABLE  XXX 

Standard  Volume  Table  Read  from  Curves  of  Volume  on  Height  for 
Different  Diameter  Classes 


Height  Classes,  Feet 

D.B.  H. 

50 

55 

60 

65 

70 

75 

80 

Inches 

Cubic  Feet 

9 

10.3 

11.8 

13.2 

14.6 

10 

13.6 

15.1 

16.6 

18.1 

11 

17.0 

18.5 

20.0 

21.5 

12 

20.2 

22.1 

24.0 

26.0 

13 

24.0 

26.2 

28.4 

30.6 

14 

28.0 

30.6 

33.2 

35.9 

38.5 

41.2 

43.8 

15 

32.4 

35.2 

38.0 

40.8 

43.6 

46.4 

49.2 

16 

40.0 

43.0 

46.0 

49.0 

52.0 

55.0 

17 

45.4 

48.6 

51.8 

54.9 

58.0 

61.1 

18 

55.3 

58.3 

61.2 

64.2 

67.1 

19 

61.2 

64.4 

67.6 

70.8 

74.0 

142.  Local  Volume  Tables — Their  Construction  and  Use.     In  the 

absence  of  a  standard  table,  or  when  for  any  reason  the  available  tables 
are  not  reliable  and  there  is  no  time  to  construct  a  table  for  all  heights 


'  Based  on  the  law  of  variation  between  volume  and  height,  this  set  of  curves 
(in  rectangular  co-ordinates  the  term  "curve"  apphes  to  any  hne,  curved  or  straight, 
which  follows  a  regular  law  and  can  be  expressed  by  a  formula)  consists  of  lines  which 
are  nearly  straight,  but  not  parallel,  since  the  difference  in  volume  increases  with 
each  diameter  class  representing  a  single  curve. 


LOCAL  VOLUME  TABLES 


175 


and  diameters,  a  local  table  based  on  diameter  alone  may  be  made 
directly,  from  whatever  number  of  measurements  can  be  secured.  The 
volumes  of  all  trees  of  the  same  diameter  are  averaged  regardless  of 
height.  These  averages  must  then  be  plotted,  and  a  single  curve  drawn 
similar  to  that  shown  in  Fig.  27  but  containing  trees  of  all  heights. 
From  this  curve  average  volumes  for  each  diameter  class  are  read. 

When  diameter  is  shown  in  the  table,  such  tables  are  useful  only 
within  the  same  stand,  age  class  or  site  class  in  which  they  are  con- 
structed. Timber  whose  average  height  is  greater  or  smaller,  for  any 
cause,  for  trees  of  the  same  diameter  classes,  cannot  be  measured  by 
this  local  table  but  require  a  new  basis  of  volumes.  If  it  is  found  that 
the  heights  do  average  the  same  for  each  diameter  the  local  table  can 
be  used  unless  it  is  known  that  other  factors  influence  form  sufficiently 
to  require  its  correction.  But  where  no  record  is  made  of  heights  of 
the  trees  used  in  constructing  the  table,  as  frequently  happens,  the 
cruiser  has  no  way  of  knowing  whether  the  table  applies  to  any  stand 
but  that  in  which  it  was  made.  Where  it  is  expected  that  such  local 
tables  may  be  used  again,  heights  should  be  measured  as  well  as  diam- 
eter, and  a  curve  of  height  on  diameter  drawn.  The  full  data  for  such 
a  local  table,  which  is  to  be  saved  for  possible  future  use,  are: 


TABLE  XXXI 
Local  Volume  Table,  Form 


D.  B.H. 

Volume. 

Height. 

Inches 

Cubic  feet 

Feet 

12 

20.2 

50 

13 

25.3 

53 

14 

32.1 

58 

1.5 

39.1 

62 

16 

46.0 

65 

etc. 

143.  The  Derivation  of  Local  Volume  Tables  from  Standard  Tables. 

Where  a  reliable  standard  volume  table  is  available,  it  is  not  necessary 
to  construct  a  local  volume  table  based  solely  on  diameter.  If  the 
estimator  does  not  need  or  desire  to  distinguish  different  heights  in 
tallying  trees,  he  may  select  the  volumes  from  the  standard  table  which 
represent  trees  of  the  average  heights  of  the  given  stand,  and  tally 
diameter  only. 

The  first  step  is  to  determine  the  average  height  of  trees  of  each 
diameter  class,  by  means  of  a  few  measurements,  and  the  plotting  of 


176  CONSTRUCTION  OF  STANDARD  VOLUME  TABLES 

a  curve  to  show  the  average  height  of  trees  of  each  diameter  (§  209). 
The  volumes  corresponding  to  these  heights  in  the  standard  table  are 
taken.  When  the  height  for  a  diameter  class  falls  between  the  fixed 
heights  given  in  the  table,  the  volume  for  this  class  must  be  interpolated. 
For  instance,  a  height  of  54  feet  in  a  table  showing  volumes  for  50- 
and  60-foot  trees,  would  require  an  addition  to  the  50-foot  volume, 
of  four-tenths  of  the  difference  between  those  of  the  50-  and  60-foot 
classes. 

The  standard  volume  table  therefore  permanently  replaces  all  local 
tables,  provided  the  average  form,  the  unit  of  volume,  and  the  merchant- 
able units  used  correspond  to  the  conditions  for  the  timber  to  be  meas- 
ured (§  205). 

144.  Volume  Tables  for  Peeled  or  Solid-Wood  Contents.  To 
obtain  volume  tables  for  solid  or  peeled  contents,  the  original  tree 
volumes  are  computed  from  D.I.B.  measurements  taken  at  stump  and 
at  each  section.  The  D.B.H.  of  each  tree  is  based  on  the  measurement 
outside  bark  just  as  for  volume  tables  with  bark.  This  permits  the 
comparison  of  the  volumes  with  and  without  bark  for  trees  of  the  same 
size  class. 

References 

Volume  Tables  and  the  Bases  on  Which  They  May  Be  Built,  Judson  F.  Clark, 

Forestry  Quarterly,  Vol.  I,  1903,  p.  6  (Schiffel's  formula). 
Volume  Tables,  Henry  S.  Graves,  Forestry  Quarterly,  Vol.  Ill,  1905,  p.  227. 


CHAPTER  XII 

STANDARD   VOLUME   TABLES   FOR   MERCHANTABLE   CUBIC 
VOLUME  AND  CORDS 

145.  Purpose  and  Derivation  of  Tables  for  Cubic  Volume  of  Trees. 

Volume  tables  for  merchantable  cubic  volume  are  intended  to  measure 
the  merchantable  portion  of  trees,  thus  excluding  the  stump,  top  and 
branches  too  small  for  use.  In  America  these  tables  are  used  for  the 
measurement  of  firewood,  pulp  or  acid  wood,  or  products  to  be  totally- 
consumed  or  disintegrated  (§  18).  The  volumes  in  this  class  of  tables 
may  be  obtained  from  those  for  total  cubic  volume  by  subtracting 
the  waste  or  unused  portion  of  the  stem  represented  by  stump  and 
top,  or  the  merchantable  portion  of  the  bole  may  be  computed  directly. 
For  board  contents  or  other  units,  different  tables  are  employed. 

146.  Branch-wood  or  Lapwood.  Where  branch-wood  is  of  sufficient 
size  for  use,  which  occurs  with  many  hardwoods  used  for  firewood,  its 
volume  is  computed  separately  from  the  stem,  usually  in  4-foot  lengths, 
each  of  which  is  calipered  at  the  center  of  the  stick  (by  Huber's  formula) . 
The  additional  volume  of  branches  is  termed  lapwood.  The  better 
method  is  to  keep  this  volume  separate  from  that  of  the  main  bole 
in  the  volume  table,  and  express  it  by  diameter  classes  as  a  per  cent 
to  be  added  to  the  volumes  in  the  table.  Lapwood  is  an  exceedingly 
variable  quantity,  chiefly  found  in  hardwoods,  practically  absent  in 
conifers,  and  dependent  entirely  upon  the  degree  of  density  of  the  stand, 
which  also  affects  the  form  of  the  bole  itself.  Where  lapwood  is  included 
with  the  volume  of  the  bole,  the  trees  should  be  separated  not  only  by 
diameter  but  by  crown  classes,  dependent  on  the  degree  of  crowding 
and  the  relative  spread  of  crowns.  No  more  than  three  such  classes 
would  be  practical,  namely  open-grown  or  large  spreading  crowns 
containing  a  large  per  cent  of  merchantable  lapwood,  medium  crowns 
containing  an  appreciable  quantity  of  lapwood,  and  trees  without 
lapwood  in  quantity  sufficient  to  affect  the  estimates. 

Standard  volume  tables  (§140)  will  seldom  include  lapwood  but  will 
be  confined  to  the  volume  of  the  main  stem.  Where  lapwood  is  included, 
the  tables  will  usually  be  local  in  character,  and  based  solely  on  diam- 
eter, with  a  separate  table  for  each  crown  class. 

147.  Merchantable  Limit  in  Tops  and  at  D.B.H.  Where  cubic 
volume  is  utilized,,  the  limit  of  merchantable  size  in  the  tops  lies  between 

177 


178  STANDARD  VOLUME  TABLES 

2  and  3  inches,  outside  bark.  The  same  standard  apphes  to  branches. 
The  "  merchantable  "  top  diameter  for  European  conifers  is  about  7 
centimeters  or  3  inches  outside  bark,  but  this  apphes  to  wood  for  manu- 
facture, and  practically  the  whole  tree  may  be  taken  by  the  use  of  fagots ; 
i.e.,  brushwood,  done  up  in  bundles.  There  is  considerable  range  in 
top  diameters  even  for  these  purposes,  the  top  diameter  limit,  and 
consequently  the  waste,  increasing  in  regions  of  poor  markets.  The 
top  diameters  used  in  constructing  tables  of  merchantable  volume 
must  be  clearly  stated.     For  peeled  wood,  diameter  inside  bark  is  given. 

The  minimum  top  diameter  usually  does  not  coincide  with  an 
exact  merchantable  length,  but  when  a  length  of  4  feet  is  used,  the 
practice  may  be  adopted  of  accepting  the  last  4-foot  stick  which  measures 
the  minimum  diameter  at  the  middle  of  piece.  The  average  top  diameter 
will  then  coincide  with  the  minimum  established,  half  the  sticks  being 
slightly  below  this  limit  at  the  top  end. 

The  merchantable  top  diameter,  combined  with  the  minimum  length 
of  a  merchantable  piece,  indicates  the  smallest  size  of  tree  measured 
at  B.H.  which  can  be  shown  in  the  volume  table.  Ordinarily,  the  mini- 
mum commercial  diameter  limit  will  be  somewhat  larger  than  this, 
based  on  the  inclusion  of  cost  of  logging  as  a  factor  preventing  the 
marketing  of  trees  with  the  minimum  merchantable  contents.  Volumes 
of  trees  of  still  smaller  sizes  can  be  shown  only  in  tables  for  total  cubic 
volume.  Since  the  merchantable  limit  of  top  diameters  for  cordwood 
is  small,  in  constructing  standard  volume  tables  for  cubic  feet  or  cords 
the  trees  are  classed  by  D.B.H.  and  total  height,  in  5-  or  10-foot  height 
classes,  as  for  tables  giving  total  volume. 

148.  Stump  Heights.  Stump  height  varies  with  local  custom  and 
with  the  scarcity  and  value  of  the  wood.  Stump  heights,  especially 
for  large  trees,  are  not  uniform  but  increase  with  the  diameter  of  the 
tree,  and  rules  for  cutting  usually  recognize  this  fact,  specifying  for 
instance  that  the  height  of  stump  shall  not  exceed  one-half  its  diameter. 
For  small  timber,  uniform  stump  heights  may  be  specified,  as  low  as 
from  1  foot  to  6  inches.  If  the  stump  heights  used  in  constructing  the 
volume  table  are  stated  it  enables  the  cruiser  not  only  to  know  whether 
the  table  conforms  to  local  usage,  but  to  correct  it  for  difference  in 
practice. 

The  cutting  of  low  stumps  not  only  increases  the  merchantable 
contents  of  the  tree  but  will  greatly  increase  the  possibility  of  error 
by  use  of  Smalian  formula  for  volume.  This  error  is  always  plus  and 
will  require  special  measurement  of  short  lengths  in  butt  log. 

149.  Merchantable  versus  Used  Length.  Where  the  portion  of  the 
tree  which  is  actually  used  falls  short  of  the  full  possibility,  due  to  care- 
less supervision  or  to  failure  to  appreciate  the  economic  conditions, 


WASTE,  DEFINITION  AND  MEASUREMENT  179 

there  arises  a  difference  between  the  definition  of  merchantable  length, 
and  used  length.  Merchantable  length  is  the  total  length  of  a  stem 
which  can  he  used  under  given  conditions.  Used  length  is  the  total 
length  of  a  stem  actually  utilized  in  commercial  operations.  There 
is  therefore  no  fixed  or  absolute  merchantable  length,  since  the  very 
definition  of  the  term  "  merchantable  "  indicates  that  the  product 
must  be  salable.  When  an  operator  is  actually  utilizing  all  the  material 
that  he  can  manufacture  or  market  at  a  profit  used  length  and  merchant- 
able length  coincide. 

150.  Waste,  Definition  and  Measurement.  Waste  is  therefore 
defined  in  two  ways.  First,  there  is  the  unavoidable  waste  in  twigs, 
branches,  stump  and  top,  that  cannot  be  used  under  existing  economic 
conditions,  logging  costs,  and  markets.  A  better  term  for  this  material 
is  refuse.  This  waste  was  large  in  earlier  periods  and  tends  constantly 
to  diminish.  Second,  there  is  avoidable  waste,  caused  by  the  fact 
that  the  markets  and  logging  possibilities  have  changed  faster  than 
the  logging  practice.  During  the  war  this  form  of  waste  increased  in 
certain  sections  due  to  the  inefficienc}^,  indifference  and  independence 
of  woods  labor.  The  amount  of  this  avoidable  waste  is  somewhat  a 
matter  of  judgment.  When  w^aste  is  demonstrated,  practice  tends 
to  take  up  the  slack,  and  used  lengths  are  readjusted  to  coincide  with 
merchantable  lengths. 

The  unavoidable  waste  is  usually  taken  as  the  difference  between 
the  total  and  merchantable  volumes  of  the  bole,  excluding  branches. 

For  tops,  the  paraboloidal  formula  V^-l  is  used,  while  for  stumps, 

the  cylindrical  contents  of  the  stump  based  on  its  upper  area  is  usually 
accepted  in  place  of  its  actual  total  volmiie. 

The  avoidable  waste  represents  the  cubic  volume  of  the  top  section 
between  the  upper  limit  of  used  length  and  the  merchantable  diameter 
limit,  plus  the  cylinder  representing  the  difference  between  actual 
height  of  stump  and  height  to  which  it  should  have  been  cut. 

A  more  complicated  method  applied  to  board-foot  contents  is  to 
re-scale  the  contents  of  the  tree,  measuring  the  top  diameter  of  each 
log  at  a  point  lower  than  the  existing  point  by  the  difference  in  stump 
height.  The  difference  in  total  tree  scale  so  obtained  is  regarded  as 
indicating  the  waste. 

151.  Defects  or  Cull.  For  pulpwood,  defective  or  rotten  pieces  are 
not  merchantable.  This  raises  the  question  of  cull  or  deductions  from 
the  cubic  volume  table.  The  question  is  far  more  serious  for  board- 
foot  volume  tables.  No  such  deductions  should  be  made  for  cull  in 
the  volume  tables  themselves,  especially  in  standard  tables.  The  cull 
per  cent  varies  without  any  reference  to  tree  form  or  total  volume. 


180  STANDARD  VOLUME  TABLES 

The  deduction  of  a  given  per  cent  for  cull  would  ruin  the  table,  making 
of  it  a  local  table  applicable  only  to  timber  which  is  assumed  (one  can 
never  know  certainly)  to  show  the  given  per  cent  of  defect.  Even  if 
the  per  cent  of  deduction  is  stated,  the  table  would  require  complete 
recalculation  for  stands  varying  from  this  per  cent  of  cull.  By  contrast, 
tables  made  for  sound  trees  permit  of  the  calculation  of  total  volume 
for  trees  or  stand,  after  which  the  estimated  per  cent  of  cull  may  be 
deducted  from  this  total. 

All  volume  tables  should  be  constructed  to  show  only  the  volume 
of  trees  as  if  sound.  They  are  based  on  exterior  measurements  or 
form,  without  deduction  for  interior  defects,  which  must  alwaj's  be  made 
b}'  the  cruiser  from  observation  of  the  character  of  each  separate  tree 
or  stand. 

152.  Conversion  of  Volume  Tables  for  Cubic  Feet,  to  Cords.  As 
seen  in  Chapter  IX  the  ratio  of  cubic  to  stacked  volume  increases  with 
the  diameter,  straightness  and  smoothness  of  the  average  stick  and  vice 
versa.  Tables  of  cubic  volume  may  be  converted  into  cords  by  the 
use  of  ratios  or  converting  factors,  but  if  a  constant  ratio  is  used  for 
trees  of  all  sizes,  the  corded  or  stacked  contents  of  small  trees  will  over- 
run the  values  shown,  while  that  of  the  larger  trees  will  fall  below  it. 
Fixed  ratios,  of  which  90  cubic  feet  per  cord,  or  70  per  cent  is  an  example, 
have  the  merit  of  standardizing  the  cubic  or  solid  contents  per  stacked 
foot  for  trees  of  all  sizes,  regardless  of  their  actual  stacked  volume. 
By  mixing  the  cordwood  from  large  and  small  trees,  the  average  ratio 
might  be  attained  in  practice.  The  best  example  of  this  principle  is 
the  Humphrey  caliper  rule,  which  converts  cubic  to  stacked  measure 
by  the  ratio  of  100.5  cubic  feet  per  cord  or  78.5  per  cent.  If  this  principle 
is  adopted,  the  volume  for  each  tree  class  is  divided  by  the  number  of 
cubic  feet  per  cord,  which  converts  the  table  to  the  form  desired. 

Where  actual  stacked  volume  is  desired  for  trees  of  each  size,  the 
ratio  of  conversion  must  be  found  separately  for  the  different  size 
classes.  The  tree,  and  not  the  bolt  of  cordwood,  is  the  unit  to  be  meas- 
lu-ed,  hence  the  average  size  of  the  cordwood  from  trees  of  different 
sizes  determines  the  converting  factor.  But  few  tables  have  been  pre- 
pared on  this  basis.  The  most  satisfactory  method  is  to  stack  the  cord- 
wood from  trees  of  different  diameters  separately  and  determine  the 
factors  directly.  A  simpler  method  is  to  determine  the  diameter  of  the 
average  stick  in  the  tree,  and  apply  the  ratio  previously  found  to  hold 
good  for  cordwood  of  this  average  size. 

The  ratio  or  ratios  used  for  conversion  should  always  be  shown 
in  connection  with  cordwood  volume  tables. 

An  example  of  the  converting  factors  used  in  constructing  cord  wood  volume 
tables  for  second-growth  hardwoods  is  given  in  Table  XXXII. 


DEFECTS  OR  CULL 


181 


TABLE  XXXII 

Conversion  Factors  for  Second-growth  Hardwoods  by  D.B.H.  Classes  with 
Corresponding  Diameters  of  the  Average  4-foot  Stick  in  the  Tree  or 
IN  THE  Stack  * 


Chestnut 

Black  Oaks 

White  Oaks 

Tree 

diameter 

breast-high. 

Diameter 

Conversion 

Diameter 

Conversion 

Diameter 

Conversion 

average 

factor 

average 

factor 

average 

factor 

stick. 

per  cord. 

stick. 

per  cord. 

stick. 

per  cord. 

Inches 

Inches 

Cubic  feet 

Inches 

Cubic  feet 

Inches 

Cubic  feet 

1 

0.9 

2 

1.8 

63 

1.8 

63 

1.8 

63 

3 

2.6 

70 

2.5 

69 

2.5 

69 

4 

3.3 

75 

3.1 

74 

3  1 

74 

5 

4.0 

79 

3.6 

77 

3,5 

76 

6 

4.7 

83 

4.1 

80     . 

3.9 

79 

7 

5.2 

85 

4.5 

82 

4.2 

81 

8 

5.8 

88 

4.8 

84 

4.5 

82 

•     9 

6.2 

89 

5.0 

85 

4.7 

83 

10 

6.7 

91 

5.3 

86 

4.9 

84 

11 

7.0 

92 

5.4 

86 

5.0 

85 

12 

7.4 

93 

5.6 

87 

5.1 

85 

13 

7.7 

94 

5.7 

88 

5.2 

85 

14 

7.9 

94 

5.7 

88 

5.2 

85 

15 

8.2 

95 

5.8 

88 

5.3 

86 

16 

8.4 

95 

5.9 

88 

5.4 

86 

17 

8.5 

95 

5,9 

88 

18 

8.7 

95 

6.0 

89 

19 

8.9 

96 

6.0 

89 

20 

9.0 

96 

*  Second-Growth  Hardwoods  in  Connecticut,  E.  H.  Frothingham,  U.  S.  Forest  Service,  Bui.  96, 
1912,  p.  64. 


From  a  table  showing  the  contents  in  cords,  by  either  of  the  above 
standards^  for  trees  of  each  size  class,  a  second  table  can  be  constructed, 
giving  the  number  of  trees  of  each  class  required  to  produce  one  cord 
of  wood.  The  cubic  contents  of  a  cord,  according  to  the  ratio  adopted, 
is  divided  by  that  of  the  tree  as  shown  in  a  volume  table.  This  gives 
the  number  of  trees  required.  These  tables  may  be  of  value  in  estimat- 
ing cordwood,  by  making  rough  counts.  The  principle  involved  is 
the  same  as  that  used  in  estimating  board  feet  by  log  run  (§  120). 


CHAPTER  XIII 
VOLUME  TABLES  FOR  BOARD  FEET 

153.  The  Standard  or  Basis  for  Board-Foot  Volume  Tables.     In 

Chapter  X  it  was  shown  that  the  basis  of  measurement  for  standing 
timber  intended  for  sale  is  either  the  possible  sawed  output  for  tracts 
that  are  cut  by  local  mills,  or  the  log  scale  for  timber  to  be  transported 
to  mills  at  some  distance  from  the  area.  Even  in  the  first  instance 
the  measurement  of  tree  volumes  requires  a  local  log  rule  based  on 
mill  tallies. 

Volume  tables  for  board  feet  must  be  based  upon  the  contents  of 
the  logs  which  can  be  cut  from  sound  trees,  as  measured  by  the  stand- 
ard or  log  rule  which  forms  the  basis  of  sale  of  the  timber.  For  the 
purpose  of  timber  estimating  for  which  these  tables  are  required,  it 
is  not  permissible  to  substitute  volumes  representing  a  different  stand- 
ard even  if  a  more  accurate  one. 

But  it  is  recognized  that  existing  conditions  requiring  the  scaling 
of  logs  by  defective  log  rules  may  change  and  for  purposes  of  stock 
taking  or  inventory  of  standing  timber  required  by  an  owner  for  the 
management  of  forest  property  which  he  intends  to  retain,  and  for  the 
prediction  of  growth,  volumes  of  standing  timber  are  preferably  meas- 
ured by  tables  based  on  log  rules  which  give  an  accurate  measurement 
of  the  board-foot  contents  of  the  trees. 

This  conflict  between  a  temporary  economic  condition  and  a  per- 
manent basis  of  management  may  require  a  double  standard  of  measure- 
ment, and  two  separate  volume  tables.  The  first  step  in  the  con- 
struction of  volume  tables  for  board  feet  is  to  decide  upon  the  log  rule 
to  be  used  in  obtaining  the  tree  volumes. 

For  second-growth  timber,  and  for  the  purpose  of  inventory  and 
basis  of  growth  studies,  this  should  if  possible  be  a  rule  such  as  the 
International,  or  one  based  on  mill  tallies  of  lumber  such  as  the  Massa- 
chusetts log  rule. 

For  commercial  timber  estimating  it  must  of  necessity  at  present 
be  the  log  rule  in  common  use  in  the  locality. 

154.  Adoption  of  a  Standard  Log  Length.  The  standard  practice, 
in  measuring  the  contents  of  entire  trees  for  the  construction  of  board- 
foot  volume  tables  is  to  disregard  the  actual  log  lengths  as  sawed,  and 
to  measure  the  diameter  on  the  bole  at  fixed  points  corresponding  to 

182 


TOP  DIAMETERS,  FIXED  OR  VARIABLE  LIMITS  183 

logs  of  a  standard  length,  since  this  basis  coincides  with  the  application 
of  the  table  by  timber  cruisers  (§  119).  Sixteen  feet  is  the  standard 
most  commonly  adopted,  to  which  is  added  a  trimming  allowance  of 
.3  foot.  Volume  tables  for  hardwoods  Yna.y,  if  advisable,  be  based  on 
logs  12  feet  long  but  this  is  the  exception.  The  objections  to  the  alter- 
native method  of  scaling  the  contents  of  the  logs  as  sawed  are  summed 
up  in  §  135,  but  this  latter  method  has  been  extensively  used  in  the  past 
in  volume-table  construction.  The  base  from  which  log  lengths  are 
measured  is  usually  the  actual  height  of  the  stump,  as  sawed.  This 
introduces  a  variable  factor  dependent  upon  the  standard  of  heights 
secured  in  felling. 

155.  Top  Diameters,  Fixed  or  Variable  Limits.  The  field  measure- 
ments of  tree  volumes  are  the  same  as  for  cubic  contents  of  logs  (§  135). 
If  16  feet  is  the  standard  log  length,  the  taper  measurements  are  com- 
monly recorded  for  each  8-foot  point  as  w^ell.  The  purpose  of  the  work 
is  to  determine  the  merchantable  contents.  This  evidently  calls  for 
the  omission  of  the  volume  of  the  top  portion  of  the  bole,  which  is  not 
merchantable.  But  shall  the  length  of  the  rejected  top  be  based  upon 
the  actual  utilization  of  the  specific  tree?  If  so,  the  last  saw  cut  will 
indicate  the  limit  of  merchantability,  beyond  which  the  contents  of 
the  top  is  classed  as  waste.  By  the  method  of  measuring  the  volume 
of  the  logs  as  sawed,  this  top  is  rejected  as  it  lies,  regardless  of  whether 
the  utilization  of  the  tree  has  been  close  or  wasteful.  If  on  the  other 
hand  diameters  are  taken  at  fixed  intervals,  the  point  of  measurement 
will  seldom  coincide  with  that  of  the  last  cut,  but  will  fall  above  or 
below  it. 

If  actual  utilization  practice  is  to  be  adopted  as  the  basis  of  the 
table,  while  at  the  same  time  the  fixed  length  of  section  is  to  be  retained, 
the  top  diameter  of  the  last  "  merchantable  "  log  for  the  volume  table 
should  be  taken  at  the  point  which  falls  the  nearest  to  the  last  saw  cut, 
whether  this  point  is  above  or  below  the  cut.  When  the  saw  cut  is 
midway  between  two  points,  the  lower  measurement  may  be  taken, 
or  else  the  character  of  the  bole  may  be  made  the  basis  of  choice  (p.  184, 
Fig.  30). 

When,  by  method  B,  only  the  merchantable  volume  is  desired,  if  last  cut  is 
at  (1),  the  volume  will  be  taken  to  the  nearest  8-foot  point  Be.  If  cut  at  (2),  Be 
is  still  the  nearest  point.  But  if  cut  at  (3)  equidistant  from  Be  and  Bj,  either  the 
upper  point  By  would  be  chosen  on  alternate  trees  or  the  point  best  representing 
merchantable  volume,  in  this  case  Be. 

Utilization,  especially  where  sawlogs  are  cut  from  trees  with  limby 
tops,  is  seldom  to  a  uniform  diameter.  The  actual  top  diameter  varies 
widely  but  the  average  increases  with  the  D.B.H.  of  the  tree.  By  the 
method  outlined  above,  the  contents  of  the  volume  table  are  made  to 


184 


VOLUME  TABLES  FOR  BOARD  FEET 


t§^) 


Qi      O 


42     o 

ii 


a  =  „i 


3 


coincide  with  the  portion  of  the  tree  which  is  actually  used,  and  the 
average  top  diameter  with  that  which  is  actually  cut. 

But  the  variable  practice  of  sawing  and  the  arbitrary  standards 
set  by  saw  crews  as  to  waste  in  the  tops,  differing  with  different  crews, 
logging  jobs,  regions  and  seasons,  is  a  strong 
argument  for  adopting  a  fixed  standard  for 
top  diameters  for  saw  timber.  This  stand- 
ard may  either  conform  to  the  average 
diameter  utilized,  or  may  depart  from  it 
and  be  smaller;  e.g.,  as  at  B7. 

Where  a  fixed  top  diameter  is  chosen, 
instead  of  the  variable  one  coinciding  with 
utilization  practice,  the  last  taper  measure- 
ment will  usually  fall  above  or  below  this 
diameter,  as  before.  Here  the  same  rule 
of  give  and  take  can  be  applied;  but  if  the 
diameter  limit  is  small  the  top  tapers  rap- 
idly and  it  may  be  preferable  to  take  no 
measurement  of  less  than  the  minimum  top 
diameter.  The  last  top  measurements  will 
then  fall  always  either  at  or  below  the 
point. 

Where  16-foot  measurements  only  are 
made,  it  is  necessary  to  take  an  8-foot 
length  at  the  top  whenever  the  last  cut 
falls  more  than  4  feet  distant  from  the  last 
16-foot  taper.  This  is  another  reason  for 
taking  8-foot  tapers  throughout. 

156.  Defective  Trees,  Measurement. 
Frequently  one  or  two  top  logs  in  certain 
trees  will  not  be  utilized  because  of  defects 
in  the  upper  portion  of  the  bole.  Where 
the  table  is  based  on  actual  utilization, 
such  trees  should  be  rejected  for  measure- 
ment or  else  the  defective  logs  should  be 
measured,  since  the  cull  is  not  due  to  form 
but  to  defect.  Where  the  top  diameter  is 
fixed  independent  of  the  last  cut,  these  defective  trees  should  be 
measured.  All  trees  are  suitable  for  volume  measurements  except 
forked-topped  trees,  those  with  abnormal  D.B.H.  dimensions  due 
to  butt  swelling  and  frequently  caused  by  fire  scars,  and  trees 
deformed  in  such  a  manner  that  a  series  of  normal  taper  measure- 
ments   cannot    be    obtained.     Abnormalities  at  a  given  taper  point 


e2      b 


^  <<  :S  ^ 


BASIS  FOR  TREE  CLASSES  185 

can  be  overcome  by  proper  methods  of  measm-ement  (§  25).  It 
is  the  purpose  of  volume  tables  to  show  average  volumes  for  sound 
trees.  Since  defective  logs  or  trees  will  be  scaled  as  if  sound  in  volimie 
table  construction,  they  are  suitable  for  this  purpose. 

157.  Total  versus  Merchantable  Heights  as  a  Basis  for  Tree  Classes. 
Where  cubic  contents,  either  total  or  merchantable,  are  the  basis  of 
tree  volumes,  the  total  height  of  the  tree  to  tip  of  crown  is  the  only 
serviceable  basis  of  classification  by  height  (§137).  Where  the  volume 
of  the  tree  is  desired  in  merchantable  units  of  product,  such  as  board 
feet,  the  height  desired  in  practice  is  the  merchantable  length  of  the 
bole  or  height  of  the  top  of  the  last  log.  Timber  cruisers  commonly 
use  the  number  of  logs  of  given  length  in  a  tree,  and  not  the  total  height 
in  feet,  to  obtain  the  contents.  The  practice  of  basing  height  on  the 
merchantable  length  of  bole  is  most  useful  where  the  proportion  of  total 
length  used  is  most  variable,  as  in  large  hardwoods  or  heav^'-limbed 
conifers,  and  where  there  is  an  evident  variation  between  actual  top 
diameters  utilized.  Total  heights  in  dense  stands  of  tall  old  trees  are 
hard  to  see  and  measure  while  the  top  diameter  limit  is  usually  visible. 
This  basis  is  used  almost  universally  in  the  estimation  of  old-growth 
timber  of  all  species. 

The  same  height  basis  must  be  used  in  timber  estimating  as  is  used 
in  the  tables,  if  volume  tables  are  to  be  employed.  Hence  the  method 
of  measuring  heights  in  cruising  will  be  either  determined  by  the  existing 
tables,  or  else  the  tables  must  be  constructed  on  the  basis  desired  for 
the  estimating.  The  measurement  of  trees  for  the  construction  of  vol- 
ume tables  should  therefore  include  both  the  total  and  merchantable 
height,  to  permit  of  constructing  tables  on  each  basis  for  use  as  desired. 

158.  The  Coordination  of  Merchantable  Heights  with  Top  Diam- 
eters. The  use  of  volume  tables  to  determine  contents  of  standing 
trees  requires  the  determination  in  the  field  of  but  two  dimensions, 
namely  D.B.H.  and  height,  and  is  based  on  the  assumption  that  the 
volume  of  an  average  tree  of  these  dimensions  gives  the  average  volume 
of  the  trees  of  the  same  sizes  in  the  stand  to  be  estimated.  Where 
total  height  is  used  as  the  basis,  there  is  little  opportunity  for  error  in 
applying  the  volumes  in  the  table,  since  but  one  point  on  the  tree  can 
be  measured  for  height,  namely  the  tip.  But  where  merchantable 
height  is  the  basis,  a  second  variable  is  introduced,  the  top  diameter. 
The  volume  now  depends,  not  on  one  definite  factor  of  height  as  before, 
but  on  securing  coordination  between  these  two  variables,  i.e.,  height 
of  merchantable  top,  and  diameter  of  merchantable  top,  in  the  apphca- 
tion  of  the  volume  table. 

The  choice  of  top  diameter  limits  has  been  discussed.  But  the 
effect  of  this  choice  upon  the  merchantable  length  (the  height),  in 


186 


VOLUME  TABLES  FOR  BOARD  FEET 


such  tables,  needs  special  emphasis.  If  a  large  top  diameter  is  adopted, 
the  merchantable  height  is  correspondingly  less  for  trees  of  the  same 
total  height  and  form.  A  tree  100  feet  high  may  have  five  logs,  16 
feet  long,  if  cut  to  10  inches,  but  if  cut  to  16  inches  instead,  it  may  be 
only  a  four-log  tree.  A  6-inch  top  may  in  turn 
give  88  feet  or  5|  logs  from  the  same  tree.  Thus 
top  diameter  increases  as  merchantable  length 
diminishes.  Whatever  coordination  between 
these  two  variables  is  adopted  in  constructing 
the  volume  table  will  have  to  be  used  in  applying 
it;  i.e.,  the  same  top  diameters  used  for  the 
table  must  be  used  as  the  basis  of  merchant- 
able heights  in  timber  estimating.  Failure  to 
observe  this  rule  may  result  in  serious  errors 
and  has  sometimes  brought  the  use  of  such 
volume  tables  into  disfavor  among  practical 
cruisers. 

The  results  of  such  lack  of  coordination  are  easily- 
illustrated,  by  comparing  the  volumes  of  trees,  when 
divided  into  16-foot  cylinders  and  scaled  as  logs. 
Since  the  frustum  of  a  cone  is  a  regular  solid  resembling 
the  merchantable  portion  of  the  bole,  it  serves  to  illus- 
trate the  principle  in  question.  Assume  that  a  6-inch 
top  has  been  adopted  as  a  standard,  and  all  trees  meas- 
ured to  that  point. 

A  four-log  tree,  15  inches  at  the  top  of  the  first  log, 
inside  bark,  is  assumed  to  have  3  inches  taper  per  log. 
The  volume  of  this  tree,  by  the  International  log  rule, 
will  then  be 


Fig.  31.— Cause  of 
errors  in  use  of  vol- 
ume tables,  when 
based  on  merchant- 
able heights  and 
fixed  top  diameters. 


Logs 

First 

Second 

Third 

Fourth 

Total  for 
four  logs 

Diameter,  inches 

Volume,  board  feet 

15 
175 

12 
105 

9 
55 

6 
20 

355 

In  estimating,  if  this  table  is  to  be  used,  the  only  15-inch  four-log  tree  whose 
volume  can  be  correctly  measured  is  one  which  tapers  3  inches  per  log,  and  hence 
has  a  6- inch  top  diameter.  But  the  cruiser  may  fail  to  observe  the  same  coordi- 
nation between  merchantable  length  and  top  diameter,  and  may  tally  a  15-inch  tree 
which  tapers  2  inches  per  log,  as  a  four-log  tree.  The  dimensions  of  this  tree  up  to 
the  top  of  the  fourth  log  are 


Logs 

First 

Second 

Third 

Fourth 

Total  for 
four  logs 

Diameter,  inches 

Volume,  board  feet .... 

15 
175 

13 
130 

11 
90 

.1 

450 

MERCHANTABLE  HEIGHTS  WITH  TOP  DIAMETERS 


187 


This  tree,  if  measured  to  6  inches,  has  the  additional  length  of  1|  logs,  whose 
volume  is 


Logs 

Fifth 

Half  of 
sixth 

Total 
additional 

Total  for 
5i  logs 

Diameter,  inches 

Volume,  board  feet 

7 
30 

6 
10 

40 

490 

The  recording  of  this  tree  as  a  four-log  tree  was  probably  based  on  the  fact 
that  it  would  actually  be  cut  at  9  inches  in  the  top  instead  of  at  6  inches.  But 
the  cruiser,  if  he  uses  this  volume  table,  does  not  obtain  from  it  the  volume  of  a 
tree  with  a  9-inch  top,  but  of  one  with  a  6-inch  top.  The  initial  error  for  this  tree 
consists  in  not  tallying  it  as  a  S^-log  tree  with  a  6-inch  top.  If  the  full  contents 
of  the  four  actual  logs  which  it  contains  could  be  obtained  from  the  table,  the 
error  would  be  the  loss  of  40  feet  in  the  I5  logs  not  measured.  This  is  8  per  cent 
of  the  total  tree  volume.  But  instead,  a  much  greater  additional  error  is  incurred. 
The  volume  given  in  the  table  is  for  a  four-log  tree  with  a  6-inch  top  containing 
355  board  feet  instead  of  one  measuring  9  inches  at  top.  This  error,  due  to  differ- 
ence in  top  diameter  not  only  of  the  last  log  but  of  the  remaining  logs,  is  95  board 
feet  (450-355)  or  21  per  cent. 

If  the  purpose  of  the  estimate  is  to  obtain,  not  the  volume  of  all  trees  to  6  inches, 
but  the  volume  actually  to  be  cut,  the  attempt  to  obtain  this  by  dropping  the 
merchantable  length  of  this  tree  to  the  9-inch  point,  1^  logs  below  the  6-inch  point, 
has  made  the  use  of  the  above  volume  table  impossible,  for  in  place  of  a  correct 
deduction  of  8  per  cent  from  the  true  volume  of  a  52-log  tree,  which  would  give 
the  true  volume  merchantable,  the  use  of  the  table  has  lowered  the  estimate  by 
27  per  cent,  which  is  fff  of  the  desired  estimate  or  21  per  cent  too  low.  Errors 
of  this  magnitude  and  even  greater  may  and  have  been  made  in  use  of  volume  tables, 
solely  from  this  source. 

The  coordination  evidently  demands: 

The  estimation  of  height  to  the  same  point  which  has  been  used 

in  constructing  such  a  table. 
The  deduction  of  the  requisite  per  cent,  representing  the  small 
top  log  or  logs,  to  obtain  net  merchantable  volume,  in  case 
utilization  falls  short  of  this  point. 
Errors  in  estimating  merchantable  heights,  if  consistently  too  great 
or  too  small,  incur  both  the  above  errors  when  the  tally  is  applied  to 
the  volume  table.     Other  methods  of  avoiding  these  errors  are: 
To  use  total  height  as  a  basis. 
To  measure  a  few  heights  carefully  instead  of  guessing  at  many 

or  all  heights. 
To  construct  the  table  so  as  to  coincide  with  used  top  diameters, 
and  then  exercise  care  in  employing  this  same  standard  in 
estimating.^ 

'  The  writer's  initial  experience  in  timber  cruising  was  with  W.  R.  Dedon,  in 
Minnesota.     Mr.  Dedon  did  not  believe  in  the  use  of  volume  tables,  claiming  that 


188  VOLUME  TABLES  FOR  BOARD  FEET 

159.  Construction  of  Board-foot  Volume  Tables.  The  basis  agreed 
upon  as  to  the  top  diameter  to  use,  if  merchantable  heights  are  utilized, 
will  determine  the  height  class  into  which  each  tree  falls.  The  steps 
in  construction  are  the  same  as  for  tables  of  total  cubic  volume  (§  131) 
with  the  following  exceptions. 

Compute  the  volume  of  each  tree  by  means  of  the  log  rule  chosen, 
by  scaling  each  16-foot  log.  In  volume  table  work,  this  scale  per  log 
should  preferably  be  interpolated  to  yVinch  values,  for  which  purpose 
the  values  of  the  log  rule  can  be  tabulated  for  the  given  interpolations. 
The  last  or  top  log  if  8  feet  long  is  scaled  as  one-half  the  volume  of  a 
16-foot  log  of  equal  diameter.  If  the  logs  are  not  scaled  to  xV-inch 
they  are  rounded  off  to  nearest  inch  above  or  below  (§  137)  but  where 
but  a  few  trees  are  measured  in  each  size  class,  this  incurs  the  risk  of 
unnecessary  variations  in  volume  of  the  tree  classes. 

When  merchantable  heights  are  taken  to  fixed  lengths,  the  variable 
at  this  point  will  be  the  top  diameter.  Therefore,  the  average  top 
diameters  should  be  shown  for  each  diameter  and  height  class.  These 
tops  may  later  be  averaged  solely  on  the  basis  of  diameter  at  breast 
height. 

160.  Data  Which  Should  Accompany  a  Volume  Table.  Because 
of  the  errors  possible  in  misapplying  tables  for  merchantable  volumes, 
as  set  forth,  the  use  of  such  volume  tables  presupposes  knowledge  of 
their  reliability  and  applicability.  For  this  purpose  the  following  data 
should  always  accompany  the  tables: 

Species. 

Region  or  locality  where  measurements  were  taken. 

Age  of  trees  to  which  values  apply,  when  distinguished. 

Sites  or  quality  to  which  values  apply,  when  distinguished. 

Unit  of  volume  used. 

Log  rule  if  in  board  feet,  or  mill  tallies  specifying  character  and 

thickness  of  lumber  included. 
Specifications,  if  for  piece  products. 
Number  of  trees  measured  as  basis,  by  diameter  classes. 
Height  of  stumps. 

on  the  only  occasion  on  which  he  had  attempted  it,  the  table  gave  just  half  of  the 
true  estimate.  This  was  unquestionably  due  to  the  cause  explained  above,  that  is, 
trying  to  coordinate  large  top  diameters  with  a  table  made  to  smaller  tops.  The 
first  impression,  in  using  a  table  constructed  to  a  small  top  diameter  is  that  it 
"secures  a  greater  volume  per  tree."  The  error  is  just  the  reverse  of  this — it 
under-estimates  the  timber.  If,  on  the  other  hand,  the  top  diameters  in  the  table 
are  larger  than  those  applied  in  the  field  and  the  per  cent  of  total  contents  less, 
the  error  in  applying  the  table  is  an  over-estimate  equally  great.  These  possi- 
bilities of  error  in  the  use  of  volume  tables  based  on  merchantable  length  have 
been  commonly  overlooked  in  practice. 


CHECKING  THE  ACCURACY  OF  VOLUME  TABLES  189 

Top  diameters  used — by  diameter  classes  if  variable. 
Method  used  in  constructing  table, 

a.  Based  on  measurements  at  fixed  intervals. 

b.  Based  on  measurements  of  logs  as  cut. 

c.  From  tables  of  taper  or  form  (Chapter  XV). 

d.  From  form  factors  (Chapter  XVI) 
Author,  and  year  of  preparation. 

The  basis  of  classification  of  volumes,  as  to  height  and  diameter, 
is  shown  in  the  table  itself.  But  tables  based  solely  on  diameter  will 
have  their  value  increased  if  the  average  heights  used  in  constructing 
the  table  are  also  shown  (§  162). 

161.  Checking  the  Accuracy  of  Volume  Tables.  Volume  tables 
make  no  pretense  of  giving  accurately  the  volume  of  single  trees  (§  121). 
If  the  average  values  given  coincide  with  the  average  of  the  volumes 
of  the  trees  to  be  measured,  the  table  is  accurate  for  the  purpose  in  hand. 

But,  although  applied  correctly  (§  158)  volume  tables  will  gi\c 
inaccurate  results,  first,  if  the  table  itself  is  inaccurately  made  and  does 
not  give  correctly  the  volumes  of  the  trees  from  which  it  was  constructed, 
second,  if  the  trees  to  be  measured  average  greater  or  smaller  volumes 
for  given  diameters  and  heights  than  those  given  in  the  table,  on  account 
of  fuller  form  or  vice  versa. 

Volume  tables  made  in  one  locality  may  be  serviceable  in  other 
regions,  covering  the  entire  range  of  a  species.  If  the  estimates  are 
made  to  conform  with  the  top  diameters  and  log  rules  used  in  the  table 
the  only  possible  variation  in  volume  from  such  tables  is  that  of  average 
form,  and  variations  due  to  this  factor  can  be  determined  without 
constructing  an  entirely  new  table  (§  171). 

To  check  the  accuracy  of  construction  of  a  table,  the  basis  in  trees 
is  first  considered.  Tables  based  on  from  500  to  1000  trees  or  more 
are  regarded  as  fairly  reliable,  while  if  fewer  trees  have  been  used  the 
table  is  open  to  question.  The  total  actual  volume  of  the  trees  used 
in  constructing  the  table  can  be  checked  against  the  total  volume  of 
the  same  trees  figured  from  the  table.  This  gives  a  basic  check  which 
may,  however,  conceal  compensating  errors.  The  average  volume  of 
the  trees  in  each  diameter  and  height  group  may  then  be  checked 
against  the  tabular  values  in  the  same  way,  and  the  errors  recorded 
in  terms  of  per  cent.  These  errors  should  compensate.  A  still  more 
accurate  check  is  to  record  the  divergence  in  volume  of  each  tree  from 
the  tabular  volume  and  total  the  per  cents  of  error  plus  and  minus, 
which  should  compensate.  Or,  the  plus  and  minus  errors  may  be 
plotted  to  detect  any  trend  towards  high  or  low  values  at  one  end  or 
the  other  of  the  curves. 


190  VOLUME  TABLES  FOR  BOARD  FEET 

To  test  the  accuracy  of  a  table  of  proved  value,  when  applied  to 
a  specific  stand  or  region,  the  volume  of  as  many  trees  as  convenient, 
preferably  about  100  trees,  is  determined  by  the  same  standards  as  used 
in  the  table.  The  per  cent  of  divergence  of  the  actual  volumes,  one 
by  one,  from  those  of  the  table,  is  computed.  These  per  cents 
may  be  tabulated  and  averaged  by  diameter  and  by  height;  if  they 
reveal  a  consistent  difference  in  volume,  the  values  of  the  table  can  be 
raised  or  lowered  by  the  average  per  cent  indicated. 

References 

The  Problem  of  Making  Volume  Tables  for  Use  on  National  Forests,  T.  T.  Munger, 

Journal  of  Forestry,  XV,  1917,  p.  574. 
The  Height  and  Diameter  Basis  for  Volume  Tables,   Donald   Bruce,   Journal  of 

Forestry,  Vol.  XVIII,  1920,  p.  549. 
A  Proposed  Standardization  of  the  Checking  of  Volume  Tables,   Donald   Bruce, 

Journal  of  Forestry,  Vol.  XVIII,  1920,  p.  544. 
Top  Diameter  in  Construction  and  Application  of  Volume  Tables  Based  on  Log 

Lengths,  H.  H.  Chapman,  Proc.  Soc.  Am.  Foresters,  Vol.  XI,  1916,  p.  221. 


CHAPTER  XIV 

VOLUME    TABLES    FOR    PIECE    PRODUCTS,    COMBINATION 
AND  GRADED  VOLUME  TABLES 

162.  Volume  Tables  for  Piece  Products.  The  purpose  of  volume 
tables  for  piece  products  is  identical  with  that  for  board  feet — to  enable 
the  timber  estimator  to  dispense  with  the  necessity  of  judging  by  eye 
the  contents  of  separate  trees,  and  substituting  therefor  merely  the 
record  of  diameters  and  heights. 

Volume  tables  for  piece  products  are  limited  in  scope.  The  speci- 
fications as  to  size  of  the  product  are  the  governing  factor.  For  poles, 
no  volume  table  is  needed.  For  small  products  such  as  staves,  it  is 
almost  impossible  to  make  volume  tables,  on  account  of  the  effect  of 
cull  in  reducing  the  output  and  the  difficulty  of  judging  this  in  the 
standing  timber.  Even  here,  tables  showing  the  number  of  staves 
of  given  dimensions  in  perfect  trees  of  different  diameters,  or  in  sections 
or  bolts  of  different  diameters  may  be  of  help  in  estimating.  Here, 
as  elsewhere,  the  cull  factor  cannot  be  introduced  into  volume  tables 
but  must  be  applied  as  a  reduction  factor  to  their  contents. 

To  construct  a  volume  table  for  any  specific  product,  the  same 
methods  used  in  constructing  log  rules  can  be  applied;  first,  the  number 
of  pieces  of  certain  dimensions  which  can  be  cut  from  logs  or  bolts  of 
given  diameters  can  be  found  by  plotting  with  cross-section  of  the 
standard  piece  upon  the  areas  of  cii-cles.  Second,  these  theoretical 
results  can  be  checked  against  the  actual  number  of  pieces  hewn  or 
sawed  from  logs  or  bolts  of  the  same  diameter.  The  second  check 
is  to  ascertain  the  effect  of  u-regular  shapes,  and  of  methods  of  cutting 
or  manufacture,  as  affected  by  the  grain  of  the  wood  and  tools  used. 
In  such  a  check,  only  sound  logs  are  taken,  but  the  factor  of  cull  may 
be  studied  at  the  same  time.  The  contents  of  these  logs  can  then  be 
combined  into  volume  tables  by  the  methods  outlined  in  Chapter  XI. 

163.  Volume  Tables  for  Railroad  Cross  Ties.  The  most  useful 
volume  tables  for  such  products  are  those  for  railroad  cross  ties.  Just 
as  for  poles,  the  length  of  the  ties,  usually  standardized  at  8  feet,  is 
a  partial  indication  of  the  number  of  ties  which  can  be  cut  from  trees 
of  given  sizes.  Hewn  or  pole  ties,  flattened  on  the  faces  only,  are  cut 
only  from  trees  or  the  upper  portion  of  boles  which  are  too  smaU  to 
produce  two  or  more  ties  from  one  bolt.     Volume  tables  are  needed: 

191 


192  VOLUME  TABLES  FOR  PIECE  PRODUCTS 

1.  For  trees  of  larger  diameter,  to  show  the  number  of  ties  which 
can  be  obtained  from  each  bolt,  hence  from  the  tree. 

2.  To  show  the  number  of  ties  of  different  grades  as  determined 
by  size,  which  can  be  obtained  from  each  l)olt,  and  from  the  tree. 

This  latter  requisite  also  applies  to  bolts  from  which  but  one  tie 
can  be  cut. 

A  good  example  of  a  tie-volume  table  is  that  prepared  '  for  western  larch  and 
Douglas  fir,  Kootenai  National  Forest,  Idaho,  in  1919,  for  the  five  standard  grades 
of  hewn  railroad  ties  specified  by  the  U.  S.  R.  R.  Administration.  The  dimensions 
called  for  are: 

No.  1.  6  inches  by  6  inches  by  8  feet. 

No.  2.  6  inches  by  7  inches  by  8  feet. 

No.  3.  7  inches  by  7  inches  by  8  feet. 

No.  4.  7  inches  by  8  inches  by  8  feet. 

No.  5.  7  inches  by  9  inches  by  8  feet. 

Each  tree  was  measured  at  8-foot  intervals  for  diameter  inside  bark.  The 
method  was  to  construct  a  taper  table  (§  167)  from  which  the  sizes  of  pole  ties 
which  could  be  cut  from  each  bolt  were  determined.     The  steps  were: 

1.  Determine  the  average  top  diameter  inside  bark  required  to  produce  a  tie 
for  each  standard  size.     These  were: 

For  No.  1.  8.5  inches. 

No.  2.  9.2  inches. 

No.  3.  9.9  inches. 

No.  4.  10.6  inches. 

No.  5.  11.4  inches. 

2.  Separate  the  trees  measured  into  D.B.H.  and  height  classes.  The  height 
classes  used  were  the  number  of  8-foot  lengths  in  the  merchantable  bole,  to  a  top 
diameter  of  8.5  inches. 

3.  Determine  the  average  diameter  at  each  8-foot  point,  for  the  trees  in  each 
of  these  separate  groups.  This  gives  a  series  of  taper  measurements  and  an  average 
form  for  the  tree. 

4.  With  distance  above  stump  as  the  independent  variable,  on  the  horizontal 
scale,  and  top  diameter  of  each  tie  (each  8-foot  point)  as  the  dependent  variable 
on  vertical  scale,  plot  the  average  diameter  at  each  8-foot  point.  By  connecting 
these  points  the  form  of  the  tree  is  shown.  These  curves  are  used  to  smooth  out 
irregularities  in  values. 

5.  From  the  average  upper  diameter  of  each  8-foot  bolt,  for  trees  of  each  D.B.H. 
class,  and  separate  height  classes,  as  5- tie  trees,  6-tie  trees,  etc.,  the  class  of  tie 
which  can  be  cut  from  each  bolt  is  indicated,  and  the  number  of  ties  of  each  grade 
in  the  tree  is  shown.  This  constitutes  the  tie-volume  table.  Instead  of  recording 
merely  the  total  number  of  ties,  regardless  of  grade,  which  could  be  done  without 
the  table,  the  estimator  now  has  his  products  classified. 

The  same  method  can  be  used  for  trees  whose  dimensions  permit  of  sawing  or 
splitting  two  or  more  ties  from  one  bolt,  but  usually  trees  of  this  diameter  will 
be  measured  in  part  as  sawlogs  in  board  feet  rather  than  as  sawed  or  split  ties. 

1  James  W.  Girard  and  W.  S.  Schwartz. 


COMBINATION  VOLUME  TABLES  193 

164.  Combination   Volume   Tables   for   Two    or   More   Products. 

Close  utilization  of  tree  volumes  requires  the  measurement  of  two  or 
more  classes  of  products,  such  as  saw  timber  and  residual  cordwood, 
saw  timber  and  residual  mine  props,  railroad  ties  and  residual  mine 
props. 

In  all  tables  of  this  class,  the  method  of  construction  is  to  determine 
the  diameter  which  limits  the  sizes  used  for  the  higher  purpose,  and  then 
to  measure  the  contents  of  the  remainder  of  the  bole  to  the  smaller 
diameter  which  limits  the  sizes  used  for  the  residual  product.  The 
measurements  must  be  taken  on  the  felled  tree  before  any  portion  is 
skidded  off. 

For  example,  in  constructing  a  sawlog,  tie,  prop  table  for  lodgepole 
pine,  on  the  Arapahoe  National  Forest,  Colorado,  6  inches  was  used 
as  the  top  diameter  for  sawlogs,  to  be  scaled  by  Scribner  Decimal  C 
log  rule.  Five  inches  was  the  top  diameter  for  mine  props.  The 
number  of  feet  remaining  in  the  top,  between  6  and  5  inches,  was 
recorded  as  linear  feet.  In  the  same  manner,  10  inches  was  fixed  as 
the  top  diameter  for  the  production  of  hewn  ties  (this  has  now  been 
lowered  to  8.5  inches  by  new  specifications),  and  the  number  of  ties 
in  each  tree,  to  this  point,  recorded.  Above  10  inches,  the  8-foot 
lengths  are  entered  as  prop  material.^ 

The  residual  cordwood  in  the  tops  of  trees  cut  for  sawlogs  or  ties 
is  measured  as  for  cubic  feet.  Where  the  volumes  for  the  more  valu- 
able product  are  measured  to  a  fixed  top  diameter,  the  problem  of  resid- 
ual volume  is  easily  solved.  Where  top  diameter  varies  with  other 
factors,  the  amount  of  cordwood  in  the  tops  varies  accordingly.  This 
variation  is  further  increased  when  branch-wood  or  lapwood  is  included. 
Tables  usually  express  the  volume  of  residual  cordwood  in  terms  of 
decimal  fractions  of  cords  per  tree,  and  the  data  are  frequently  simplified 
by  averaging  the  contents  on  basis  of  diameter. 

165.  Graded  Volume  Tables.  A  graded  volume  table  is  an  attempt 
to  show  the  amount  of  different  standard  grades  of  lumber  which  may 
be  sawed  from  trees  of  different  dimensions.  Its  purpose  is  to  aid  in 
estimating  the  value  of  standing  timber.  The  preparation  of  graded 
volume  tables  is  one  of  the  objects  of  mill-scale  studies  (§  74).  The 
basis  of  these  tables  is  the  sawed  lumber  produced  from  logs.  To 
coordinate  these  data  with  the  volume  of  standing  trees,  the  following 
points  must  be  'considered : 

1.  The  logs  sawed  are  usually  cut  into  variable  log  lengths  and 
cannot  be  standardized  to  a  given  length,  such  as  16  feet. 

2.  In  sawing  logs,  especially  hardwoods,  the  resultant  output  will 

1  Ref .  Volume  Table  for  Lodgepole  Pine,  A.  T.  Upson,  Forestry  Quarterly, 
Vol.  XII,  1914,  p.  319. 


194  VOLUME  TABLES  FOR  PIECE  PRODUCTS 

be  determined  by  the  amount  of  defect  in  the  log  as  well  as  the  grades 
of  lumber — the  net,  not  the  gross  scale  will  be  obtained. 

But  the  same  objections  hold  against  introducing  into  graded  tables 
the  variable  factor  of  the  cull  due  to  a  great  range  of  defects  as  have 
operated  to  exclude  such  deductions  from  all  standard  tables.  Hence 
the  only  safe  standard  on  which  to  construct  such  tables  is  sound  logs. 

3.  The  grades  of  lumber  are  first  determined  in  logs  of  given  diam- 
eters and  lengths,  from  which  graded  log  rules  may  be  constructed. 
Such  rules  are  of  course  never  used  in  scaling  logs  (§  87)  but  solely  to 
aid  in  the  determination  of  the  average  price  to  be  paid  for  the  contents 
as  scaled. 

4.  The  grades  of  lumber  in  trees  of  different  sizes  must  be  obtained 
by  correlating  the  sizes  of  the  logs  graded  with  the  logs  contained  in 
the  trees. 

One  standard  method  used  in  constructing  such  tables  is  to  follow 
the  logs  from  different  trees  through  the  mill,  by  numbering  the  logs 
in  the  woods,  a  process  impossible  without  much  delay  except  in  small 
jobs. 

Separation  of  butt  logs  and  top  logs  is  a  less  detailed  method  of 
classification  of  logs. 

A  third  plan  is  to  prepare  separately  the  graded  log  table  without 
reference  to  the  trees,  and  then  determine  the  sizes  of  logs  in  trees  of 
different  D.B.H.  applying  the  grades  to  the  given  logs  to  get  the  grades 
for  the  tree.  Of  the  three  methods,  this  is  the  most  practical  and  use- 
ful. In  this  the  graded  log  table  is  the  real  basis,  local  graded  volume 
tables  being  constructed  from  this  table  for  use  in  each  different  stand 
of  timber  (§  87). 

5.  To  show  the  actual  contents  of  trees  of  each  separate  diameter 
and  height  class,  expressed  in  from  four  to  eight  standard  grades  would 
call  for  a  table  of  considerable  bulk,  and  when  in  addition  to  this  draw- 
back the  actual  volumes  shown  are  based  on  an  arbitrary  net  sawed 
output  minus  whatever  cull  happens  to  have  been  present  in  the  logs 
measured,  the  advisability  of  using  such  a  form  of  standard  table  is 
questionable. 

6.  Where  graded  volume  tables  of  greater  permanent  value  are 
desired  the  purpose  of  the  tables  will  be  accomplished  by  the  following 
simplification: 

a.  Substitute  per  cents  of  sawed  contents  for  actual  sawed  con- 
tents for  each  grade  of  lumber  scaled. 
h.  Substitute  D.B.H.  alone  for  D.B.H.  and  height,  as  the  basis 
of  classification  of  the  trees. 
If  these  per  cents  apply  to  sound  logs,  they  may  require  modifica- 
tion in  the  case  of  defective  timber.     Where  heart  rot  is  prevalent 


GRADED  VOLUME  TABLES  195 

it  causes  a  greater  loss  in  the  middle  portions  of  logs  which  on  account 
of  the  presence  of  knots  are  of  lower  grade  than  the  sound  outer  portion. 
On  the  other  hand,  cat  face  and  exterior  defects  reduce  the  amount 
of  clear  lumber  of  upper  grades.  Unless  such  factors  can  be  judged 
correctly,  the  same  per  cents  of  grades  must  be  accepted  for  defective 
logs  as  are  shown  in  the  table  for  sound  logs. 

It  has  been  the  common  practice,  in  preparing  graded  volume 
tables  for  hardwoods,  to  base  the  table  upon  the  net  sound  contents 
after  deducting  cull.  Where  sufficient  typical  sound  logs  of  the  larger 
sizes  cannot  be  obtained,  the  drawbacks  of  a  table  based  on  a  partial 
scale,  i.e.,  culled,  can  be  in  a  measure  overcome  by  reducing  this  table 
to  per  cent  form  as  indicated  above.  Such  a  table  should  include  a 
statement  of  the  basis  on  which  it  was  made,  the  average  per  cent 
of  cull  deducted,  and  the  general  character  of  the  defects  and  influence 
on  the  different  grades.  On  this  basis,  its  application  to  other  timber 
is  possible.^ 

Graded  log  tables  are  of  permanent  value,  and  the  utility  of  these 
tables,  if  expressed  in  per  cent,  may  be  greater  than  is  now  imagined. 
The  permanence  of  such  a  table  depends  entirely  on  the  maintenance 
of  the  standard  of  grading,  or  grades  of  lumber  on  which  the  graded 
table  is  based,  hence  such  tables  cannot  have  the  permanent  scientific 
value  of  tables  giving  volume  in  standard  units  for  sound  trees. 

References 

A  Volume  Table  for  Hewed  Railroad  Ties,  James  W.  Girard  and  W.  S.  Schwartz, 

Journal  of  Forestry,  Vol.  XVII,  1919,  p.  839. 
Graded  Volume  Tables  for  Vermont  Hardwoods,  Irving  W.  Bailey  and  Philip  C. 

Heald,  Forestry  Quarterly,  Vol.  XII,  1914,  p.  5. 
The  Ashes,   Their  Characteristics  and    Management,   W.   D.  Sterrett,    Bui.  299, 

U.  S.  Dept.  Agr.,  1915,  p.  35.  (Table  based  on  per  cents.) 
Grades  and  Amounts  of  Lumber  Sawed  from  Yellow  Poplar,  Yellow  Birch,  Sugar 

Maple,  and  Beech,  E.  A.  Braniff,  Bui.  73,  Forest  Service,  1906.     (Table  by 

per  cents  for  Yellow  Poplar.) 
Assortment  Tables,  Mitteilungen  der  Schwarzerischen  Centralanstalt  ftir  das  forst- 

liche  Versuchswesen,    Vol.   XI,   2   Heft,   pp.    153-272.      Review  in   Forestry 

Quarterly,  Vol.  XIV,  p.  752. 
Graded  Log  Tables  for  Loblolly  Pine,  W.  W.  Ashe,  Bui.  24,  North  Carolina  Geolog- 
ical Survey,  1915. 

1  European  investigations  have  shown  that  the  per  cent  of  total  volumes  which 
is  obtained  in  the  different  grades  of  product  varies  with  the  diameter  but  does 
not  differ  appreciably  with  height.  "In  proportion  as  the  shorter  stem  is  less 
in  volume  than  the  longer,  the  assortment  contents  decreases  but  the  per  cent 
relation  remains  the  same."     Ref.  Forestry  Quarterly,  Vol.  XIV,  1916,  p.  752. 


CHAPTER  XV 

THE  FORM  OF  TREES  AND  TAPER  TABLES 

166.  Form  as  a  Third  Factor  Affecting  Volume.  While  standard 
volume  tables  (Chapter  XI)  differentiate  the  volumes  of  trees  of  dif- 
ferent D.B.H.  and  heights,  they  make  no  distinction  between  trees 
having  paraboloidal  forms  and  those  approaching  the  cone  or  neiloid 
(§  26)  in  form,  but  seek  to  average  the  differences  in  volume  caused  by 
these  variations.  Occasionally  two  separate  tables  are  made  for  a 
species,  one  for  old  trees,  the  other  for  young  second-growth,  since 
it  has  been  found  that  the  average  volume  of  trees  of  these  two  age 
classes  differed  considerably.  Any  such  difference,  whatever  its  cause, 
is  due  to  difference  in  form  as  indicated  above,  for  trees  which  have  the 
same  D.B.H.  and  height. 

Volume  tables  have  come  to  stay,  since  they  substitute  accurate  measurements 
of  D.B.H.  and  of  height,  which  may  be  checked  by  calipers  or  hypsometers  (§  193), 
for  too  e.xclusive  a  use  of  the  eye,  and  for  the  very  uncertain  method  of  guessing 
at  or  figuring  out  the  volume  of  an  average  tree  whose  dimensions  are  in  turn 
arrived  at  by  guess  or  judgment. 

The  difficulty  of  having  to  depend  solely  on  volume  tables  of  this  character  lies 
not  in  the  tables  themselves  but, 

(1)  in  their  incorrect  application  (§  124); 

(2)  in  their  not  being  based  on  the  same  factors  of  volume  determination  as  are 
desired  for  the  estimate; 

(3)  in  the  possibility  of  not  having  any  tables  and  being  forced  to  construct  them. 
To  summarize  here  the  factors  in  which  the  tables  must  agree  with  the  basis  of 
estimating  we  find:  (o)  Choice  of  unit  of  measurement  as  board  feet,  specific  log 
rules,  cross-ties,  cords.  (6)  Closeness  of  utilization  in  tops  and  stump,  (c)  Point 
of  diameter  and  height  measurement,  (d)  Thickness  of  bark.  (e)  Variations 
caused  by  form  independent  of  diameter  and  height. 

For  these  reasons  the  demand  for  some  form  of  universal  volume  table  in  esti- 
mating is  very  strong. 

The  substitution  of  a  fixed  taper  per  log,  and  the  use  of  tables  showing  volumes 
for  trees  of  the  same  diameter  and  height  but  with  different  rates  of  taper  (§  122) 
is  an  attempt  to  differentiate  between  trees  with  different  form,  but,  in  effect, 
this  plan  assumes  that  all  trees  have  the  same  form,  that  of  the  frustum  of  a  cone 
and  differ  only  in  being  tall  or  short,  or  tapering  slowly  or  rapidly  up  to  the  top 
diameter. 

The  only  satisfactory  basis  of  a  universal  volume  table  is  one  in 
which  all  three  of  the  variables,  namely  diameter,  height,  and  form 

196 


TAPER  TABLES,  DEFINITION  AND  PURPOSE  197 

classes  are  distinguished.  In  tables  based  upon  diameter  and  height 
only,  no  record  of  form  is  shown.  The  volumes  as  given  in  the  table 
do  not  indicate  whether  the  tree  is  full-boled  or  conical.  This  draw- 
back is  further  aggravated  by  the  use  of  board-foot  log  rules  whose 
values  are  not  interchangeable. 

167.  Taper  Tables,  Definition  and  Purpose.  There  are  two  methods 
for  recording  differences  in  the  form  of  trees,  form  tables  or  taper  tables, 
and  form  classes  or  form  factors. 

A  table  which  does  not  show  the  volume  of  the  tree,  but  shows 
the  actual  form  by  diameters  at  fixed  points  from  base  to  tip,  is  com- 
monly termed  a  taper  table.  From  such  a  table,  the  volume  of  the  aver- 
age tree  for  each  diameter  and  height  class  can  be  measured  as  readily 
in  the  office  as  from  the  felled  tree.  Tables  of  volume  can  thus  be 
constructed  from  a  taper  table,  using  any  desired  unit  of  product, 
such  as  cubic  feet,  board  feet  or  piece  products.  They  therefore  form 
the  basis  for  any  required  future  volume  table.  For  this  reason,  if 
taper  measurements  are  taken  at  regular  intervals,  preferably  8.15  feet, 
from  stump  to  top  of  tree,  they  constitute  a  permanent  scientific  record 
of  tree  form  which  will  make  it  unnecessary  to  measure  felled  trees 
again  for  new  volume  tables. 

168.  Methods  of  Constructing  Taper  Tables.  Taper  tables  are 
based  on  total  height  and  hence  they  should  record  the  form  of  the 
entire  bole. 

A  separate  table  is  required  for  each  height  class  showing  the  taper 
of  trees  of  each  diameter  in  this  class;  e.g.,  for  white  ash  ^  tapers  are 
shown  for  trees  of  10-foot  height  classes  from  30  to  120  feet. 

For  each  height  class,  and  D.B.H.  class,  the  diameter  of  the  tree 
inside  bark  must  be  given  at  each  fixed  point,  8.15  feet  or  multiples 
thereof  above  the  stump. 

The  bole,  below  D.B.H. ,  tapers  much  less  regularly  than  above 
that  point,  but  a  complete  taper  table  should  give  the  average  diam- 
eter inside  bark  preferably  at  1,  2,  3  and  4  feet  from  the  ground. 

In  Table  XXXIII,  p.  198,  stump  tapers  are  given,  the  diameter  inside  bark 
at  B.H.  and  the  upper  diameters  at  8.15-foot  intervals  from  stumps  taken  as 
uniformly  1  foot  high.  But  one  class  is  shown,  namely,  90-foot  trees.  A  similar 
table  is  constructed  for  trees  of  each  separate  height  class,  such  as  80-foot  or  70-foot 
trees. 

When  the  taper  measurements  have  been  taken  at  fixed  points 
on  all  trees,  the  average  diameters  at  these  points  may  be  obtained 
directly  from  the  original  data.     The  process  is  shown  in  Table  XXXIV. 

'  Bui.  299  U.S.  Dept.  Agr.,    The  Ashes,  W.  D.  Sterrett. 


198 


THE  FORM  OF  TREES  AND  TAPER  TABLES 
TABLE  XXXIII 


Form  or  Taper  for  White  Ash  Trees  of  Different  Diameters   under    75 
Years  of  Age,   Giving  Diameters   inside  Bark  at  Different    Heights 

ABOVE  THE  GrOUND 

90-foot  Trees 


Height  above  Ground — Feet 

Diam- 

eter 
breast- 
high. 

Inches 

1 

2 

3 

4.5 

9.15  17.3  23.45  33.6  41.75  49.9  58.05  66.2  74.35 

Basis 
Trees 

Diameter  inside  Bark — Inches 

8 

9.2 

8.5 

7.9 

7.3 

6.8 

6.4 

6.0 

5.5 

4.9 

4.2 

3.3 

2.3 

1.4 

9 

10.4 

9.5 

8.9 

8.2 

7.6 

7.2 

6.8 

6.2 

5.5 

4.8 

3.8 

2.7 

17 

10 

11.7 

10.6 

9.9 

9.1 

8.5 

8.0 

7.5 

6.9 

6.2 

5.4 

4.3 

3.1 

1.9 

I 

11 

12.9 

11.7 

10.9 

10.1 

9.3 

8.7 

8.2 

7.5 

6.8 

6.0 

4.9 

3.5 

2.2 

.. 

12 

14.1 

12.8 

11.9 

11,0 

10.2 

9.6 

9.1 

8.3 

7.6 

6.6 

5.4 

3.9 

2.5 

13 

15.3 

14.0 

13.0 

11.9 

11.0 

10.3 

9.8 

9.0 

8.2 

7.3 

5.9 

4.3 

2.8 

14 

16.5 

15.1 

14.0 

12.8 

12.0 

11.2 

10.5 

9.8 

9.0 

7.9 

6.5 

4.9 

3.2 

15 

17.6 

16.2 

15.0 

13.8 

12.7 

11.9 

11.2 

10.4 

9.6 

8.5 

7.0 

5.3 

3.5 

16 

18.8 

17.3 

16.1 

14.7 

13.6 

12.7 

11.9 

11.1 

10.3 

9.2 

7.6 

5.7 

3.9 

17 

20.0 

18.4 

17.1 

15.6 

14.5 

13.4 

12.6 

11.8 

11.0 

9.8 

8.1 

6.2 

4.2 

18 

21.2 

19.7 

18.2 

16.5 

15.3 

14.2 

13.3 

12.5 

11.7 

10.4 

8.6 

6.2 

4.6 

19 

22.3 

20.6 

19.2 

17.4 

16.1 

14.8 

14.0 

13.2 

12.3 

11.0 

9.2 

6.7 

4.9 

20 

23.5 

21.7 

20.2 

18.4 

17.0 

15.7 

14.7 

13.9 

13.0 

11.5 

9.7 

7.2 

5.3 

21 

24.6 

22.8 

21.3 

19.3 

17.7 

16.3 

15.3 

14.5 

13.7 

12.2 

10.4 

8.2 

5.8 

22 

25.8 

23.9 

22.3 

20.2 

18.6 

17.1 

16.1 

15.3 

14.5 

12.9 

10.9 

8.6 

6.1 

26 

Original  Curves,  Tapers  Based  on  Heights  above  Stump}  In  the 
form  shown,  these  average  tapers  or  upper  diameters  may  be  insufficient 
to  bring  out  the  true  average  form  for  large  numbers  of  trees.  The 
irregularities  of  form,  occasioned  by  the  variation  in  form  of  individual 
trees  and  lack  of  sufficient  number  of  trees  to  secure  a  true  average  by 
arithmetical  means,  are  best  shown  by  plotting  the  forms  of  the  result- 
ant average  trees.  For  this  operation,  height  above  stump  is  taken 
as  the  independent  variable  i)lotted  on  the  horizontal  scale  while  upper 
diameter  is  the  dependent  variable  plotted  on  the  vertical  scale.  A 
separate  curve  is  required  for  trees  in  each  D.B.H.  class. 

1  The  details  of  constructing  taper  curves  are  fully  discussed  by  W.  B.  Barrows, 
Proc.  Soc.  Am.  Foresters,  Vol.  X,  1915,  p.  32. 


METHODS  OF  CONSTRUCTING  TAPER  TABLES 


199 


TABLE  XXXIV 

Tapers  of  Loblolly  Pine,  Two  Trees  * 
Tree  Class,  15-inch,  80-foot 


Stump 

Height  above  Stump — Feet 

D.B.H. 

2 

8 

16 

24 

32 

40        48 

56 

64 

72 

Total 
height. 

Diameter  inside  Bark — Inches 

Feet 

15.4 
15  1 

16.1 
15.0 

13.5 
13.3 

12.4 
13.2 

11.4 
12.5 

11.7 
11.9 

11.1    10.0 
10.8      9.6 

8.8 
8.0 

5.9 
6.3 

3.0 
3.8 

76 
84 

30.5 

Average 

15.2 

.51,1 
15,5 

26.8 
13.4 

25.6 
12.8 

23.9 
11.9 

23.6 

11.8 

21.9 
10.9 

19.6 

9.8 

16.8 

8.4 

12.2 
6.1 

6.8 
3.4 

160 
80 

Data  taken  from  loblolly  pine  tapers  at  8-foot  intervals,  without  stump  tapers.      Two  trees. 


21 
20 

19 

\ 

"^^s^ 

^  '^  0  r 

\ 

\ 

^r 

^/>r^ 

\ 

X 

^^^ 

V 

\ 

■>„ 

X 

\, 

•<i'i 

^> 

v^ 

IS 

\ 

1  (  J '/ 

■^ 

\ 

X, 

k 

^•^v 

^^ 

^^  N 

\ 

1 

C|\^ 

\ 

1: 

^--^ 

^■^ 

^\ 

\ 

X 

\  ^ 

s  \ 

-A^ 

A 

^^ 

Sv 

5 

V 

sV 

XV 

3 
2 
1 

X 

^ 

\ 

\. 

v^ 

>^ 

32  40  48  56  04 

Height  above  Stump,  Feet 


Fig.  32. — Actual  upper  diameters  or  tapers  of  four  loblolly  pine  trees,  inside  bark, 
based  on  height  above  stump,  plotted  to  show  form  of  trees.    90-foot  trees. 


200  THE  FORM  OF  TREES  AND  TAPER  TAB1.ES 

From  these  plotted  forms  of  trees  the  diameters  at  any  desired  point  or  height 
on  the  boles  can  be  read. 

The  nature  of  these  original  averages  is  shown  in  Fig.  32  in  which  four  single 
trees  of  different  D.B.H.,  14.4  inches,  17.7  inches,  19.4  inches,  and  21  inches,  but 
falling  in  the  same  height  class,  90  feet,  are  plotted.  The  eccentricities  of  form 
in  this  table  are  partly  due  to  branches,  partly  to  failure  to  obtain  the  true  average 
diameter  at  each  point,  and  partly  to  the  natural  variations  in  form  for  individual 
trees. 

As  in  the  preparation  of  volume  tables,  the  averages  obtained  from  a  number 
of  trees  are  more  consistent  than  the  forms  of  single  trees.  A  graph  plotted  in 
this  manner  from  averaged  upper  diameters  instead  of  single  trees,  will  be  fairly 
regular  in  the  relation  of  the  curves  for  successive  D.B.H.  classes  and  will  resemble 
Fig.  35,  p.  204. 

When,  as  is  sometimes  the  case,  the  upper  diameters  are  measured 
on  logs  as  cut  by  the  saw  crews,  in  irregular  lengths,  and  hence  fall  at 
different  heights  above  the  stump,  only  the  measurements  falling  at 
the  same  height  can  be  averaged,  as  at  12,  14,  16,  18  and  20  feet.  This 
will  be  done,  and  all  of  the  resultant  upper  diameters  for  trees  of  a  given 
D.B.H.  and  height  class  will  be  plotted,  to  obtain  the  curve  of  average 
form.  From  this  curve,  the  desired  upper  diameters  at  regular  inter- 
vals of  8  or  10  feet  can  be  read. 

These  curves  of  form  are  not  in  final  shape  for  a  standard  table  of  form.  Although 
the  averages  are  improved  by  the  use  of  larger  numbers  of  trees,  the  values  will 
be  shghtly  irregular  for  two  reasons.  The  average  D.B.H.  may  be  larger  or 
smaller  than  the  exact  inch  class  desired,  and  the  forms  of  the  average  trees  of  the 
consecutive  D.B.H.  classes  may  vary  in  fullness.  These  two  sources  of  variation 
are  well  shown  in  Fig.  32.  There  is  no  reason  why  average  21-inch  and  18-inch 
trees  should  have  a  fuller  form  than  19-inch  trees. 

Values  required  are  based  on  exact  D.B.H.  classes,  and  vary  regularly  with 
D.B.H.,  as  would  be  the  case  were  sufficient  trees  included  in  the  mechanical 
average. 

Second  Set  of  Curves,  Tapers  Based  on  D.B.H.  For  trees  of  each 
successive  D.B.H.  class  which  have  the  same  total  height  and  the  same 
general  form,  the  diameters  at  each  given  height  on  the  boles  will 
diminish  in  dkect  proportion  with  diminishing  D.B.H.  If  D.B.H.  is 
then  taken  as  the  independent  variable  in  a  second  set  of  curves,  and 
upper  diameters  plotted  on  D.B.H.  as  the  dependent  variable,  the 
form  of  these  new  curves  approaches  straight  lines  as  did  those  of  volume 
based  on  height  (§  141),  and  the  irregularities  between  the  forms  or 
upper  diameters  of  different  average  trees  are  easily  reduced.  In  this 
second  operation  as  in  the  first,  the  trees  of  a  given  height  class  form 
the  basis  for  a  set  of  curves;  e.g.,  90-foot  trees  only  are  included  in  the 
one  set  of  taper  curves,  separate  sets  being  required  for  70-foot  or  80-foot 
trees.  For  this  set  of  curves  the  same  scale  can  be  used  for  both  vari- 
ables, e.g.,  2  inches  =1  inch. 


METHODS  OF  CONSTRUCTING  TAPER  TABLES 


201 


To  plot  this  second  set  of  curves  the  values  for  a  given  tree,  or  set  of  tapers, 
are  transferred  to  this  new  sheet,  in  which  process  the  strip  method  described  in 
§  141  is  most  convenient. 
The  diameter  of  upper 
tapers  diminishes  with  in- 
creasing height;  each  tree 
is  plotted  in  a  single 
vertical  column,  with 
the  D.B.H.  at  the  top. 

The  D.B.H.  column 
must  be  that  of  the 
actual  average  D.B.H., 
e.g.,  14.4  inches,  not  14 
inches.  When  each  set 
of  values  has  been 
transferred  and  plotted 
above  its  respective 
D.B.H.,  the  points  rep- 
resenting equal  heights 
above  stump  are  con- 
nected by  lines.  The 
guide  line  for  this  set 
of  curves  is  a  line  drawn 
at  45°  angle  whose  value 
would  be  D.I.B.= 
D.B.H.  For  any  tree, 
the  D.I.B.  at  D.B.H. 
is  less  than  the  DOB., 
and  at  upper  points, 
D  I.B.  is  still  less;  hence 
all  points  above  D.B.H. 
will  fall  below  this  line. 

Regular  forms  such 
as  are  shown  in  Fig.  35 
could  be  drawn  directly 
on  Fig.  32  guided  by 
the  original  averages, 
which  will  usually  be 
far  more  regular  in 
themselves  than  those 
shown  in  the  diagram. 
But  the  desired  shifting 
of  the  basis  to  e.xact 
D.B.H.,  e.g.,  14  inches 
instead  of  14.4  inches, 
and  the  far  greater  ac- 
curacy in  harmonizing 
tapers  secured  by  plot- 
ting (Fig.  33)  makes  the 
method  of  plotting  a 
second  set  of  curves 
almost  obligatory. 


18  19 
Inches 
Fig.  33. — Tapers  of  the  four  trees  shown  m  Fig.  32,  plot- 
ted on  basis  of  D.B.H.  for  each  8-foot  point,  and 
results  evened  off  by  curves.  Separate  curves  arc 
made  for  each  height  above  stump.  Effect  is  to 
reduce  the  irregularities  of  form  in  Fig.  32. 


202 


THE  FORM  OF  TREES  AND  TAPER  TABLES 


With  more  regular  original  averages,  the  curves  will  coincide  very  closely  with 
the  original  data,  instead  of  showing  the  wide  variations  indicated  in  this  figure, 
caused  by  the  great  irregularity  of  the  original  unharmonized  values  of  Fig.  32. 

The  effect  of  this  second  plotting  upon  the  irregular  forms  shown  in  Fig.  32  is 
illustrated  in  Fig.  35,  in  which  the  curved  or  harmonized  tapers  from  Fig.  33  are 
replotted  in  the  original  form.i 

The  values  when  read  from  the  curves  are  taken  from  the  ordinates  repre- 
senting exact  diameter  classes.  This  set  of  curves  therefore  is  evened  off  for  values 
of  the  diameter  classes,  and  progresses  regularly  by  1-inch  or  2-inch  diameters. 

Third  Set  of  Curves,  Tapers  Based  on  Total  Heights  of  Trees.  We 
now  have,  fii'st,  true  averages  of  the  original  form  of  each  separate 
class,  second,  true  averages  for  exact  diameter  classes  instead  of  for 
average  diameters  larger  or  smaller  than  these  exact  classes.     Both 


1 

1 

8' 
16 
24 

_ 

, 

— 

1 — 

^ 

\Z--^— 

32 
40 

__^ 

- — ' 



^ - 

-^ 

^,^ 

__,,^-^ 

■ 

56' 

■^ 

^ 

,^-- 

^-^^ 

^^ 

^^-^ 

, 

^ 

- 

■-' 

^^ 

^ 

^ 

^^ 

^-""^ 

^ 

-^ 

72' 

^ 

^ 

^ 

^ 

^^^,-^ 

^ 

^ 

^ 

^ 

^ 

y^ 

y 

L^ 

^ 

■ 

Total  height  of  Tree,  feet 

Fig.  34. — Tapers  based  on  total  heights  of  trees.     For  trees  of  the 
D.B.H.  class.     14-inch  trees. 


sets  of  curves  deal,  however,  only  with  one  separate  height  class.  It 
may  happen  that  the  trees  of  the  80-foot  class  are  all  slender,  tapering 
trees,  while  those  of  the  70-foot  or  90-foot  class  are  more  cylindrical. 
There  is  no  reason  why  in  a  general  table  which  seeks  average  form, 
the  accidental  departure  of  form  from  the  average,  by  a  set  of  trees 
in  one  height  class,  should  be  accepted  if  this  deviation  can  be  easily 
shown  and  corrected. 

To  do  this,  it  is  necessary  to  compare  the  upper  diameters  of  the 
trees  of  different  height  classes,  at  the  same  points  on  the  stem.  D.B.H. 
must  therefore  be  eliminated  as  a  variable  and  height  substituted. 


1  Since  height  above  stump  is  the  basis  of  curves  in  Figs.  32  and  35,  the  tree 
form  is  shown  as  if  lying  on  its  side.  The  diameter,  instead  of  being  plotted  sym- 
metrically on  both  sides  of  an  axis,  is  plotted  on  the  vertical  scale  above  the  base 
of  the  figure.  But  by  holduig  this  figure  at  right  angles,  the  form  of  the  bole  is 
suggested. 


METHODS  OF  CONSTRUCTING  TAPER  TABLES  203 

A  set  of  curves  (the  third)  will  therefore  be  made  from  all  trees  of 
the  same  D.B.H.,  such  as  the  14-inch  class.  In  this  set  the  independent 
variable  which  is  plotted  on  the  horizontal  scale  is  the  total  height  of 
the  tree  in  feet.  The  dependent  variable  is  diameter  or  taper  at  upper 
points,  as  in  all  the  graphs  used  in  this  method. 

The  set  of  points,  which  is  transferred  from  curves  in  Fig.  33  and  falls  in  the 
vertical  column  above  the  height  of  the  tree,  is  the  diameter  of  a  14-inch  tree, 
90  feet  high,  at  each  taper  measurement,  the  larger  diameters,  beginning  with 
D.B.H.,  falling  highest  in  the  column. 

After  each  series  of  points  for  14-inch  trees,  representing  trees  of  different  total 
heights  as  80,  70,  60  and  50  feet,  has  been  taken  from  the  separate  sets  of  curves 
prepared  in  step  2,  for  each  of  these  height  classes,  and  plotted  successively  on 
Fig.  34,  the  points  representing  diameters  at  the  same  height,  e.g.,  at  8  feet  from 
stump,  are  connected. 

Irregularities  in  the  resultant  curves  show  departure  in  form  for  one  height 
class  as  compared  with  others.  By  smoothing  out  these  curves,  the  tapers  of  treas 
of  different  height  classes  are  harmonized.  The  scale  used  in  this  set  is  5  feet 
per  inch  for  the  horizontal  scale,  2  inches  per  inch  for  the  vertical  scale.  In  Fig.  34 
only  the  resultant  harmonized  values  are  shown 

Fourth  Set  of  Curves,  Tapers  Replotted  on  Basis  of  D.B.  H.  To  utilize 
the  data  from  Fig.  34  the  values  may  be  read  off  direct,  forming  tables, 
but  it  is  customary  to  have  these  tables  classified  by  height  classes, 
as  in  Fig.  33  instead  of  by  diameter  classes.  To  bring  together  these 
values,  the  curved  values  for  the  separate  diameters  may  again  be  assem- 
bled on  one  sheet  as  in  Fig.  33  with  a  separate  sheet  for  each  height, 
diameters  on  the  horizontal  scale,  upper  diameters  on  the  vertical  scale, 
and  a  curve  for  each  fixed  height  above  the  stump.  This  rcplotting 
should  still  further  u'on  out  any  irregularities  in  taper  values.  The 
taper  table  can  be  read  from  this  set  direct,  but  only  for  the  fixed  heights 
given  in  the  table,  e.g.,  for  8,  16,  24  feet,  etc. 

Final  Set  of  Curves,  Tapers  Replotted  on  Basis  of  Height  above  Stump. 
One  further  step  completes  the  curves  of  form,  by  restoring  them  to 
the  shape  of  the  separate  trees  as  shown  in  Fig.  32.  In  this  final  step  the 
values  are  plotted  as  for  Fig.  35,  with  separate  graphs  for  height  classes, 
height  above  ground  on  the  horizontal  scale,  upper  diameter  or  tapers 
on  the  vertical  scale  and  a  curve  for  each  diameter  class. 

The  form  of  such  a  set  of  tapei*s  for  universal  use  should  be  graphic, 
thus  showing. the  upper  diameter  at  every  point  on  the  stem.  From 
this  set  of  graphs,  board-foot  volume  tables  for  any  log  rule,  length  of 
log,  upper  diameter  limit  or  stump  height,  cubic  volume,  number  and 
dimensions  of  ties,  poles  or  other  piece  products,  can  be  determined. 
It  is  apparently  a  universal  basis  for  the  construction  of  volume  tables, 
and  while  the  number  and  diversity  of  such  tables  would  remain  as 
great  as  ever,  the  field  work  of  gathering  data  on  form  or  volume  would 


204 


THE  FORM  OF  TREES  AND  TAPER  TABLES 


be  obviated  by  the  printing  and  general  distribution  of  the  graphs 
giving  the  average  form,  from  which  tables  could  be  prepared  in  the 
office  for  whatever  use  was  desired. 

169.  Limitations  of  Taper  Tables.  The  real  weakness  in  this 
apparently  sound  method  of  preparing  the  basis  for  volume  tables  lies 
in  the  fact  that  the  i-esult  obtained  does  not  differentiate  form  classes 
of  trees,  but  averages  them  on  exactly  the  same  basis  as  do  the  standard 
volume  tables.     Its  only  merit  therefore  is  in  the  transferring  of  records 


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Fig.  35. — Tapers  read  from  Fig.  33  for  four  diameter  classes,  showing  effect  of  har- 
monized curves  in  smoothing  out  the  irregularities  of  form  shown  in  Fig.  32. 

Similar  curves  are  obtained  from  tapers  replotted  inform  of  Fig.  33  frojn  curves 
shown  in  Fig.  34.     Such  tapers  will  be  harmonized  by  diameter  and  height 


of  average  tree  forms  to  the  office  as  a  basis  for  future  volume  tables. 
The  form  of  the  tables  is  bulky  and  does  not  lend  itself  to  the  further 
extension  necessary  to  show  the  form  of  trees  of  several  different  form 
classes  for  each  diameter  and  height  class,  though  in  the  preparation 
of  standard  volume  tables  by  the  U.  S.  Forest  Service,  such  taper  tables 
have  been  extensively  employed.  The  use  of  taper  tables  in  connec- 
tion with  standard  form  classes  as  a  basis  for  universal  volume  tables 
is  discussed  in  Chapter  XVI. 

By  preparing  separate  sets  of  taper  tables  for  each  form  class  based 
on  absolute  or  normal  form  of  trees  (§  174)  a  permanent  basic  standard 
of  tree  form  is  obtained  which  will  fill  all  possible  future  requirements. 


CHAPTER  XVI 
FORM  CLASSES  AND  FORM  FACTORS 

170.  The  Need  for  Form  Classes  in  Volume  Tables.  Trees  which 
have  the  same  D.B.H.  and  total  height  may  vary  in  form,  as  shown, 
according  as  the  tree  is  full  boled,  with  "  good  "  form,  or  concave 
boled,  with  "  bad  "  form.  These  gradations  of  form  correspond  with 
differences  in  cubic  volume.  In  order  to  further  classify  the  volumes 
of  trees  of  the  same  D.B.H.  and  height,  this  range  of  volume  due 
solely  to  form  must  be  separated  into  arbitrary  classes  or  divisions. 
Such  a  series  is  based  on  measurable  differences  in  form,  and  the 
classes  thus  established  are  termed  form  classes.  The  adoption  of 
form  classes  as  a  third  variable  in  constructing  volume  tables  has 
been  retarded  in  this  country  by  the  necessity  for  expressing  volumes 
in  terms  of  board  feet,  by  the  labor  of  constructing  even  the  simpler 
tables  based  on  diameter  and  height,  and  by  the  belief  that  the  vari- 
ations due  to  form  could  be  more  simply  overcome  by  averaging  them. 

A  second  difficulty  lay  in  the  application  of  such  form-class  tables 
in  timber  estimating,  since  cruisers  were  unaccustomed  to  judging 
upper  diameters  by  eye  with  the  accuracy  needed  to  distinguish  between 
the  form  classes.  Differences  in  taper  were  readily  recognized,  but 
differences  in  form  were  further  obscured  by  the  method  of  using 
merchantable  top  diameter  limits  instead  of  total  height.  Practical 
cruising  did  not  seem  to  require  such  tables.  But  with  the  increasing 
use  of  the  cubic  foot  and  the  cord  for  pulpwood  and  in  second-growth 
timber,  and  the  need  for  closer  estimating,  the  desirability  of  distinguish- 
ing form  classes  in  volume  tables  is  increasing.  Such  efforts  as  have 
been  made  so  far  in  this  country  follow  standards  prevailing  in  Europe, 
where  the  universal  use  of  the  cubic  unit,  close  utilization  and  high 
values  have  made  it  necessary  and  possible  to  obtain  more  accurate 
measurements  of  the  standing  timber. 

One  great  possibility  in  this  field  is  the  demonstration  that  when 
form  classes  are  distinguished  and  the  true  form  of  the  tree  inside  the 
bark  is  made  the  basis,  all  species  of  trees  will  be  shown  to  have  practi- 
cally the  same  forms  and  total  volumes  for  the  same  form  classes;  hence 
a  single  general  table  so  classified  would  suffice  for  all  field  work.  Were 
this  fact  established,  a  basic  table  might  then  be  constructed  for  each 

205 


206  FORM  CLASSES  AND  FORM  FACTORS 

of  various  units  of  measure  in  addition  to  cubic  feet.  Once  the  average 
form  class  of  the  trees  or  stand  were  determined,  then  volumes  could 
be  obtained  from  these  basic  tables.  Recent  research  in  Sweden  tends 
to  show  that  this  generalization  holds  true  for  certain  species  already 
investigated,  nameh'  spruce,  fir,  larch  and  Scotch  pine. 

171.  Form  Quotient  as  the  Basis  of  Form  Classes.  The  first  real 
step  towards  a  solution  of  this  problem  was  made  by  Schiffel  in  1899, 
who  developed  a  method  of  expressing  differences  in  form,  previously 
used  (Schuberg,  1891)  and  known  as  the  form  quotient,  which  is  the 
percentage  relation  that  the  diameter  at  one-half  the  height  bears  to 
the  D.B.H. 

The  differences  in  form  of  the  entire  boles  of  trees  (Chapter  III) 
are  expressed  by  their  divergence  from  a  cylindrical  form  through  a 
series  marked  at  definite  stages  by  the  complete  paraboloid,  cone,  and 
neiloid.     Each  of  these  solids  can  be  measured  by  Newton's  formula: 

F=(B+46.+6)| 
b 

The  middle  point  on  the  stem  of  a  tree,  regarding  the  entire  bole  as  a 
single  complete  solid,  is  evidently  the  point  of  greatest  weight  in  deter- 
mining its  form  and  volume  with  respect  to  the  cylinder  whose  base  is 
B  and  height  li. 

By  a  complicated  calculation,-  Schiftei  derives  tne  formula  for 
obtaining  at  one  operation  the  true  cubic  contents  of  an  entire  stem  as, 

F=(.16B  +  .666.,)/i. 

This  is  known  as  Schiffel's  formula. 

Newton's  formula,  regarding  the  tree  as  a  perfect,  i.e.,  complete 
conoid,  and  the  diameter  at  top  as  zero  would  be, 

7=(.16f5+.66f6.)/i. 

The  "  universal  "  character  of  Schiffel's  formula  failed  to  make  the 
headway  expected  when  it  was  first  introduced  in  the  United  States 
for  the  reasons  that,  to  apply  it,  one  must  measure  the  diameters  of 
trees  at  one-half  the  stem  height,  and  that  the  cubic  unit  of  volume 
was  little  in  demand. 

The  really  valuable  part  of  Schiffel's  work  was  not  the  formula, 
which  was  nothing  new,  but  the  form  quotient.  This  was  his  demon- 
stration that  the  true  form,  and  consequently  the  variation  in  form  of 

i"New  Method  of  Measuring  Conifers,"  Review  by  B.  E.  Fernow  of  Article 
by  Schiffel,  "Dber  die  Kubirung  und  Sortierung  Stehender  Nadelholz  Schafter," 
Centralblatt  fiir  das  gesammte  Forstwesen,  Dec,  1906,  pp.  493-505,  Forestry  Quar- 
terly, Voi.  V,  1907,  p  29. 


FORM  QUOTIENT  AS  THE  BASIS  OF  FORM  CLASSES 


207 


different  trees,  could  be  indicated  by  the  relation  between  diameter  at 
one-half  height  and  D.B.H.  (not  diameter  at  stump). 
In  its  standard  form  of  expression: 


Form  quotient: 


D' 


In  1908  Tor  Jonson  corrected  a  slight  inconsistency  in  Schiffel's 
method  by  insisting  that  the  middle  diameter  be  taken  not  at  the  middle 
point  of  the  stem  but  at  the  middle  point  measuring  from  B.H.  This  he 
termed  the  absolute  form  quotient.  This  improvement  finally  secured  a 
consistent  basis  for  expressing  tree  forms,  eliminated  height  as  a  varia- 
ble, and  got  rid  of  the  great  drawback  of  butt  swelling.  The  absolute 
form  quotients  of  trees  were  now  found  to  vary  between  .575  and 
.825,  i.e.,  the  diameter  at  the  middle  point  above  B.H.  bore  this 
relation  to  the  D.B.H. ,  whether  both  measurements  were  taken  out- 
side or  inside  the  bark. 

It  was  also  discovered  that  in  most  cases  the  form  quotient  if  reduced  by  a 
constant  would  give  the  form  factor  for  cubic  contents  of  the  tree.  For  instance, 
J.  F.  Clark  found  that  the  reduction  factor  for  the  form  quotients  for  balsam  in  the 
Adirondacks  was  0.21.  This  fact  is  of  minor  importance  since  it  aids  only  in 
obtaining  the  cubic  contents  of  trees. 

This  standard  of  measuring  form  permitted  the  classification  or 
differentiation  of  the  third  variable  of  volume,  namely,  form  independ- 
ent of  diameter  or  of  height.  Trees  could  be  grouped  into  form  classes 
expressed  by  form  quotients.  Seven  main  form  classes  were  formed, 
namely,  .50,  .55,  .60,  .65,  .70,  .75,  .80.  Five  sub-classes  were  also  inter- 
polated as  .575,  625,  .675,  .725,  .775.  The  extreme  lower  and  upper 
classes  shown  will  be  found  only  in  individual  trees.  The  average 
form  class  for  a  given  stand  will  fall  usually  between  .575  and  .75  and 
may  be  correlated  with  the  density  of  the  stand  as  shown  below. 


Character  of  stand 

Form  class, 

based  on 

form  quotient  * 

0.575-0.625 
.65 

.675-   .70 
.72.5-  .75 

Fairly  good  density 

Good  density 

Overcrowded 

But  most  important  of  all,  the  question  as  to  whether  the  form  of 
trees  was  independent  of  species,  site  and  region  and  dependent  on  gen- 
eral laws,  could  now  be  determined. 


208  FORM  CLASSES  AND  FORM  FACTORS 

172.  Resistance  to  Wind  Pressure  as  the  Determining  Factor  of 
Tree  Form.  The  theory  explaining  the  form  of  the  boles  of  trees, 
v/hich  is  now  generally  accepted,  was  first  advanced  by  Prof.  C. 
Metzger,  a  German.  This  was,  that  the  stem  or  bole  is  constructed 
as  a  girder  to  withstand  the  pressure  of  wind.  Based  on  this  theory, 
A.  G.  Hoejer,  a  civil  engineer  of  Stockholm,  devised  the  general  formula 
for  tree  form  discussed  in  §  173.  Prof.  Tor  Jonson  applied  this 
formula  first  to  spruce  and  then  to  Scotch  pine,  and  demonstrated  its 
correctness;  as  a  consequence,  developing  the  basis  for  tables  of  abso- 
lute form  and  volume  for  trees,  and  a  new  method  of  estimating 
timber  (§  203). 

Jonson's  conclusions,  based  on  these  investigations,  are  that  tree 
form  depends  entirely  on  the  mechanical  stresses  to  which  the  tree  is 
exposed,  and  is  therefore  independent  of  diameter,  and  height,  and  also 
of  species,  age,  site  or  any  other  factor,  except  as  these  factors  in- 
fluence the  form  .of  the  crown.  The  force  of  the  wind  operates  on 
the  crown  of  the  tree  and  is  focused  or  centered  on  a  point  representing 
the  geometric  center  of  the  crown.  The  pressure  of  the  wind  on  the 
tree  crown  constitutes  a  force  which  compels  the  tree  to  construct  its 
stem  in  such  a  manner  that  the  same  relative  resistance  to  strain  is 
found  at  all  points,  the  smallest  possible  amount  of  material  being 
used.  As  the  concentrated  force  of  the  wind  strikes  a  point  situated 
lower  or  higher  on  the  tree,  dependent  on  the  crown  area  presented, 
we  get  larger  or  smaller  taper  respectively,  which  means  bad  or 
good  form  class.  As  the  location  of  the  point  of  attack  of  the  bend- 
ing force  is  determinative  of  form,  this  point  is  called  the  form  point, 
and  can  be  expressed  as  a  per  cent  of  total  height. 

Here  is  a  natural  law,  to  which  growth  of  trees,  as  mechanical  struc- 
tures designed  to  stand  up  against  wind,  corresponds.  The  full  bole 
of  the  forest-grown  tree  in  a  crowded  stand,  coinciding  with  a  small 
crown  and  high  form  point,  meant  that  this  location  of  the  strain 
required  nearly  equal  strength  along  the  total  length  of  bole,  which 
could  be  attained  by  rapid  growth  of  the  upper  bole.  If  the  tree 
were  open-grown  with  a  consequent  long  crown  and  a  low  form  point, 
this  would  permit  of  smaller  upper  diameters  and  require  greater 
strength  lower  down  on  the  bole. 

Since  the  form  of  the  crown,  especially  its  length,  with  relation 
to  the  length  of  bole,  determines  this  form  point,  this  relation  of  crown 
to  bole,  expressed  by  form  point  serves  as  an  index  to  classify  trees  as 
to  their  relative  form  classes  or  form  quotients. 

Any  variation  in  average  form,  such  as  the  admitted  fact  that  the 
average  form  quotient  increases  with  age,  is  explained  by  a  coincident 
change  in  this  crown  and  forrp  point  relationship.     Open-grown  trees 


A  GENERAL  FORMULA  FOR  TREE  FOR]\I  209 

possess  a  low  form  quotient,  not  because  the}'  are  open-grown  but 
because  the  crowns  of  such  trees  are  long  and  the  form  point  low.  Trees 
with  long  clear  length  and  high  crowns  possess  a  high  form  quotient, 
whether  they  stand  alone  or  in  a  crowded  stand.  Short  trees  may  be 
full-boled  or  the  reverse — the  rapidity  of  taper  as  a  whole  has  no  effect, 
but  the  distribution  of  the  taper,  which  alone  affects  the  form  quotient, 
will  vary  with  short  trees  as  much  as  with  tall,  and  on  poor  soils  equally 
with  good. 

173.  A  General  Formula  for  Tree  Form.  On  this  basis,  if  the  actual 
form  of  trees  with  the  same  form  quotient  is  similar,  it  would  be  possible 
to  construct  taper  tables  based  on  each  of  the  three  variables,  diameter, 
height  and  form  class,  which  would  apply  to  all  species  of  trees.  To 
apply  this  principle  there  was  required  a  general  formula  which  would 
give  the  diameter  of  a  tree  of  given  form  quotient,  at  any  point  on  the 
stem,  and  second,  a  demonstration  that  the  actual  measurements  taken 
on  trees  of  this  form  quotient  coincided  with  the  results  of  the  formula. 

Once  this  was  shown,  the  formula  would  permit  of  the  construction 
of  a  set  of  taper  tables  of  universal  application  from  which  in  turn  any 
manner  of  volume  table  could  be  derived.  This  is  a  more  ambitious 
program  than  the  mere  determination  of  form  factors  for  cubic  con- 
tents, and  promises  permanent  results. 

The  formula  devised  by  A.  G.  Hoejer  is  based  on  the  portion  of  the  tree 
above  B.H.: 

D  =  D.B.H.  inside  bark; 
Z  =  distance  from  top  of  tree  to  section; 
d  =  diameter  of  section. 

Then 

d  c+l 

-=Clog . 

D  c 

C  and  c  are  constants  whose  value  depends  upon  the  form  quotient  of  the  tree; 

i.e.,  upon  —  when  d  is  measured  at  one-half  height  above  D.     Their  value  must  be 

found  separately  for  each  form  class,  and  will  then  hold  good  for  diameters  at  any 
point  on  the  bole  of  trees  within  this  class,  independent  of  total  height  of  tree. 

Absolute  heights  are  not  used  m  the  formula,  but  percentage  or  relative  heights, 
regarding  the  height  of  any  tree  above  B.H.  as  100,  and  the  distance  below  the 
tip,  of  any  other  section  as  its  per  cent  of  this  length,  including  sections  below 
B.H.,  whose  per  cent  of  height  would  exceed  100. 

In  the  same  way,  absolute  diameters  are  not  used,  but  the  D.B.H.  is  taken  as 

d 
100,  and  the  relative  diameter  --  expressed  as  its  proportion  of  100. 

These  upper  diameters  are  then  measured  at  distances  equahng  tenths  of  this 
total  height  above  D.B.H, — thus  falUng  at  the  same  proportional  height  on  each 


210  FORM  CLASSES  AND  FORM  FACTORS 

tree;    e.g.,  for  the  form  class  0.70  with  diameter  at  0.5  of  height  above  B.H.,  as 
0.7  of  D.B.H.,  the  values  in  the  formula  are: 


For  upper  section, 


For  D.B.H.  section, 


^0      n^      ^+^0  M^ 


100  f  +  100 

=Clog-^ (2) 

100  ^       c  ^  ^ 

If  equation  (2)  is  divided  into  equation  (1),  then 

0.70  log  (c  +  lOO)  =log  ((-+50) +  (0.70-1)  log  C. 

The  value  of  this  constant  c  is  then  found  by  trial.  Inserting  this  value  in  equa- 
tion (2)  the  value  for  constant  C  is  found  for  the  form  class.  Values  for  the  remain- 
ing form  classes  are  found  in  a  similar  manner. 

With  the  numerical  value  of  the  constants  C  and  c  determined,  the  normal  diam- 
eter of  a  perfectly  formed  tree  can  be  found  by  this  formula  at  any  point  on  the 
stem  above  B.H.,  and  this  normal  diameter  can  also  be  calculated  for  stump  height, 
thus  disregarding  the  stump  taper. 

By  determining  these  normal  diameters  for  trees  of  each  D.B.H.  and  height 
class,  at  intervals  of  one-tenth  of  the  total  height,  and  plotting  these  diameters 
graphically,  a  set  of  taper  curves  is  constructed  (§  167),  for  normal  tree  forms, 
from  which  volume  tables  or  form  factors  can  be  constructed  which  will  have 
universal  application. 

174.  Applicability  of  Hoejer's  Formula  in  Determining  Tree  Forms.  There 
remained  to  test  accin-acy  of  these  results  by  comparing  them  with  measurements 
on  felled  trees.  The  tests  showed  that  for  the  conifers  measured,  spruce,  fir,  larch 
and  pine,  the  formula  expressed  the  form  of  the  living  tree,  when  applied  inside 
the  bark  at  all  points  including  D.B.H.,  and  that  for  species  with  thin  bark  such 
as  spruce,  the  same  relations  applied  when  measured  outside  bark.  For  Norway 
Spruce  the  volumes  of  individual  trees  fall  within  ±  3  per  cent  of  those  derived 
by  the  formula.  But  for  thick-barked  species  such  as  Scotch  pine,  a  poorer  form, 
less  cyMndrical,  was  obtained  outside  bark,  which  changed  the  form  class,  but 
did  not  seriously  interfere  with  the  application  of  the  method.  Claughton- 
WalUn  has  since  shown  that  this  formula  holds  good  for  Norway  or  red  pine 
(Pinus  rcsinosa)  and  white  pine  (Pinus  strobus). 

As  with  all  attempts  to  study  the  laws  of  tree  form,  this  formula  depends  on 
measuring  a  diameter  which  is  not  affected  by  the  abnormal  flare  at  the  butt; 
hence  any  tree  or  species  whose  butt  swelling  extends  above  B.H.  will  not  corre- 
spond in  form  to  the  diameters  in  the  formula  based  on  this  abnormal  D.B.H. 
It  was  found  impossible  to  use  the  formula  for  western  conifers  since  the  form 

d 
quotient  —  was  too  low  for  this  reason. 

For  general  application,  the  second  difficulty  is  the  factor  of  bark  thickness, 
whose  effect  upon  the  form  quotient  and  form  class  must  be  worked  out  for  different 
species  with  variable  thicknesses  of  bark,  so  as  to  correlate  the  method  with  D.B.H. 
measurements  outside  the  bark,  which  must  continue  to  be  used  in  practical 
estimating. 


FORM  FACTORS  211 

Can  these  two  variables  be  eliminated  for  American  trees,  and  taper  and  volume 
tables  constructed  for  trees  of  each  form  class,  thus  attaining  the  goal  of  universal 
volume  tables? 

For  second-growth,  or  young  timber,  in  which  the  factor  of  butt  swelling  will 
not  affect  D.B.H.,  this  can  be  done.  Taper  tables  should  be  constructed  from  this 
normal  formula  based  on  diameter  inside  bark  at  B.H.  The  average  thickness  of 
bark  at  B.H.  must  be  determined  for  the  species,  and  by  graphic  interpolation 
these  D.I.B.  taper  tables  can  be  drawn  for  trees  of  each  D.B.H.  outside  bark,  from 
which  volume  tables  can  be  constructed  in  any  desired  unit. 

For  the  larger  trees  or  species  with  butt  swelling  extending  above  B.H.,  as  for 
instance,  virgin  stands  of  timber  on  the  Pacific  Coast,  or  Southern  cypress,  the 
present  practice  of  adhering  to  D.B.H.  will  probably  be  continued,  and  trees  with 
variable  amoimts  of  stump  taper  averaged  together  in  volume  tables  regardless  of 
true  form.  The  only  alternative  is  to  attempt  a  standard  measurement  of  diameter 
at  a  higher  point  on  the  bole,  which  will  be  difficult  to  adhere  to  in  practice.  Approx- 
imate rather  than  absolute  accuracy  will  continue  in  the  preparation  and  use  of 
these  tables  for  such  timber. 

When  the  variable  influence  of  butt  swelling  is  further  aggravated  by  the 
obsolete  practice  of  basing  volume  tables  on  diameter  at  the  stump,  no  consistent 
volumes  can  be  obtained  to  serve  as  standards  for  estimating. 

175.  Form  Factors.  The  form  of  a  tree  Is  a  variable  independent 
of  diameter  or  height,  while  the  form  of  a  cylinder  does  not  vary  at  all. 
That  of  a  cone  is  a  constant,  equal  to  one-third  of  the  volume  of  a 
cylinder  of  sunilar  height.  Taidng  the  volume  of  a  cyhnder  as  the 
unit  of  comparison,  and  dividing  the  volume  of  a  cone  by  that  of  the 
cylinder'  of  equal  diameter  and  height,  the  quotient  is  always  .333  or 
one-third.  This  can  be  termed  the  form  factor  of  this  cone,  i.e.,  the 
factor  by  which  the  volume  of  the  cone  is  derived  from  that  of  the  cylin- 
der. It  expresses  the  volume  of  the  cone,  but  not  its  form.  In  the  same 
way  the  form  factor  of  the  paraboloid  is  .5. 

Form  factors  of  trees  can  thus  be  found  by  dividing  their  cubic 
volume  by  that  of  a  cylinder  of  equal  diameter  and  height. 

5  =  Basal  area  of  cylinder  equivalent  to  that  of  tree; 
/i  =  height  of  cylinder  and  of  tree; 
J5/i  =  volume  of  cylinder; 
/=form  factor  or  multiple  expressing  the  relative  volume  of  the 

tree; 
V  =  volume  of  tree. 

Then 

Bh 


and 


V=Bhf. 


212  FORM  CLASSES  AND  FORM  FACTORS 

Volumes  of  trees  can  thus  be  obtained  from  the  vokmies  of  cyhnders, 
when  once  the  average  form  factor  is  known. 

The  form  factor  is  therefore,  in  theory,  a  direct  expression  of  the 
relative  volume  of  a  tree  compared  with  a  standard  or  constant  volume, 
and  tables  of  such  factors  were  expected  to  give  the  key  to  universal 
volume  tables  showing  form  classes.  But  the  diameter  of  the  cylinder 
which  is  to  serve  as  the  unit  or  basic  volume  must  first  be  obtained  and 
must  equal  that  of  the  tree.  If  this  diameter  is  taken  at  the  stump  or 
at  ground,  the  butt  swelling  gives  an  abnormally  large  irregular  vari- 
ation in  the  cylindrical  volume.  This  method  is  known  as  the  Absolute 
Form  Factor. 

But  the  diameter  can  be  shifted  to  B.  H.  with  the  cylinder  equaling 
the  total  height  of  tree  as  before.  Form  factors  so  calculated  give  uniform 
or  consistent  results  from  which  cubic  volumes  can  be  calculated, 
and  are  termed  Breast-high  Form  Factors.  These  form  factors  in  turn 
vary  not  only  with  the  form  of  the  tree,  but  with  the  total  height  as 
well,  hence  could  not  be  used  to  indicate  absolute  form.  The  reason 
is  that  the  diameter  of  the  basic  cylinder  is  taken,  not  at  a  height  pro- 
portional to  the  total  height  of  the  tree,  but  at  the  fixed  height  of  4| 
feet.  For  short  trees  this  point  falls  proportionally  nearer  the  tip, 
with  relatively  smaller  cylinder,  than  for  tall  trees  of  identical  form. 
The  breast-high  form  factor  therefore  decreases  as  height  of  tree 
increases. 

In  an  effort  to  overcome  this  drawback  and  express  form  directly 
by  means  of  form  factors,  the  so-called  Normal  Form  Factor  was  devised, 
in  which  the  basal  area  is  measured  at  a  point  on  each  tree  represent- 
ing a  fixed  ratio  to  the  height  of  the  tree.  This  plan  has  not  proved 
practical,  owing  to  the  difficulty  of  determining  this  point  rapidly  and 
accurately. 

By  comparing  only  the  portion  of  the  tree  above  B.H.  with  the 
volume  of  a  cylinder  of  equal  height,  the  form  factor  for  this  portion 
alone  corresponds  directly  with  variations  in  form  for  the  tree.  This 
is  known  as  Riniker's   Absolute  Form  Factor. 

The  Riniker  form  factor  of  trees  of  each  form  class  was  calculated  by  Jonson 
from  the  normal  form  or  tapers  of  trees  of  each  D.B.H.  and  height  class,  taking 
the  diameters  at  points  representing  one-tenth  of  the  stem  above  B.H.     Then 

/=— -  for  the  bole  above  B.H.  only. 
Bh 

Since  form  quotients  indicate  correctly  the  relative  forms  of  trees,  absolute 
form  factors  of  trees  whose  form  quotients  are  equal  should  also  be  equal.  That 
this  is  true  is  indicated  by  the  following  test,  e.g.,  from  investigations  of  Claughton- 
Wallin  and  F,  McVicker: 


STANDARD  BREAST-HIGH  FORM  FACTORS 


213 


Species 


Form        '       Cubic 
quotient         form  factor 


Basis 
treas 


Red  pine,  Ontario,  Can .  .  . 
Scotch  pine,  Sweden 

Red  pine,  Ontario,  Can .  .  . 
Scotch  pine,  Sweden 

Red  pine,  Ontario,  Can .  .  . 
Scotch  pine,  Sweden 

White  pine,  Ontario,  Can .  . 
Scotch  pine,  Sweden 

White  spruce,  Ontario,  Can 
Scotch  pine,  Sweden 


65 

0.439 

65 

.441 

70.3 

.480 

70.3 

.484 

74.4 

.515 

74.4 

.524 

70.8 

.482 

70.8 

.489 

65.2 

.441 

65.2 

.444 

30 


40 


176.  The  Derivation  of  Standard  Breast-high  Form  Factors.     The 

two  possible  uses  for  form  factors  are  seen  to  be,  first,  an  expression  of 
relative  forms  of  trees,  second,  a  means  of  computing  their  total  vol- 
umes from  that  of  cylinders. 

It  is  not  possible  to  combine  these  two  functions  in  the  same  table 
of  form  factors.  The  absolute  form  factors  for  total  tree  volume  can- 
not be  correlated  with  D.B.H.  nor  with  any  other  point  on  the  bole, 
while  the  form  factors  which  are  based  upon  D.B.H.  and  total  volume 
are  not  absolute  but  vary'  with  height.  But  these  Riniker's  absolute 
form  factors  can  be  used  to  obtain  a  set  of  breast-high  form  factors 
which  represent  the  relative  volumes  of  normally  formed  trees  of  all 
diameters  and  heights  when  compared  with  the  corresponding  cylinders. 

The  steps  in  this  calculation  are: 

1.  Compute  the  Riniker  form  factor  for  trees  of  each  form  class. 

2.  Obtain  the  normal  stump  diameter  from  Hoejer's  formula.  Stumps  were 
taken  as  1  per  cent  of  the  height  of  the  tree.  The  actual  stump  diameter  is  always 
too  large,  due  to  butt  swelling.  The  conception  of  a  normal  stump  diameter  is 
the  diameter  which  the  stump  would  have  if  the  normal  curve  of  the  stem  from 
top  to  D.B.H.  were  prolonged  downward  to  stump  height. 

3.  Find  the  diameter  at  one-half  the  distance  from  stump  to  top,  by  Hoejer's 
formula. 

4.  Express  both  the  stump  diameter  and  the  diameter  at  one-half  height  in 
per  cent  of  D.B.H.  and  compute  the  new  form  quotient,  this  time  based  on  height 
above  stump. 

If  diameter  at  §/i  =  67.7  per  cent  of  D.B.H. 

Stump  diameter  =103.0  per  cent  of  D.B.H. 

67.7 

Form  quotient      = =0.657. 

103.0 


214  FORM  CLASSES  AND  FORM  FACTORS 

5.  From  the  table  of  absolute  form  factors  interpolate  for  the  form  factor  required 
to  coincide  with  this  form  quotient. ^ 

6.  The  basal  area  corresponding  to  the  normal  diameter  at  the  stump  is  found 
as  follows: 

Do=normal  stump  diameter; 

Z)  =  D.B.H.; 

Bo  =  normal  basal  area  at  stump; 
J5  =  basal  area  at  D.B.H. 
If  Do  =  1.0pD, 

Do2  =  1.0/;2D2, 

Bo— j- 

7rD2 

=  1.0p^  — 

=  1.0p25. 

7.  Total  volume  of  the  stem  is  then 

=  Bl.Oif'hfo. 

8.  Breast-high  form  factor  is 

=  1.0p%. 

This  series  of  breast-high  form  factors  shows  the  diminution  with  increased 
height,  the  cause  of  which  is  set  forth  in  §  175.  These  form  factors  are  given  in 
Table  LXXXII,  Appendix  C,  p.  497. 

Since  form  is  best  shown  by  taper  tables,  and  volume  is  best  obtained 
directly  from  volume  tables,  the  use  of  form  factors  in  America  has 
but  little  practical  application  and  has  been  adopted  to  a  very  limited 
extent.  Were  the  breast-high  form  factors  more  regular  they  would 
serve  as  a  means  of  constructing  volume  tables  by  graphic  methods 
(§  138)  in  which  the  curves  being  comparatively  straight  could  be 
extended  and  interpolated  with  less  chance  for  error  than  by  the  ordi- 
nary methods. 

177.  Merchantable  Form  Factors.  Form  factors  based  on  the 
merchantable  contents  of  the  tree  in  cubic  feet,  or  upon  the  net  cubic 

'  These  absolute  form  factors  are  for  the  entire  tree,  but  are  based  on  the 
theoretical  stump  diameter,  hence  are  inapplicable  for  practical  use. 


FORM  CLASSES  AND  UNIVERSAL  VOLUME  TABLES 


215 


volume  utilized  as  board  feet  or  in  any  other  unit,  can  be  computed 
by  first  ascertaining  this  net  volume.     The  form  factor  is 


/= 


Bh 
V 


These  form  factors  serve  no  useful  purpose. 

178.  Form  Height.  Form  height  is  the  product  of  form  times 
height. 

Since  V=Bhf,  tables  of  form  height  simply  eliminate  one  of  the 
two  multiplications  necessary  in  deriving  cubic  volumes. 

0.710 
0.G90 
0.G70 
0.C50 
0.G30 
O.GIO 

0  0.590 

1  0.570 

i  0.550 
o 
^  0.530 

j=  0.510 

I  0.490 

I  0.470 

0.450 

0.430 

0.410 

0.390 

0.370 


0.350 


i 

\, 

\ 
\ 

N 

1 

v^ 

s 

\ 

^ 

X 

V 

Form  class 

\\ 

\ 

\_ 

-r 



k^ 

V 

r 

— 

— 

0.775 

[ 

s^ 

K 

. 

'  ' 

— 

otJ 

^ 

"~ 

o 

V 

^ 

■^ 

■-- 

, 

«.r« 

2] 

— 

— 

V 

^ 

r- 

— 



0.2C 

r 

— 

— 

— 

W\ 

V 

^ 

< 

^"^ 

' 

— 

.^ 

O.S-c 

r 

— 

__ 



.^ 

C^ 

^■^ 

^ 

— 

, 

o";r- 

— 

r~ 

— 





_ 

k 

"^^ 

-^ 



r~~i — 

— ^ — 1 

— 

1 — 

, 

, 

_ 

^ 

f^ 

^ 

"^~~ 

^ 

— 





<: 

■\ 

^ 

^ 

]]^ 

^ 

uiU 

~~j^ 

1 — 

r- 

— 

— 

— 

\ 

~— ~i 

■^ 

"~"~ 

0.5(1 



1 

_i 

— 

— 

— 

^^-. 

r- 



'H — ^^ 

-1 



20  25 


35  40  45  50  55  GO   05    70  75   80  85   90  ^95  100105110115120 
Heightin  Feet 


Fig.  36. — Curv^es  of  breast-high  form  factors  for  form  classes  from  .50  to  .80  inclu- 
sive, showing  effect  of  height  upon  the  form  factor.     From  Tor  Jonson. 


179.  Form  Classes  and  Universal  Volume  Tables  as  Applied  to 
Conditions  in  America.  The  standard  form  classes,  when  applied  to 
trees  of  different  diameter  and  height,  thus  distinguish  three  variables 
just  as  did  the  universal  volume  tables  based  on  diameter,  merchant- 
able length  and  rate  of  taper.  Universal  volume  tables  if  based  on 
total  heights  would  show  volumes  for  the  given  unit  in  three  instead 
of  two  dimensions;  D.B.H.,  Height,  Form  Class. 

But  to  derive  universal  volume  tables  by  form  classes  to  be  based 
on  merchantable  length  instead  of  total  height  would  not  be  so  simple, 
for  the  following  reasons: 


216 


FORM  CLASSES  AND  FORM  FACTORS 


If  taken  to  a  uniform  or  fixed  top  diameter,  trees  with  a  high  form 
quotient  would  be  cut  higher  in  the  top  and  fall  into  a  different  merchant- 
able height  class  than  trees  with  a  low  form  quotient.  Therefore,  for 
trees  of  different  form  quotients,  to  attain  the  same  merchantable  top 
diameter,  trees  with  the  lower  quotients  must  be  taller  than  those  whose 
form  quotient  is  high.  Hence  total  and  merchantable  heights  are 
not  interchangeable  for  trees  whose  form  quotients  differ. 

If  taken  to  variable  top  diameters,  this  second  variable  will  make 
it  practically  impossible  to  distinguish  form  classes  based  on  total 

height  in  the  volumes 
given,  for  these  tops 
would  not  vary  in  any 
definite  relation  to 
total  height  or  form. 

As  long  as  mer- 
chantable rather  than 
total  heights  are  used 
in  volume  tables  and 
timber  estimating, 
form  classes  based  on 
actual  form  of  the 
tree  cannot  be  used 
to  construct  volume 
Fig.  37.— Effect  of  cutting  to  a  fixed  top  diameter,  upon  ^^j^jgg  in  which  trees 
merchantable  height   of   trees  having   different  form      r     i-pp         j    <• 

^.    ^       .  r  ^-    *     f    r-A         •        -^u          of  different  form  are 

quotients.     A  form  quotient  oi    .60  requires  either  a 

shorter  merchantable  length  or  a  taller  tree  than  one  separated,  and  the 
of  .80.  principle  of  averaging 

the  differences  in  vol- 
ume due  to  form  must  continue  to  be  used  for  such  tables. 

But  for  cubic  feet,  basic  volume  tables  may  be  made  up  giving  the 
volume  of  each  diameter,  height  and  form  class.  Similar  tables  can  be 
constructed  in  any  unit  of  volume,  or  for  any  log  rule,  from  tables  of 
normal  taper.  In  applying  these  tables,  the  method  would  be  not  to 
attempt  to  tally  each  tree  in  its  proper  form  class,  but  to  determine 
average  form  classes  (§171)  for  stands  or  other  subdivisions  of  the 
forest,  the  volumes  for  which  can  be  taken  from  this  basic  table  to  form 
a  standard  volume  table  for  the  trees  to  which  it  applies.  Not  over 
three  such  tables  would  be  apt  to  be  needed  for  any  tract,  however 
large  and  varied. 

Methods  of  rapidly  determining  the  form  class  of  sample  trees,  in 
order  to  apply  such  a  system,  are  given  in  §  201, §  202  and  §  203. 


REFERENCES  217 


References 

New  Method  of  Measuring  Volumes  of  Conifers,  Review  of  Schiffel's  method  by 

B.  E.  Fernow,  Forestry  Quarterly,  Vol.  V,  1907,  p.  29. 
Das  Gesetz  des  Inholts  der  Baum  StJimme.     Forstwissenschaftliches  Centralblatt, 

Aug.,  1912,  pp.  397-419. 
Massatabellar    fiir    Traduppskattnung,    Tor    Jonson,    Stockholm,    Sweden,    1918. 

Review,  Forestry  Quarterly,  Vol.  XI,  1913,  p.  399. 
Article  by  L.  Mattson-Marne,Skogsverdsf6reningensTidskirft,  Feb.,  1917,  pp.  201-36. 
Form  Variations  of  Larch,  L.  Mattson-Marne,  Meddelanden  frau  Statens  Skogsfor- 

soksanstalt,  1917,  pp.  843-922;   Review,  Journal  of  Forestry,  Vol.  XVI,  1918, 

p.  725. 
The  Absolute  Form  Quotient,  H.  Claughton-Wallin,  Journal  of  Forestry,  Vol.  XVI, 

1918,  p.  523. 
Tor  Jonson,  "Absolute  Form  Quotient"  as  an  Expression  of  Taper,  H.  Claughton- 
Wallin  and  F.  McVioker,  Journal  of  Forestry,  Vol.  XVIII,  1920,  p.  346. 
Die  Formau.sbildung  der  Baumstamme,  Von  Guttenberg,    Oesterreichische  Viertel- 

jahrschrift  fiir  Forstwesen,   1915,  p.  217;    Review,  Forestry  Quarterly,    Vol. 

XIV,  1916,  p.  114. 


CHAPTER  XVII 

FRUSTUM  FORM  FACTORS  FOR  MERCHANTABLE  CONTENTS 
IN  BOARD  FEET 

180.  The  Principle  of  the  Frustum  Form  Factor.  In  an  effort  to 
simplify  the  construction  and  improve  the  accuracy  of  volume  tables 
for  board  feet,  based  upon  merchantable  heights  and  top  diameters, 
a  merchantable  form  factor  has  been  devised  by  Donald  Bruce. 

Timber  cruisers  in  the  Pacific  Northwest  had  already  made  use 
of  the  similarity  in  form  of  the  merchantable  portion  of  the  tree  to  that 
of  the  frustum  of  a  cone,  but  had  neglected  the  possible  differences  in 
form  and  volume  between  the  cone  and  the  merchantable  bole.  The  new 
method  adopts  the  frustum  of  the  cone  as  the  basic  volume,  instead  of 
the  cylinder  as  for  the  form  factors  discussed  in  Chapter  XVI,  and  then 
compares  this  volume  with  that  of  the  tree,  to  determine  their  true 
relation.    This  relation  is  expressed  as  a  form  factor  in  the  usual  manner. 

y  =  volume  in  tree; 

y  =  volume  in  frustum  of  cone; 

/=form  factor. 
Then 

and 

V^V'f. 

The  contents  of  this  frustum  were  measured  as  the  scaled  board- 
foot  contents  of  cylinders  representing  the  logs  into  which  the  bole 
would  be  cut.  The  length  of  these  sections  was  fixed  at  16  feet,  and 
their  upper  diameters  were  determined  by  the  diameter  of  the  frustum 
at  the  required  point.  The  form  factor  obtained  by  comparing  the 
total  scaled  volume  of  the  merchantable  bole  with  that  of  the  frustum 
so  measured  is  termed  the  Frustum  Form  Factor  and  is  a  merchantable 
form  factor  having  values  close  to  1,  since  the  deductions  from  full 
cubic  contents  of  bole  have  been  made  both  in  the  frustum  and  in  the 
tree. 

The  merits  of  the  frustum  form  factor  method  for  constructing 
volume  tables  are  that  it  applies  directly  to  the  merchantable  portion 


BASIS  OF  DETERMINING  DIMENSIONS  OF  THE  FRUSTUM    219 


of  the  tree,  on  the  same  basis  as  used  in  timber  estimating  to  top 
diameters,  and  that  the  vahies  of  the  form  factors  tend  to  vary  but  httle 
from  a  straight  Hne,  thus  permitting  the  construction  of  curves  of  board- 
foot  volume  with  greater  accuracy  than  when  volumes  are  plotted 
directly  (§  138).  This  advantage  permits  of  constructing  such  tables 
on  the  basis  of  fewer  measurements  of  felled  trees. 

181.  Basis  of  Determining  Dimensions  of  the  Frustum.  The  top 
diameter  of  the  frustum  is  supposed  to  coincide  with  the  top  diameter 
inside  bark  of  the  merchantable  length  of  each  tree  class.  The  diam- 
eter at  its  base,  which  is  at  stump  height  is  arbitrarily  fixed  as  equal 
to  D.B.H.  outside  bark.  No  pretense  is  made  that  this  form  factor 
is  a  scientific  basis  for  studying  tree  form.  Actual  D.I.B.  at  stump 
may  or  may  not  coincide  with  D.B.H.  outside  bark.  The  base  of  the 
cone  must  be  correlated  with  D.B.H.  rather  than  with  stump  diam- 
eters (§  175)  and  this  assumption  is  satisfactory. 

Since  the  sides  of  a  cone  are  straight,  the  upper  diameters  of  each 
"  log,"  or  standard  length  into  which  this  frustum  is  divided,  are 
determined  by  proportion,  to  the  nearest  Yt  inch. 

In  calculating  the  volumes  of  the  frustums  of  cones  the  determination  of  the 
diameter  at  the  top  of  each  successive  16-foot  log  for  cones  of  different  top  and 
base  dimensions  is  best  per- 
formed by  plotting  the  form 
of    the   cone    on    cross-section  ^ 

paper,  on   which   the  vertical 
scale  shows  diameters  and  the       £] 
horizontal  scale  shows  heights       g 
in    feet.      Plot,    first,    D.I.B.       "l 
equals    D.B.H.     at     zero     or 
stump  height;    next,  top  diam- 
eter inside  bark    at    the   mer- 
chantable    height.        Connect 
these  two  points  by  a  straight 
line    representing   the   side  of   Fig. 
the   frustum.      The  diameters 
inside  bark  at  top  of  each  log 
are   then  read   at  16  feet,  32 

feet,  etc.,  to  the  nearest  ra  inch.  The  log  rule  should  be  tabulated  to  show  the 
values  for  each  ro  inch. 

182.  Character  and  Utility  of  Frustum  Form  Factors.  That  the  frustum  form 
factor  is  a  practical  rather  than  a  scientific  basis  of  measurement  is  shown  by  the 
following  facts:  The  absolute  form  factor  of  the  total  contents  of  the  bole  (§  175) 
would  be  0.5  when  the  tree  has  the  form  of  a  paraboloid.  A  truncated  portion  of 
the  bole,  with  the  rapidly  tapering  top  eliminated,  when  compared  with  a  trun- 
cated cone  ha\'ing  the  same  top  diameter,  represents  the  lower  portion  of  a  cone 
of  considerably  greater  height  than  that  of  the  tree  or  paraboloid. 

For  cone  and  paraboloid  (or  tree)  of  equal  total  height,  the  form  factor  of  the 

tree,  compared  with  the  cone  is  - —  or  1.50,  since  0.5  and  0.33  are  the  respective 


,^-' 

B.  atb 

ise=D 

.... 

0" 

-^^ 

^-- 

^ 

-^ 

^ 

8Top 

8         16        24        32        40        48        56        64 
Feet 

38. — Method  of  plotting  a  frustum  from 
which  to  determine  the  top  diameters  of  the 
logs  which  it  contains. 


220  FRUSTUM  FORM  FACTORS 

volume  form  factors  of  the  paraboloid  and  cone  when  compared  with  a  cylinder  of 
equal  dimensions. 

The  nearer  the  top  of  the  tree  this  upper  diameter  falls,  or  the  closer  the  degree 
of  utiUzation,  the  shorter  will  the  completed  cone  become,  until  it  coincides  with 
the  paraboloid  in  height.  In  the  same  manner  the  frustum  form  factor  will  increase, 
until  it  reaches  a  maximum  of  1.50  for  the  comi)leted  cone. 

Chandler,^  in  an  extensive  investigation  of  the  frustum  form  factor  of  northern 
hardwoods,  birch,  beech  and  maple,  determined  that  this  factor  was  independent  of 
species,  site  or  other  influences,  and  independent  of  diameter  and  height,  but  was 
dependent  on  the  two  factors,  form  quotient,  and  taper  ratio.  The  form  quotient 
agrees  in  principle  with  that  of  Tor  Jonson.  Based  on  D.B.H.,  instead  of  stump, 
it  was  computed  for  merchantable  rather  than  total  height,  by  first  subtracting 
diameter  at  top  or  d  from  both  diameter  at  B.H.  and  at  middle  of  merchantable 
length.     Then 

d2-d 

The  taper  ratio  is  the  ratio  between  top  diameter  of  merchantable  bole,  and 
D.B.H. 

Merchantable  cubic  frustum  form  factors  were  found  to  diminish  as  form 
quotient  diminished  and  as  taper  ratio  increased.  The  first  result  is  obvious. 
The  second  confirms  the  conclusions  set  forth  above  as  to  the  effect  of  close  utiliza- 
tion in  increasing  the  frustum  form  factor. 

These  researches  have  definitely  proved,  on  an  empirical  basis,  the  fact  that, 
other  things  being  equal,  frustum  form  factors  based  on  a  fixed  top  diameter  do 
not  ex]Dress  a  scientific  relation  between  the  form  and  volume,  but  will  vary  with 
the  relation  between  cone  and  paraboloid.  In  its  final  analysis,  the  frustum  form 
factor  is  an  endeavor  to  express  the  paraboloidal  forms  of  trees  by  the  use  of  frustums 
of  cones  and  the  application  of  a  correction  or  form  factor.  Although  a  great 
improvement  over  older  methods  if  intelligently  applied,  it  is  not  a  universal 
method,  since  its  results  vary  with  taper  ratio,  butt  swelling,  bark  thickness,  and  the 
top  diameter  utihzed. 

On  the  other  hand,  the  natural  divergence  in  the  total  form  and  cubic  volume 
of  trees  which  gives  rise  to  the  variation  in  form  quotients  of  from  0.575  to  0.8  is 
overcome  in  a  marked  degree  by  the  substitution  of  the  merchantable  frustum 
form  factor  since,  first,  trees  with  a  high-form  quotient  and  of  the  same  total  height 
wiU  be  cut  higher  in  the  tops  than  those  with  a  low-form  quotient  (§  179).  The 
merchantable  form  factor  in  itself  coincides  with  this  greater  utilization  and  there- 
fore approaches  closer  to  unity,  for  both  forms.  If  all  trees  are  utihzed  to  a  fixed 
top  diameter,  a  cyUndrical  tree,  being  cut  nearer  to  its  tip  than  a  conical  tree, 
would  have  fallen  into  a  larger  total  height  class  than  the  conical  tree,  hence  its 
per  cent  of  cylindrical  contents  would  have  been  much  greater  for  merchantable 
form  factor  than  that  of  the  conical  tree — a  difference  not  appearing  in  the  frustum 
form  factor.  Second,  where  the  actual  top  diameter  is  made  to  coincide  with  the 
point  at  which  the  tree  is  commonly  utilized  instead  of  with  a  fixed  top,  there  is  apt 
to  be  still  closer  approach  to  unity  in  the  form  factors.  The  length  and  character 
of  the  crown  usually  determines  the  amoimt  of  taper  from  the  base  of  the  crown 
to  the  tip  of  the  tree  and  consequently  its  distribution  on  the  stem  (§  172).  In 
rough  utilization,  the  last  saw  cut  tends  to  bear  a  direct  relation  to  the  length  of 
crown  and  to  fall  nearer  to  the  base  of  the  crown  than  to  its  tip.     This  is  especially 

1  Bui.  210,  Vermont  Agr.  Exp.  Sta.  1918. 


CALCULATION  OF  THE  FRUSTUM  FORM  FACTOR  221 

true  of  hardwoods  with  branching  crowns.     Measured  from  this  point,  the  frustum 
of  the  tree  will  not  differ  greatly  from  that  of  either  a  cone  or  a  paraboloid. 

A  great  source  of  irregularity  in  frustum  form  factors,  as  in  absolute  form  factors 
for  cubic  contents,  is  found  to  be  the  influence  of  butt  swelling  extending  above 
B.H.  and  second,  the  influence  of  thickness  of  bark.  Both  of  these  factors  reduce 
the  proportion  of  woody  contents  to  the  dimensions  and  consequently  reduce  the 
form  factor. 

183.  Calculation  of  the  True  Frustum  Form  Factor.  A  far  more 
serious  difficulty  in  the  use  of  the  frustum  form  factor  Hes  in  securing 
the  exact  coincidence  of  the  top  diameters  of  the  frustums,  used  as  the 
unit  or  standard  for  volume,  and  the  average  top  diameters  of  the  trees 
whose  volumes  are  to  be  compared  for  the  determination  of  the  form 
factors.  There  is  but  one  exact  method,  namely  to  compute  the  form 
factors  of  a  given  height  separately  for  each  tree  whose  D.B.H.  and 
top  diameter  differ  even  by  yVinch,  by  using  a  frustum  whose  three 
dimensions  exactly  coincide  with  those  of  the  tree  frustum.  This 
method  gives  the  most  consistent  form  factors.  The  results  for  long- 
leaf  pine  given  in  the  table  on  p.  222  were  obtained  by  this  method. 

This  method  can  be  simplified  by  first  averaging  together  for  all 
the  trees  in  a  diameter  and  height  class  the  four  factors,  volume,  D.B.H., 
height,  and  top  diameter.  The  frustum  of  a  cone  having  these  aver- 
age dimensions  is  then  used  to  determine  the  frustum  form  factor  of 
the  class,  by  comparing  its  volume  with  that  of  the  average  tree  of 
the  class.  While  less  accurate,  this  method  reduces  the  computations 
considerably  and  is  within  the  required  limits  of  accuracy  of  the  method. 

By  this  method,  the  computation  of  the  frustum  form  factors  is 
the  first  step  in  the  construction  of  the  volume  table  for  which  they 
are  intended. 

184.  Calculation  of  the  Volumes  of  Frustums.  Influence  of  Fixed 
versus  Variable  Top  Diameters.  The  purpose  of  the  frustum  form 
factors  thus  obtained  is  to  make  possible  the  construction  of  a  volume 
table  in  board  feet,  by  applying  these  factors  to  the  volumes  of  frustums 
of  cones.  This  may  be  done  in  the  office,  once  the  factors  are  known 
and  the  dimensions  of  the  frustums  determined. 

The  second  step  is  therefore  to  determine  these  dimensions  of  frus- 
tums of  cones.  The  base  is  fixed,  being  equal  to  D.B.H. ,  in  1-  or  2-inch 
classes.  But  the  top  diameter  of  these  cones  is  a  source  of  trouble. 
As  seen  in  the  construction  of  volume  tables  (§§  157-158)  the  top  diam- 
eters to  which  trees  are  actually  utilized  tends  to  decrease  as  height 
increases,  and  to  increase  with  D.B.H.  The  table  will  be  based  on 
one  of  two  plans,  a  fixed  top  diameter,  or  variable  top  diameters  coin- 
ciding with  actual  utilization. 

Whichever  basis  is  adopted,  the  top  diameters  of  the  frustums 
must  coincide  with  the  average  top  diameter  of  the  merchantable  boles, 


222 


FRUSTUM  FORM  FACTORS 


whose  volume  is  sought.  If  frustums  having  a  fixed  top  diameter 
limit  are  used,  the  form  factors  should  have  been  computed  from  trees 
measured  to  this  same  top  diameter.  If  on  the  other  hand,  an  attempt 
is  made  to  base  the  table  on  variable  or  actual  used  top  diameters,  then 
the  average  actual  top  diameter  for  each  diameter  and  height  class 
should  first  be  found  and  the  frustum  having  the  requisite  top  dimen- 
sion for  each  class  computed. 

TABLE  XXXV 

True  Frustum  Form  Factors  for  Longleaf  Pine,  from  Frustums  Whose  Top 
Diameters  Coincide  Exactly  with  the  Average  Top  Diameter  of  Trees 
of  Each  D.B.H.  and  Height  Class 

Merchantable  Length  in  16-foot  Logs 


D.B.H. 

2 

2i 

3 

3i 

4 

4J 

Averaged  by 
diameter. 
Weighted 

Inches 

Frustum  Form  Factors 

12 

0.98 

0.98 

0.980 

13 

.97 

1.21 

0.99 

.992 

14 

.96 

.87 

.97 

1.03 

.952 

15 

.90 

1.01 

1.03 

1.05 

.958 

16 

.92 

.94 

1.04 

0.94 

1.10 

.953 

17 

.89 

.95 

.91 

.99 

.99 

.932 

18 

.89 

.98 

.90" 

.96 

1.13 

1.00 

.934 

19 

.96 

.90 

.94 

.98 

.99 

.954 

20 

1.05 

.95 

.88 

.97 

.94 

.99 

.937 

21 

.90 

.88 

.94 

.92 

.902 

22 

.92 

.89 

.94 

.96 

.99 

.938 

23 

.93 

,97 

.94 

.88 

1.00 

.91 

.926 

24 

.93 

.94 

.87 

.95 

.921 

25 

.96 

.94 

.98 

1.04 

1.000 

26 

.94 

.90 

1.07 

.90 

.934 

27 

.93 

.96 

.95 

.93 

.95 

.941 

28 

.93 

.80 

.101 

.913 

29 

1.01 

.93 

.970 

30 

.98 

.85 

.96 

.948 

31 

.94 

.80 

.84 

1.13 

.927 

32 



.94 

.89 

.915 

33 

34 

.... 

.92 

.85 

.80 

.817 

Av'g'd  by  height, 

Weighted 

weighted 

0.939 

0.961 

0.932 

0.958 

0.966 

0.962 

average  0.9468 

It  is  possible,  of  course,  to  prepare  a  table  of  frustum  volumes  using 
fixed  top  diameters,  and  compute  the  form  factors  of  trees  for  those 
classes  whose  top  diameters  are  larger  or  smaller,  but  in  this  case  the^ 


CALCULATION  OF  THE  VOLUMES  OF  FRUSTUMS 


223 


form  factors  vary  not  with  form  alone  but  also  with  difference  in  volume 
due  to  difference  in  top  diameter  independent  of  form.  The  results 
are  shown  in  Table  XXXVI  where  an  average  top  of  13.2  inches  was 
used  on  all  frustums. 

TABLE  XXXVI 

Fbustum  Form  Factors  for  555  Longleaf  Pines,  Coosa  Cou^fTY,  Alabama, 
Based  on  Average  Top  Diameter  of  13.2  Inches  for  Frustums 

Merchantable  Length  in  16-foot  Logs 


2 

2§ 

3 

3^ 

4 

41 

D.B.H. 

Inches 

Frustum  Form  Factors 

14 

0.53 

0.53 

0.54 

15 

.57 

.59 

.50 

.55 

16 

.71 

.51 

.56 

0.53 

0.57 

17 

.67 

.76 

.65 

.69 

.60 

18 

.88 

.55 

.72 

.74 

.77 

.69 

19 

1.03 

.81 

.84 

.81 

.78 

20 

1.13 

1.00 

.87 

.96 

.87 

.86 

21 

1.31 

.98 

.85 

.79 

22 

1.39 

1.00 

.99 

1.01 

.88 

23 

1..54 

1.39 

1.19 

.98 

1.09 

24 

1.40 

1.40 

1.13 

1.26 

25 

1.37 

1.34 

1.33 

1.06 

26 

2.60 

.95 

1.85 

1.21 

1.47 

.97 

27 

1.97 

1.52 

1.22 

1.23 

1.14 

28 

1.26 

.97 

1.27 

29 

.... 

1  67 

1.35 

30 

1.98 

1.37 

1.17 

31 

2.36 

1.04 

1.18 

1.68 

1.51 

32 

.... 

1.76 

1.43 

Such  a  table  serves  no  useful  purpose. 

The  variation  of  top  diameters  actually  utilized  is  shown  in  Table 
XXXVII. 

The  values  in  this  table,  evened  off  by  curves,  would  give  proper 
dimensions  for  frustums  for  the  volume  table  desired. 

The  two  steps  described  mean  a  double  calculation  of  frustum 
volumes,  first,  as  a  basis  of  regular  form  factors,  second  as  a  basis  of 
regular  volumes.  The  second  set  of  frustums  also  serves  the  purpose 
of  obtaining  the  volumes  for  exact  diameter  and  height  classes,  instead 
of  for  the  actual  average  diameters  and  heights  of  the  trees  measured 
(§  137). 


224 


FRUSTUM  FORM  FACTORS 


TABLE  XXXVII 
Actual  A\'Erage  Top  Diameters  of  Merchantable  Lengths,  Longleaf  Pine, 
Coosa  Co.,  Ala.     Basis  555  Trees;    Average  of  All  Top  Diameters   13.2 
Inches 

Merchantable  Length  in  16-foot  Logs 


D.B.H. 
Inches 


3^ 


^ 


Top  Diameters,  Inside  Bark — Inches 


18.0 
17.4 


21.3 
21.6 


25.3 


8.5 

1       7.5 

8.8 

9.2 

9.3 

8.7 

10.3 

8.9 

9.1 

10.4 

9.3 

8.6 

7.8 

11.5 

10.4 

10.2 

9.1 

12.7 

11.5 

10.7 

9.7 

9.6 

12.3 

12.1 

11.3 

10.9 

9.2 

1     13.5 

13.1 

13.1 

12.3 

11.6 

14.1 

13.2 

12.1 

11.4 

17.4 

14.2 

13.7 

13.5 

11.7 

17.0 

15.8 

14.2 

14.1 

13.8 

17.7 

16.2 

15.9 

14.1 

17.2 

17.5 

16.7 

13.3 

15.4 

19.7 

16.9 

17.7 

14.1 

19.4 

16.3 

17.1 

16.0 

17.4 

16.2 

16.6 

20.5 

18.8 

24.0 

20.8 

16.2 

16.4 

18.3 
23.2 

14.6 

17.8 
21.2 

26.8 

21.0 

22.4 

11.0 


17.3 


Of  the  two  methods,  the  use  of  a  fixed  top  diameter  is  preferable 
wherever  utilization  does  not  depart  too  far  from  this  standard.  If 
necessary,  such  a  table  of  volumes  could  be  corrected  for  actual  utili- 
zation, by  subtracting  the  per  cent  of  volume  lost  by  cutting  to  a  lower 
point  and  larger  diameter.  In  this  case  the  same  method  must  be  used 
in  estimating  the  standing  timber,  namely,  to  tally  the  heights  of  the 
trees  to  the  fixed  top  diameter  used,  and  then  discount  for  waste. 

185.  Construction  of  the  Volume  Table  from  Frustum  Form  Factors. 
A  Short  Method.  The  third  and  final  step  is  to  construct  the  volume 
table  by  multiplying  the  volumes  of  the  frustums  by  the  form  factors 
for  each  class. 


FORM  FACTORS  FOR  BOARD  FEET  225 

Frustum  form  factors  can  be  computed  if  desired,  in  cubic  feet. 
For  board  feet,  any  log  rule  may  be  used  as  desii-ed. 

A  shorter  but  less  satisfactory  method  is  to  first  determine  the  top 
diameters  of  the  frustums  to  be  used  in  the  base  table  and  prepare  the 
table  of  frustum  volumes;  second,  to  compute  the  arbitrary  form 
factors  which  are  obtained  by  dividing  the  average  volumes  of  the  trees 
in  each  class  by  the  volume  of  the  proper  frustum,  disregarding  the 
possible  difference  in  top  diameter  and  average  height  for  the  class; 
and  from  these  factors,  to  construct  the  volume  table.  This  method 
works  best  when  fixed  top  diameters  are  used  in  logging  and  the  dif- 
ferences in  top  diameters  between  frustums  and  trees  is  small. 

The  method  of  frustum  form  factors  has  resulted  in  such  a  marked 
increase  in  accuracy  and  economy  in  preparation  of  standard  volume 
tables  based  on  merchantable  board-foot  contents  that  it  has  practically 
superseded  the  standard  methods  of  preparing  these  volume  tables, 
and  until  total  height  and  tables  based  on  form  classes  supersede  the 
use  of  merchantable  heights  in  timber  estimating,  this  method  will 
continue  to  be  used  extensively. 

186.  Other  Merchantable  Form  Factors  for  Board  Feet.  Merchant- 
able form  factors  based  on  the  volume  of  a  cylinder  whose  height  equals 
the  merchantable  length  in  the  tree  have  been  proposed  by  E.  I.  Terry. 

Merchantable  volume  tables  based  on  the  contents  of  frustums  of 
paraboloids  whose  top  diameters  equal  one-half  D.B.H.,  scaled  in  16- 
foot  logs,  have  been  computed  by  the  Forest  Service.  These  correspond 
in  principle  to  the  basic  volumes  of  frustums  of  cones,  and  can  be  used 
for  calculating  form  factors  in  the  same  manner,  but  offer  no  special 
advantage  over  the  frustums  of  cones  for  the  purpose  required. 

References 

A  New  Method  of  Constructing  Volume  Tables,  Donald  Bruce,  Forestry  Quarterly, 

Vol.  X,  1912,  p.  215. 
The  Use  of  Frustum  Form  Factors  in  Constructing  Volume  Tables,   Donald  Bruce, 

Proc.  Soc.  Am.  Foresters,  Vol.  VIII,  1913,  p.  278. 
Further  Notes  on  Frustum  Form  Factor  Volume  Tables,  Donald  Bruce,  Proc.  Soc. 

Am.  Foresters,  Vol.  X,  1915,  p.  3l5. 
The  Use  of  Frustum  Form  Factors  in  Constructing  Volume  Tables  for  Western 

Yellow  Pine  in  the  Southwest,  Clarence  F.  Korstian,    Proc.  Soc.  Am.  Foresters, 

Vol.  X,  1915,  p.  301. 
Top  Diameters  as  Affecting  the  Frustum  Form  Factor  for  Longleaf  Pine,  H.  H. 

Chapman,  Proc.  Soc.  Am.  Foresters,  Vol.  XI,  1916,  p.  185. 
Frustum  Form  Factors  of  Hard  Maple  and  Yellow  Birch,  B.  A.  Chandler,  Bui.  210, 

Vermont  Agr.  Exp.  Sta.,  May,  1918. 
A  Formula  Method  for    Estimating    Timber,    E.  I.  Terry,    Journal    of    Forestry, 

Vol.  XVII,  1919,  p.  413. 
Comment  on  Above,  Donald  Bruce,  Journal,  Vol.  XVII,  1919,  p.  691. 
Further  Comment,  E.  I.  Terry,  Journal,  Vol.  XVIII,  1920,  p.  160. 


CHAPTER  XVIII 
THE  MEASUREMENT  OF  STANDING  TREES 

187.  The  Problem  of  Measuring  Standing  Timber  for  Volimie. 
Standing  trees  are  measured  to  determine  their  contents  in  cubic  feet 
or  in  terms  of  manufactured  products  such  as  board  feet  or  cross-ties. 
Trees  are  measured  as  a  means  of  determining  the  contents  of  entire 
stands.  These  may  be  either  average  or  sample  trees,  of  which  only 
a  few  are  measured,  or  all  of  the  trees  in  a  stand  or  part  of  a  stand  may 
be  tallied. 

Thevolumescontained  in  standing  trees  cannot  be  measured  directly. 
Even  the  volume  of  the  logs  in  the  felled  tree  is  computed  frovi  the 
measurement  of  their  diameters  and  lengths.  These  computations, 
tabulated  as  log  rules  and  as  volume  tables  reduce  the  problem  of  esti- 
mating the  volume  of  standing  trees  to  that  of  measuring  their  merchant- 
able lengths  and  diameters. 

The  cruiser  must  determine  the  height  of  trees  either  bj'  instruments 
based  on  geometric  principles  of  similar  triangles,  at  considerable 
expenditure  of  time  or  by  the  eye,  which  is  the  only  practical  method 
where  all  or  a  large  portion  of  the  stand  is  to  be  so  measured. 

Still  more  difficult  is  the  actual  measurement  of  diameters  at  the 
top  of  each  log  in  the  standing  tree,  which  must  be  known  when  log 
rules  are  substituted  for  volume  tables  in  timber  estimating.  Instead, 
the  cruiser  measures  the  diameter  within  reach,  that  at  B.H.  or  stmnp, 
and  judges  the  rate  of  taper  as  well  as  height,  by  eye,  thus  arriving  at 
these  upper  diameters  by  calculation  from  a  known  measurement. 

Diameter  breast  high  (D.B.H)  is  the  only  actual  and  accurate 
measurement  which  it  is  practicable  to-take  upon  all  or  a  large  per  cent 
of  the  timber.  All  upper  points  are  either  measured  on  a  few  trees 
only,  to  obtain  averages,  or  else  are  judged  solely  b}'  eye;  and  since 
such  ocular  measurements  are  confined  to  dimensions,  heights  or  log 
lengths,  and  diameters  at  upper  points  on  the  bole,  the  cruiser  is  depend- 
ent entirely  on  the  computed  volumes  for  these  dimensions  shown  in 
log  rules  or  Volume  tables.  He  vcmy  by  experience  correlate  these 
volumes  with  their  respective  dimensions,  just  as  stock  buyers  learn 
to  guess  the  weights  of  animals,  and  may  arrive  directly  at  the  volume 

226 


THE  MEASUREMENT  OF  TREE  DIAMETERS  227 

of  the  tree  or  stand,  but  the  method  is  far  more  uncertain  than  if  depend- 
ence is  placed  on  the  computed  volumes  of  the  logs  or  trees  as  shown 
in  tables. 

In  the  use  of  volume  tables,  then,  the  accepted  standards  of  volumes 
set  by  these  tables  are  substituted  for  guessing  as  to  the  contents. 
The  measurements  required  may  be  : 

1.  Diameter  at  base. 

a.  Standardized  at  D.B.H.,  outside  bark. 
6.  Stump  diameter  inside  bark,  still  in  use  by  old  time 
cruisers. 

2.  Height  of  tree. 

a.  Total  height  to  tip. 
6.  Merchantable  height. 

1'.  To  a  fixed  top  diameter. 

2'.  To  a  variable  top  diameter. 

3.  Actual   measurement    of   an   upper   diameter   to    determine 

form  (when  form  classes  are  distinguished). 

a.  At  middle  of  stem  above  D.B.H.  (Jonson). 
h.  At  middle  of  stem  above  stump  (Schiffel). 
c.  At  top  of  last  log. 

188.  The  Measurement  of  Tree  Diameters — Diameter  Classes. 
Stand  Tables.  Diameters  will  be  averaged  in  either  1-inch  or  2-inch 
classes.  In  the  East  and  with  species  of  a  small  total  range  of  diameters, 
1-inch  classes  are  preferable.  Especially  with  such  species  as  spruce 
and  white  pine,  1-inch  diameter  classes  are  necessary  to  give  a  proper 
basis  for  determination  of  the  rate  of  growth,  and  the  number  of  such 
classes  is  not  great  enough  to  act  as  a  drawback  in  estimating. 

A  stand  table  is  a  tabular  statement  of  the  number  of  trees,  in 
each  diameter  class  standing  on  a  given  area.  By  dividing  the  total 
stand  table  by  the  area  in  acres,  the  stand  per  acre  is  shown,  in  which 
case  the  trees  in  each  diameter  class  are  usually  expressed  in  decimals 
to  two  places,  e.g.,  12-inch  class,  4.63  trees,  etc. 

On  the  Pacific  Coast,  with  a  wide  range  of  diameters  running  up 
to  60  inches  or  over,  it  is  unnecessary  and  inadvisable  to  make  smaller 
than  2-inch  diameter  classes.^ 

189.  Instruments  for  Measuring  Diameter.  Calipers,  Description 
and  Method  of   Use.     Calipers    have    been   the   standard    instrument 

1  In  French  forest  practice,  5  centimeters  is  the  division  used.  This  corresponds 
to  1.97  inches. 

The  centimeter  divisions  were  evidently  too  small  and  the  next  convenient 
division  point  was  5  centimeters.  This  is  not  an  argument  against  the  use  of 
1-inch  diameter  classes  for  Eastern  species. 


228 


THE  MEASUREMENT  OF  STANDING  TREES 


for  measuring  the  diameter  of  standing  trees  and  their  use  is  necessary 
in  taking  taper  measurements  on  down  timber  which  cannot  be  meas- 
ured with  diameter  tape.     The  standard  type  of  cahpers  for  eastern 


rrwwm 'ww^F: 


^jmsmmw^^^^'^m^m^ww^^^^k 


Fig.  39. — Calipers  used  in  measuring  the  diameters  of  standing  trees. 


hardwoods  has  a  beam  36  inches  long  with  arms  one-half  that  length. 
A  smaller  type  may  be  used  for  trees  whose  diameter  does  not  exceed 
2  feet  as  in  spruce  or  second-growth  timber.  The  standard  calipers 
have  a  beam  graduated  on  both  sides  to  inches  and  tenths,  and  two 
arms,  one  of  which  is  bolted  to  the  end  of  the  beam,  the  other  a  sliding 

arm,  the  beam 
passing  through  ;i 
slot. 

Fig.  40  indicates 
the  construction 
of  this  arm.  The 
essential  feature 
is  that  when  not 
pressed  against 
the  tree,  the  arm 
Fig.  40.— Construction   of   calipers,  to  secure  adjustment  of   ig     easily     moved 

movable  arm  at  right  angles  to  bar.  along  the  beam 

but  when  in  use 
it  takes  a  position  at  right  angles  with  the  beam  and  parallel  to  the 
other  arm.  The  position  of  this  arm  is  adjustable  by  the  movement  of 
the  screw   (a)  which  sets  a  movable  plate. 

In  use  the  arms  must  be  at  right  angles  to  the  beam.  If  warped  or 
out  of  adjustment,  corresponding  errors  in  measuring  diameters  will 
occur.     The  correct  diameter  can  be  obtained  only  by  holding  the  call- 


THE  DIAMETER  TAPE 


229 


pers  horizontally,  with  the  beam  in  contact  with  the  tree  at  the  point 
desired,  usually  at  B.H.  If  measui'ed  with  the  tips  of  the  calipers, 
the  errors  resulting  from  false  adjustment  or  warping  are  exaggerated. 
If  measured  with  the  calipers  held  at  an  angle,  the  point  measured  is 
probably  above  D.B.H.  and  correspondingly  too  smaU.  If  measured 
below  D.B.H.,  a  large  error  results  from  the  rapidly  increasing  diameter 
of  the  tree  due  to  stump  taper.  An  average  measurement  6  inches 
below  the  desired  point  or  at  4  feet  will  incur  from  5  to  8  per  cent  excess 
volume,  depending  upon  the  rapidity  of  the  taper. 

Where  the  exact  average  diameter  of  a  tree  is  desired,  two  measure- 
ments must  be  taken  at  right  angles  and  the  mean  recorded  to  to  inch. 
In  timber  estimating,  where  large  numbers  of  trees  are  measured,  but 
one  diameter  is  taken,  with  no  efforts  made  to  determine  the  average 
even  on  trees  of  eccentric  cross  sections  since  it  is  assumed  that  errors 
incurred  in  this  way  are  compensating.  A  precaution  sometimes  used 
is  to  measure  half  of  the  trees  in  one  cardinal  direction,  and  the  remainder 
in  the  other  (French). 

190.  The  Diameter  Tape.  The  irregularity  in  the  form  of  trees, 
both  as  to  cross  section  and  bark,  makes  it  practically  impossible  to 
obtain  consistent  results  in  two  successive  measurements  of  diameter 
of  the  same  tree 
with  calipers  even 
when  the  mean 
diameter  is  taken 
as  above  indicated. 
For  permanent 
records  on  plots 
to  be  subsequently 
measured  for  deter- 
mination of  growth, 
consistency  in 
diameter  measure- 
ment is  absolutely 
required. 

For  this  purpose  it  has  been  found  that  the  diameter  tape  must  be 
substituted  for  calipers.  The  graduations  on  the  diameter  tape  are  in 
inches  of  diameter,  each  inch  equal  to  3.1416  inches  in  girth.  In  theory, 
the  measurement  of  the  circumference  of  a  tree  gives  a  plus  error  when 
compared  with  the  actual  mean  diameter.  Actual  tests  at  the  Fort 
Valley  Experiment  Station  by  Scherer  on  one  hundred  trees  showed 
that  the  excess  in  diameter  from  tape  over  caliper  measurement  was 
2  per  cent,  but  the  consistency  of  two  successive  tape  measurements 
as  compared  with  successive  caliper  measurements  showed  that  the 


Fig.  41. — Tape  for  measuring  girths  and  diameters. 


230 


THE  MEASUREMENT  OF  STANDING  TREES 


total  error  of  calipers  over  tape  was  in  the  proportion  of  21  to  1.  The 
diameter  tape  should  therefore  be  adopted  for  aU  measurements  of 
permanent  sample  plots. 

191.  The  Biltmore  Stick.  Although  calipers  can  be  taken  apart 
for  travel  and  packing,  they  are  cumbersome  to  carry  in  timber  esti- 
mating especially  through  brush  and  over  rough  ground.  When  in 
addition  a  beam  of  60  inches  in  length  is  required,  their  use  becomes 
extremely  burdensome. 

The  Bntmore  Stick,  devised  by  Dr.  C.  A.  Schenck,  substitutes  a 
straight  stick  for  calipers  and  has  been  widely  adopted  by  foresters 
for  practical  timber  cruising. 

The  principle  of  the  Biltmore  Stick  is  as  follows:  A  straight  stick, 
if  held  horizontally,  tangent  to  or  in  contact  with  the  bole  of  the  tree, 
and  at  arm's  length  from  the  eye,  forms  the  far  side  of  a  triangle  whose 
other  two  sides  are  lines  of  sight  from  eye  to  each  side  of  the  tree,  and 
which  intersect  the  stick  at  definite  points.     When  the  stick  is  held 

so  that  one  of 
these  lines  of 
sight  intersects 
one  end,  a  scale 
can  be  placed 
upon  the  stick 
starting  at  zero 
at  this  end,  and 
the  point  of  in- 
tersection of  the 
other  line  of 
sight,  if  the  eye 
is  held  in  its  original  position  without  turning  the  head,  will  indicate 
on  the  scale  the  diameter  of  the  tree  at  this  point. 

Since  this  intercepted  distance  on  the  stick  is  evidently  less  than  the  diameter 
of  the  tree,  which  is  at  a  greater  distance  and  cannot  even  be  seen  correctly,  the 
distances  corresponding  to  the  diameters  wanted  will  be  less  than  these  diameters 
and  this  difference  increases  with  diameter  of  tree,  so  that  the  graduations  on  the 
stick  for  successive  diameters  fall  closer  together  for  the  larger  diameters.  The 
values  of  the  graduations  on  the  stick  are  directly  dependent  on  the  dimensions 
of  the  triangle  which  is  determined  by  the  length  of  the  arm  or  reach.  This  ranges 
from  23  to  27  inches  with  an  average  of  25  inches. 


Fig.  42. — Principle  upon  which  the  Biltmore  stick  is 
constructed. 


The  formula  for  computing  the  values  of  this  scale  is 
a  =  length  of  reach  in  inches; 
D  =  D.B.H. 


THE  BILTMORE  STICK  231 

„     ,  aD 


Va{a^D) 

The  derivation  of  this  formula  is  as  follows: 

. 

AB     AB' 
BC    B'C'\ 

D 

AB  =  a  inches,     and    B'C'  =  -. 

Substituting  these  values, 

a      AB' 
BC       D  ' 

2 

aD 

—  =AB'XBC. 

aD 

(I) 

By  substitution, 

(AB'y-  =  (AC'y-{B'C')\ 
iABr=(a+^'-(^'  =  iar+aD  =  a(a+D) 

(ID 

AB'  =  Va(a+D). 

Substituting  this  value  for  AB'  in  equation  (1), 

aD 
BC=         ^       - 

^a{a+D) 

Since  BC  is  the  scale  for  \  of  the  diameter  of  the  circle,  the  formula  for  the  scale 

for  the  whole  circle  is  ' 

aD  laD^ 

Scale =^=^^  =\—-f:- 
Vaia+D)       \a+D 

The  Biltmore  stick  is  less  accurate  than  the  cahpers  or  diameter 
tape  and  should  therefore  never  be  used  for  scientific  measurements  or 
permanent  records.     To  insure  complete  accuracy  in  the  use  of  a  prop- 
erly graduated  stick,  the  following  conditions  are  necessary : 
The  tree  must  be  circular  in  cross-section. 

The  stick  must  be  held  against  the  tree  at  a  point  4^  feet  from  the 
ground. 

aD  VaVaD         VaD  j  aD'- 

Va{a+D)     VaVa+D     V^+D      \a+D' 


THE  MEASUREMENT  OF  STANDING  TREES 


The  eye  must  be  on  a  level  with  the  stick  (assuming  that  the  tree 
is  erect). 

The  eye  must  be  at  the  proper  distance  from  the  tree. 

The  stick  must  be  held  horizontal  (assuming  again  that  the  tree 
is  erect). 

The  stick  must  be  held  perpendicular  to  the  line  of  sight  from  the 
eye  to  the  center  of  the  tree  at  the  point  of  measurement. 

Errors  of  1  per  cent  in  the  measurement  of  diameter  are  incurred 
under  the  following  conditions: 

The  figures  given  represent  the  distances  by  which  the  position 
of  stick  or  eye  departs  from  the  above  conditions. 

TABLE  XXXVIII 
Errors  in  Using  Biltmore  Stick  * 


Cause 

Resulting  in  Error  of 
1  Per  Cent  in  Diameter 

Sign 

D.B.H.  of  trees 

10 

Inches 

30 

Inches 

60 
Inches 

Eve  above  or  below  stick  bv 

9.2 

4.6 

4.9 
1.4 

(Variabl 

7.3 

4.2 

4.9 
0.65 

-)       ■ 

7  1 

+ 

Stick  not  horizontal — one  end  higher  than 

4.1 

+ 

± 
UsuaUy 

Stick  not  perpendicular  to  hne  of  sight — one 

end  nearer  the  eye  than  the  other  by 

Eye  too  near  to  or  too  far  from  tree  by 

5.1 
0.45 

ably    g 
caUper 

greater    tl 

3) 

lan    with 

*  Donald  Bruce,  Proc.  Soc.  Am.  Foresters,  Vol.  IX,  1914,  p.  46. 

A  still  more  serious  error  is  incurred  through  the  inevitable  tendency  of  the 
cruiser  to  raise  the  stick  to  the  level  of  the  eye,  rather  than  lower  the  eye  to  the 
level  of  the  stick.  If  the  stick  is  held  at  4|  feet  and  the  eye  remains  at  5  feet 
3  inches,  with  a  difference  of  7  inches  in  height,  the  error  is  but  1  per  cent  of  the 
diameter,  but  if  the  stick  is  raised  to  the  level  of  the  eye,  the  diameter  at  the  point 
measured  Ls  appreciably  less  than  D.B.H.  The  resultant  average  error  varies  from 
3  to  6  per  cent,  dependent  upon  the  rapidity  of  taper,  and  increases  consequently  with 
the  diameter  of  the  tree. 

The  following  table  gives  the  graduations  which  should  be  placed  upon  Biltmore 
sticks  for  a  reach  of  from  23  to  27  inches  respectively: 


THE  BILTMORE  STICK 


233 


TABLE  XXXIX 

Figures  to  be  Used  in  Graduating  a  Biltmore  Stick 


Distance  from  Eye  to  Tree— Inches 

Diameter 

of 

23 

24 

25 

26 

27 

tree. 

Inches 

Distance  to  be  marked  on  stick — Inches 

3 

2.82 

2.83 

2.83 

2.84 

2.85 

5 

4.53 

4.55 

4.56 

4.58 

4.59 

7 

6.13 

6.10 

6.19 

6.21 

6.24 

9 

7.63 

7.  OS 

7.72 

7.76 

7.79 

11 

9.05 

9.11 

9.17 

9.22 

9.27 

13 

10.39 

10.47 

10  54 

10.61 

10.68 

15 

11.67 

11.77 

11.86 

11.94 

12.03 

17 

12.89 

13.01 

13.12 

13.22 

13.32 

19 

14.06 

14.19 

14.32 

14.44 

14.56 

21 

15.18 

15.34 

15.48 

15.62 

15.75 

23 

16.26 

16.44 

16.60 

16.75 

16.90 

25 

17.31 

17.50 

17.68 

17.85 

18.01 

27 

18.31 

18.52 

18.72 

18.91 

19.09 

29 

19.29 

19.51 

19.73 

19.94 

20.14 

31 

20.23 

20.48 

20.71 

20.94 

21.15 

33 

21.15 

21.41 

21.67 

21.91 

22.14 

35 

22.04 

22.32 

22.59 

22.85 

23.10 

37 

22.91 

23.21 

23.50 

23.77 

24.03 

39 

23.75 

24.07 

24.37 

24.67 

24.94 

41 

24.58 

24.91 

25.23 

25.54 

25.84 

43 

25.38 

25.74 

26.07 

26.40 

26.71 

45 

26.17 

26.. 54 

26.89 

27.23 

27.56 

47 

26.94 

27.33 

27.70 

28.05 

28.39 

49 

27.69 

28.10 

28.48 

28.85 

29.21 

51 

28.43 

28.85 

29.25 

29.04 

30.01 

53 

29.10 

29.59 

30.01 

30.41 

30.79 

55 

29.87 

30.31 

30.75 

31.16 

31.56 

57 

30.56 

31.03 

31.47 

31.90 

32.32 

59 

31.25 

31  73 

32.19 

32.63 

33.06 

61 

31  92 

32.41 

32.89 

33.35 

33.79 

63 

32.58 

33.09 

33.58 

34.05 

34.51 

65 

33.23 

33.75 

34.26 

34.74 

35.21 

*W.  B.  Barrows,  Journal  of  Forestry,  Vol.  XVI,  1918,  p.  747 

In  this  table,  the  graduations  are  given  for  odd  diameters  instead  of  even  ones. 
For  instance,  when  diameters  are  talhed  in  2-inch  classes,  every  tree  larger  than 
13  inches  and  smaller  than  15  inches  in  diameter  is  talhed  as  a  14-inch  tree. 
These  graduations  thus  mark  the  upper  and  lower  hmits  of  size  of  each  2-inch 


234  THE  MEASUREMENT  OF  STANDING  TREES 

D.B.H.  class,  instead  of  the  average  size,  as  14  inches,  enabling  the  cruiser  to 
classify  accurately  all  trees  on  the  border  hne  between  two  diameter  classes. 

In  measuring  trees  of  eccentric  or  irregular  cross  section,  the  errors  incident  to 
caliper  measurement  are  exaggerated  by  the  use  of  the  Biltmore  stick,  but  as  before, 
these  errors  tend  to  compensate  and  can  be  neglected. 

Bruce  has  suggested  that  the  volume  tables  standardized  at  D.B.H.  should  be 
converted  to  values  for  diameter  at  the  height  of  the  eye,  or  D.E.H.,  standardized 
at  5  feet  3  inches.  To  do  this,  taper  measurements  are  taken  to  estabUsh  the 
D.E.H.  of  trees  of  given  D.B.H.  By  interpolation,  the  volumes  corresponding  to 
given  even  D.E.H.  inches  can  easily  be  obtained. 

In  the  ordinary  use  of  the  Biltmore  stick,  it  is  necessary  to  bevel  the  edge 
opposite  the  figures  so  that  the  measurement  may  be  taken  in  contact  with  the  bole. 
Otherwise  the  thickness  of  the  stick  reduces  the  distance  from  the  eye  and  incurs 
an  error  whose  magnitude  is  determined  by  this  thickness.  By  deducting  this 
thickness  (0  from  the  distance  (a)  in  the  formula,  so  that  this  formula  reads, 

Scale  = 


Vaia+D) 
the  resulting  valu6s  are  correct  for  the  face  of  the  stick. 

192.  Ocular  Estimation  of  Tree  Dimensions.  Where  the  diameter 
of  every  tree  on  a  given  area  must  be  recorded,  the  time  consumed  in 
actually  measuring  the  diameters  is  a  considerable  item  of  expense. 
Except  when  scientific  measurements  or  permanent  plot  records  are 
required,  estimators  plan  to  educate  the  eye  to  read  as  large  a  percent- 
age as  possible  of  the  diameters  dii-ectly  without  measurement,  using 
the  calipers,  diameter  tape  or  Biltmore  stick  merely  as  a  check.  This 
is  especially  desirable  when  the  cruiser  is  doing  his  own  tallying. 

While  the  eye  can  be  trained  with  considerable  rapidity  to  a  sufficient 
degree  of  accuracy  for  estimating,  it  is  constantly  liable  to  error  and 
must  never  be  relied  upon  for  even  a  single  day  without  instrumental 
checks.  These  should  be  made  on  starting  work  and  at  intervals  during 
the  day.  The  eye  may  be  trained  to  judge  diameters  at  different 
distances  equally  well.  Some  men  develop  this  faculty  more  rapidly 
and  to  greater  degree  than  others.  It  is  the  general  tendency  in  ocular 
estimation  to  favor  a  tree  of  a  given  size,  diameters  of  trees  of  lesser 
size  being  over-estimated  while  larger  diameters  are  under-estimated. 
The  use  of  2-inch  diameter  classes  greatly  facilitates  ocular  estimating. 

In  training  the  eye  to  estimate  diameters,  the  greatest  progress  is 
made  by  repeated  guesses  followed  immediately  by  the  measurement 
of  the  tree  which  is  then  closely  observed  to  fix  the  known  diameter  and 
correct  the  faulty  observation.  Since  ocular  estimating  is  not  a  matter 
of  reasoning  but  of  impression,  the  decision  as  to  the  dimensions  of  the 
tree  should  be  made  instantly.  Otherwise  fatigue  and  consequent 
inaccuracy  ensue. 


THE  MEASUREMENT  OF  HEIGHTS  235 

193.  The  Measurement  of  Heights.  While  in  measuring  diameters 
it  is  possible  to  use  the  instrument  upon  every  tree  as  a  practical  measure 
when  necessary,  the  greater  difficulty  and  time  required  in  measuring 
heights  makes  the  general  use  of  an  instrument  for  even  a  large  per 
cent  of  the  trees  impossible.  Only  on  small,  permanent  sample  plots 
will  the  height  of  each  tree  be  actually  measured.  Height  measures, 
or  so-called  hypsometers,  are  commonly  used  to  obtain  the  height 
of  average  trees  from  which  the  average  height  of  the  remaining  trees 
is  determined,  or  to  check  the  eye  when  the  merchantable  heights  of 
all  trees  are  recorded. 

In  the  latter  case,  ocular  estimation  of  the  number  of  merchantable 
logs  in  each  tree,  or  total  merchantable  height,  is  the  only  practical 
means  possible.  It  takes  no  longer  to  estimate  the  height  of  a  tree 
by  eye  than  its  diameter,  but  the  measurement  of  height  by  hypsometer 
takes  about  ten  times  as  long  as  to  caliper  the  tree. 

The  eye  is  slightly  more  unreliable  in  measuring  heights  than  diam- 
eters. The  height  scale  is  more  difficult  to  fix  in  the  mind.  Con- 
sequently the  tendency  is  to  arrive  at  the  height  of  trees  by  comparison 
with  other  trees.  The  result  is  that  the  standard  of  height  for  all  trees 
tends  to  shift  from  day  to  day  unless  heights  are  carefully  checked  at 
the  beginning  of  each  day's  work  in  order  to  maintain  this  mental 
basis  or  standard.  In  no  other  feature  of  ocular  timber  estimating 
are  such  serious  errors  made  even  by  experienced  cruisers  as  in  estimat- 
ing heights,  and  the  novice  should  never  trust  his  judgment  over- 
night. 

194.  Methods  Based  on  the  Similarity  of  Isoceles  Triangles. 
Measurement  of  heights  is  based  on  the  principles  of  similar  triangles. 
From  the  observer's  eye,  the  tree  forms  one  side  of  a  large  triangle, 
the  other  two  sides  of  which  are  the  lines  of  sight  to  the  top  and  base 
of  the  tree.  The  base  of  this  triangle  can  be  measured.  The  length 
of  the  vertical  side  which  is  the  height  of  the  tree  is  the  dimension 
sought.  To  determine  this  inaccessible  dimension,  a  smaller,  measure- 
able,  similar  triangle  is  used. 

Similar  triangles  must  have  their  three  sides  proportional  and  the 
three  angles  equal.  This  is  secured  when  either  two  sides  are  propor- 
tional and  one  angle  equal,  or  one  side  is  proportional  and  two  angles 
equal. 

The  isosceles  triangle  with  two  sides  of  equal  length  forms  the 
simplest  method  of  measuring  the  height  of  a  standing  tree.  In  this 
triangle  the  base  from  the  eye  to  the  foot  of  the  tree  is  equal  to  the 
height  of  the  tree  and  may  be  directly  measured.  The  small  triangle 
in  this  case  is  used  to  find  the  point  on  the  ground  at  which  this  base 
will  be  equal  to  tree  height.     A  triangle  which  has  its  own  base  and 


236 


THE  MEASUREMENT  OF  STANDING  TREES 


/' 


X 


height  equal  and  whose  Hne  of  sight  from  eye  to  top  coincides  with  that 
from  eye  to  tip  of  tree  gives  this  result. 

A  straight  stick  or  short  pole  may  be  grasped  by  the  thumb  and  first 
finger  at  a  distance  from  its  top  exactly  equal  to  the  distance  from  the 
eye  to  the  point  thus  marked.  Holding  this  stick  vertically,  which 
is  best  accomplished  t»y  having  the  greatest  weight  below  the  hand 
to  act  as  a  pendulum,  the  observer  moves  backward  or  forward  until 
the  line  of  sight  Ah  m  Fig.  43  cuts  the  desired  upper  point  on  the  tree, 
and  at  the  same  time  the  line  of  sight  Ac  cuts  the  tree  at  its  base.  At 
this  point  the  triangle  Ahc  has  become  similar  to  the  triangle  ABC, 
and  AC  is  equal  to  BC.     The  measured  distance  from  eye  to  base  of 

tree  is  then   equal  to  the 
B 

/I 


height  of  the  tree.  This 
distance  can  be  measured 
along  the  ground  to  the 
point  below  the  eye  with 
sufficient  accuracy,  pro- 
vided the  slope  is  even. 
This  measurementof  height 
can  be  taken  from  any 
point  of  elevation,  either 
on  a  level  with,  above, 
or  below  the  base  of  the 
tree  without  affecting  its 
accuracy. 

195.  The  Principle  of 
the  Klaussner  Hypsom- 
eter.  For  height  meas- 
urements which  require 
greater  accuracy  than  is  obtainable  by  such  ocular  methods  as  the 
one  just  described,  the  small  triangle  is  constructed  in  the  form 
of  an  instrument  called  a  hypsometer,  on  which  two  of  the  sides 
corresponding  respectively  to  the  lines  AC  and  BC,  or  distance 
to  tree  and  height  of  tree,  are  graduated  to  units  of  distance.  This 
enables  the  observer  to  first  adjust  the  scale  AC  for  distance, 
to  equal  in  feet  the  known  distance  from  the  tree,  hence  to  determine 
what  this  distance  shall  be.  The  line  of  sight  from  the  eye,  beginning 
at  the  zero  point  of  this  scale  or  apex  of  the  small  triangle  is  now  brought 
into  line  with  the  point  on  the  tree  whose  height  is  to  be  measured, 
which  makes  the  small  and  large  triangles  similar.  The  point  at  which 
this  line  of  sight  cuts  the  scale  BC,  whose  graduations  are  equal  to  those 
on  the  scale  AC  indicates  the  height  of  the  tree.  These  graduations 
may  be  of  any  size  so  long  as  both  scales  are  graduated  equally.     They 


Fig.  43. — Similar  isosceles  triangles  formed  by  use 
of  pole,  for  measuring  height  of  trees. 


THE  PRINCIPLE  OF  THE  KLAUSSNER  HYPSOMETER 


237 


will  serve  to  read  height  in  feet,  or  in  any  other  unit  of  distance,  as 
meters,  since  whatever  unit  is  used 
to  measure   the  distance   from  the 
tree  applies  as  well  to  its  height. 

The  Klaussner  Hypsometer.  In 
hypsometers  based  upon  similar 
triangles  as  show^n  in  Fig.  43  the 
vertical  scale  represents  tree  height, 
the  scale  at  base,  distance  to  the 
tree.  If  the  scale  be  is  on  a  movable 
arm,  it  may  be  set  on  the  scale  Ac 
at  any  required  distance.  By  sight- 
ing along  Ac  towards  C  and  by  rais- 
ing the  sight  or  bar  A  6  to  intersect 
the  line  of  sight  AB,  the  total 
height  of  tree  is  read  directly  from 
the  scale  be.  The  standard  hyp- 
someter of  this  make  is  known  as 
the  Klaussner,  Fig.  44.  The  verti- 
cal scale  is  weighted  to  insure  its 
vertical  position. 

As  is  seen,  two   lines  of   sight 
must  be  adjusted  for  this  reading.     The  instrument   is   therefore  used 
with  a  tripod  and  is  rather  slow  in  execution.^ 


Fig.  44. — ^The  Klaussner  hypsometer. 


^^--:b^ 


Fig.  44a. — Method  of  application  of  the  Klaussner  hypsometer. 

1  In  Forestry  Quarterly,  Vol.  XIII,  1915,  p.  442,  S.  B.  Detwiler  has  suggested  a 
simple  hypsometer  based  upon  this  principle,  which  for  practical  work  does  away 
with  the  tripod  apparently  without  sacrificing  accuracy. 


238  THE  MEASUREMENT  OF  STANDING  TREES 

The  Klaussner  principle  differs  from  that  shown  in  Fig.  43  onlj'- 
in  that  the  height  is  measured  on  the  vertical  scale  be,  the  measure- 
ment may  be  taken  at  any  point  from  the  tree  by  adjusting  the  scale 
Ac  to  correspond  with  this  distance,  and  the  triangles  may  be  of  any 
form,  provided  one  side  is  vertical. 

Merritt  Hypsometer.  The  Merritt  hypsometer  is  a  scale  placed  on 
the  reverse  side  of  the  Biltmore  stick  (§  191)  and  is  read  by  holding  the 
stick  in  a  vertical  position  at  arm's  length,  when  standing  at  a  given  dis- 
tance from  the  tree. 

Six  inches  on  the  stick  will  give  the  height  of  a  16.3-foot  log  under 
the  following  conditions: 

Arm  length,  inches 2.3         24        25        26        27 

Distance  from  eye  to  tree,  feet 62.5     65.2     67.9     70.6     73,3 

The  similar  triangles  used  here  correspond  in  principle  with  those 
of  the  Klaussner  hypsometer. 

For  accurate  results  the  stick  must  be  held  vertically  and  not  raised 
or  lowered  during  the  reading.  Only  approximate  accuracy  can  be 
secured,  but  the  method  serves  as  a  ready  check  on  ocular  measure- 
ments of  log  lengths. 

196.  Methods  Based  on  the  Similarity  of  Right  Triangles.  The 
second  general  method  for  measuring  heights  is  the  use  of  the  right 
triangle.  This  method  is  based  on  securing  a  horizontal  line  of  sight 
from  the  eye  to  a  point  on  the  bole  of  the  tree,  and  requires  two 
readings,  one  above,  the  other  below  this  point  of  intersection,  the  sum 
of  which  gives  the  height  of  the  tree.  This  disadvantage  is  offset  by  the 
fact  that  these  instruments  may  be  held  in  the  hand,  thus  eliminating 
the  tripod,  and  making  them  compact  and  portable. 

The  horizontal  line  of  sight  may  be  secured  by  using  either  a  bubble 
or  a  plumb-bob.  The  simplest  application  of  this  method  is  that  of  a 
right  isosceles  triangle,  for  which  purpose  a  clinometer  is  used.  This 
is  an  instrument  with  bubble  mounted  on  a  graduated  arc  reading  in 
per  cents,  or  in  degrees.  In  the  latter  case  the  graduations  must  be 
reduced  to  per  cents. 

When  the  arc  on  this  clinometer  is  set  at  an  angle  of  45°,  the  line 
of  sight  Ab  coincides  with  the  line  AB  at  a  definite  distance  from  the 
tree,  from  which  a  horizontal  line  of  sight,  which  can  then  be  taken  by 
setting  the  arc  at  zero,  gives  a  distance  to  the  tree  equal  to  the  height 
of  the  tree  above  the  intersection  of  this  line  with  the  bole.  If  used 
on  fairly  level  ground,  the  distance  below  this  point  is  within  reach  and 
can  be  measured  on  the  tree  and  added  to  the  distance  to  the  tree  to 
get  its  total  height. 

This  instrument  can  also  be  used  to  measure  heights  from  any  dis- 
tance from  the  bole,  by  taking  two  readings  or  angles,  one  to  the  upper 


HYPSOMETERS  BASED  ON  PENDULUM  OR  PLUMB-BOB        239 

point,  and  one  to  the  base.  In  this  case  the  actual  angle  from  station 
to  point  on  tree  is  read,  and  indicates  the  height  in  per  cent  of  the  hori- 
zontal distance.  At  100  feet  distance,  an  80  per  cent  angle  to  tip 
equals  a  height  of  80  feet  above  the  eye.     If  the  lower  angle  to  base  is 


Fig.  45. — The  Abney  hand  level  and  clinometer. 

now  5  per  cent,  the  additional  height  is  5  feet,  total  height  85  feet. 
At  50-foot  distance  these  per  cents  applied  to  50  feet  give  a  total  height 
of  42^  feet.  It  is  convenient  therefore  to  read  heights  by  this  method 
from  distances  easily  converted  into  equivalent  heights. 


Fig.  46. — Goulier's  Clinometer. 


197.  Hypsometers  Based  on  the  Pendulum  or  Plumb-bob.  These 
angles  can  be  read  as  easily  from  a  pendulum,  with  graduated  arc  placed 
below.  A  clinometer  constructed  on  this  principle,  and  used  as  a 
hypsometer,  is  illustrated  in  Fig.  46. 


240  THE  MEASUREMENT  OF  STANDING  TREES 

The  Faustmann  Hypsometer.  Instead  of  graduating  a  circular  arc 
in  per  cents,  which  requires  a  decreasing  scale  with  increasing  per  cent 
(since  the  tangents  of  the  angles  increase  faster  than  the  angle),  the 
height  scale  corresponding  with  this  arc  may  be  placed  on  a  straight 
arm  as  in  other  hypsometers  (§  195)  and  graduated  evenly. 

The  Faustmann  hypsometer  employs  this  principle  of  the  pendulum, 
using  a  plumb-bob  to  determine  the  angles  BAD  and  CAD,  and  indicat- 
ing the  height  of  the  tree  above  and  below  the  point  D  by  the  intersec- 
tion of  this  plumb-bob  string  with  the  "  height  "scale  on  the  base  of  the 
hypsometer.  This  instrument  is  illustrated  in  Fig.  47.  Its  method 
of  use  is  shown  in  Fig.  48. 


Fig.  47. — The  Faustmann  hypsometer. 

The  slide  is  first  moved  upAvards  until  the  number  of  units  on  the 
vertical  scale,  from  zero,  thus  set  off,  equals  the  distance  to  the  tree 
in  feet  (or  in  yards).  When  sighted  at  the  upper  point  on  the  tree, 
the  plumb-bob  falls  to  the  near  side  towards  the  eye,  and  the  number  of 
units  or  height  is  read  in  the  mirror.  The  second  reading  is  shown  in 
Fig.  48,  the  plumb-bob  falling  to  the  far  side.  The  horizontal  scale  thus 
extends  in  both  directions  from  zero.  On  fairly  level  ground,  this 
second  reading  is  sometimes  omitted,  providing  the  height  of  the  eye 
above  the  base  of  tree  is  regarded  as  a  constant  and  added  for  total 
height.     For  accurate  measurements  both  readings  must  be  taken. 

Practice  has  demonstrated  that  the  use  of  a  plumb-bob  and  weight 
reduces  the  serviceable  character  of  the  instrument,  since  the  seweights 
are  easily  lost  and  the  strings  broken.  The  mirrors  also  are  easily 
damaged. 

Weise  Hijpsometer.  The  Weise  hypsometer  (Fig.  49)  is  the  same 
in  principle  as  the  Faustmann  but  substitutes  a  metal  pendulum  for 


HYPSOMETERS  BASED  ON   PENDULUM  OR   PLUMB-BOB       241 

the  string  and  plumb-bob.  The  two  arms  when  not  in  use  can  be  placed 
within  the  cylinder.  The  instrument  is  more  durable  than  the  Faust- 
niann  but  slightly  less  accurate. 

Forest  Service  Hypsometer.  A  more  durable  type  of  hypsometer 
based  upon  this  principle  is  known  as  the  Forest  Service  hypsometer. 
The  distance  at  which  this  instrument  reads  the  heights  BD  and  DC 
is  fixed  at  100  feet.  The  scale  showing  these  heights  is  computed  from 
the  tangents  of  the  angles  read  at  this  distance  and  expressed  in  terms 
of  feet  in  height.     This  scale  is  placed  on  a  circular  pendulum  which 


Fig.  48. — Mot  hod  of  application  of  the  Faustmann  hypsometer. 


is  released  by  pressing  a  small  knob  with  the  thumb  while  sighting 
through  a  peep-hole  along  the  line  of  sight  AB  ov  AC.  This  scale  is 
enclosed  in  a  metal  frame  in  the  form  of  a  disk,  and  the  instrument  is 
practically  indestructible  and  can  be  operated  with  one  hand.  If  read 
at  50  feet,  the  readings  shown  must  be  divided  by  two.  If  at  200  feet, 
they  must  be  multiplied  by  two,  and  proportionately  for  other  distances. 
As  in  the  case  of  other  clinometers  this  hypsometer  may  be  used  to  read 
per  cents  of  grade. 

The  Winkler  Hypsometer.  The  same  principle  may  be  used  in 
constructing  a  hypsometer  in  the  form  of  a  square  or  rectangular 
board  or  cardboard.  In  this  instrument  the  line  of  sight,  AB,  coin- 
cides with  the  top  edge  of  the  board, 

A  board  whose  top  and  bottom  edges  are  parallel  is  laid  off  with  a 


242 


THE  MEASUREMENT  OF  STANDING  TREES 


horizontal  scale  at  base  and  a  vertical  scale  ad  intersecting  the  scale 
at  base  at  right  angles,  at  a  point  to  permit  this  horizontal  scale  to  extend 
in  both  directions  as  in  the  Faustmunn  Hypsonieter.  Both  scales  are 
marked  off  in  the  number  of  equal  units  or  graduations  desired,  to  cor- 
respond with  the  distance  from  the  tree  at  which  the  hypsometer  is  to 
be  used.  A  plumb-bob  is  suspended  from  point  a,  and  the  heights  above 
and  below  the  eye  read  as  usual.  If  but  one  fixed  distance  is  desired 
this  is  represented  by  a  scale  reproduced  on  the  line  at  base  of  card. 


Fig.  49. — The  Weise  hypsometer. 


This  board  may  be  graduated  to  read  at  lesser  distances  from  the 
tree,  by  placing  other  horizontal  scales  upon  the  board  intersecting 
the  vertical  or  "  distance  "  scale  ad  at  the  point  below  the  apex  a, 
representing  the  distances  desired,  and  graduating  these  horizontal 
lines  to  the  same  scale  as  the  base.  This  home-made  hypsometer  is 
described  in  Farmers'  Bulletin  715,  U.  S.  Dept.  of  Agriculture,  1916, 
p.  18. 

The  original  instrument  from  which  this  type  of  hypsometer  was 
derived  is  known  as  the  Winkler  hypsometer,  shown  in  Fig.  50.  This 
instrument  is  also  used  as  a  dendrometer  (§  200). 


THE  PRINCIPLE  OF  THE  CHRISTEN  HYPSOMETER 


243 


198.  The  Principle  of  the  Christen  Hypsometer.  Many  hj^psom- 
eters  have  been  invented,  principall}'  by  Continental  foresters,  using 
one  or  the  other  of  these  general  principles.  The  Christen  hypsometer 
introduces  a  different  principle  but  has  no  special  merit  except  the 
simplicity  of  its  operation.  Description  of  this  instrument,  taken 
from  Graves'  Mensuration  is  as  follows : 

This  instrument  consists  of  a  metal  strip  16  inches  long,  of  the  shape  shown  in 
Fig.  51.     The  instrument  is  made  of  two  pieces  hmged  together,  which  are  folded 


Fig.  50. — Winkler  Hypsometer. 


when  it  is  not  in  use.  A  hole  is  pierced  in  the  upper  end,  from  which  it  is  suspended 
between  the  fingers.  Along  the  inner  edge  is  a  notched  scale  which  gives  directly  the 
readings  for  heights.  The  instrument  is  used  as  follows :  A  10-foot  pole  is  set  against 
the  tree.  The  observer  stands  at  a  convenient  station  whence  he  can  see  the  tip  and 
base  of  the  tree  and  also  the  top  of  the  10-foot  pole.  The  instrument  is  suspended 
before  the  eye  and  moved  back  and  forth  until  the  edge  6  is  in  line  of  vision  to  the 
top  of  the  tree  and  the  edge  c  in  line  of  vision  with  the  base.  The  point  where  the 
line  of  vision  from  the  eye  to  the  top  of  the  10-foot  pole  intersects  the  inner  edge 
of  the  instrument  indicates  on  the  scale  the  height  of  the  tree. 


244 


THE  MEASUREMENT  OF  STANDING  TREES 


JJach  instrument  is  constructed  for  use  with  a  specified  length  of  pole.     The 

-.       instrument   described  above   is  one  designed   by  the  author  for 

convenience  with   the  use  of    English  units.     It  was  constructed 

in  the  following  way:    The  distance    be    on    the    instrument  was 

chosen  arbitrarily  as  15  inches  and  the  length  of  the  pole  as  10 

feet.     It  would,  of  course,  be  possible  to  construct  an  instrument 

for  a  pole  12  feet   or    any  other  length    and  on    a    basis  of  any 

desired  length  of  instrument.      The  theory  of  the  construction  of 

Christen's  instrument  may  be  shown  by  Fig.  52.     When  used  as 

above  described,  two  pairs  of  similar  triangles  are  formed:  ABC, 

bcXDC  bcXDC 

and  Abe:   ADC,  and  Ade,  in  which  BC  = and  de= . 

dc  BC 

With  a  known  value  of  DC  and  be,  dc  may  be  determined  for  all 

different  heights  which  are  likely  to  be  required.     Thus  it  may  be 

assumed  that  it  would  not  be  necessary  to  measure  trees  less  than 

20  feet  high,  so  that  the  lowest  graduation  on  the  instrument  is 

made  for  that  height.     To  find  the  proper   point   for   the  20-foot 

graduation  on  the  scale,  the  following  formula  was  used : 

BC     be  20     15  150 

DC  =  ^     °^     To^Jc    °^     ^^  =  ^  = 


=  5.7  inches. 


md'^ 


''^  ,  I  ■■V  tiiiw.w<s^> 


Fig.  51.— The 
Christen  hyp- 
someter.  Fig.  52. — Method  of  application  of  the  Christen  hypsometer. 


THE  TECHNIQUE  OF  MEASURING  HEIGHTS  245 

This  same  method  was  used  to  determine  the  value  of  dc  for  a  25-,  30-,  35-, 
40-foot  tree,  etc.,  up  to  150  feet,  and  the  proper  graduations  made  on  the  scale. 
The  scale  is  somewhat  more  easily  read  when  a  notch  is  made  at  each  graduation. 

The  instrument  is  light  and  compact,  and  with  practice  can  be  used  very  rapidly, 
provided  one  has  an  assistant  to  manage  the  10-foot  pole.  It  requires  no  measure- 
ment of  distance  from  the  tree,  and  the  height  is  obtained  by  one  observation. 
It  is  more  rapid  than  either  the  Faustmann  or  Weise  instrument. 

Its  disadvantages  are  that  it  requires  a  very  steady  and  practiced  hand  to  secure 
accuracy,  that  it  cannot  be  used  accurately  for  tall  trees,  and  that  it  is  not  adapted 
for  steady  work  because  it  is  extremely  tiresome  to  hold  the  arm  in  the  position 
required.  This  last  objection  may  be  overcome  by  using  a  staff  to  support  the 
hand. 

199.  The  Technique  of  Measuring  Heights.  In  rough  checks  for 
timber  cruising,  the  distances  used  in  obtaining  heights  are  usually- 
paced.  Care  must  of  course  be  taken  to  carefully  check  the  paced 
distance  desired  to  avoid  incurring  a  cumulative  error.  For  the  measure- 
ment of  average  trees,  depended  upon  to  secure  the  heights  of  stands, 
the  distance  should,  if  possible,  be  measured  with  the  tape.  This 
latter  method  is  the  only  one  permissible  in  measuring  the  heights 
of  trees  on  permanent  sample  plots. 

By  the  method  illustrated  by  the  Klaussner  hypsometer,  this  dis- 
tance is  measured  along  the  ground  whether  the  slope  be  level,  gradual 
or  steep.  By  the  method  of  right  triangles  the  distance  must  be  meas- 
ured horizontally  to  the  bole  of  the  tree,  and  a  considerable  error  would 
be  incurred  in  measuring  it  along  the  sui'face  on  very  sloping  ground. 

Since  the  entire  basis  of  the  similar  triangles  used  assumes  that  the 
tree  which  forms  one  side  of  the  larger  triangle  stands  in  a  vertical 
position,  the  consequences  of  measuring  a  tree  which  leans  either  towards 
or  away  from  the  observer  are  very  serious  (Fig.  53). 

From  the  position  A,  the  distance  to  the  base  of  the  tree  is  AC. 
But  if  the  observer  sights  at  the  tip  of  the  tree  Bi  which  leans  towards 
him,  its  height,  when  compared  to  the  distance  AC  will  be  read  as  B'lC, 
an  error  of  +16  per  cent.  If  the  distance  is  measured  instead  to  the 
point  directly  below  the  tip  Bi  the  height  is  read  as  BiCi,  with  an  error 
of  —  2  per  cent.  Again,  if  the  tree  Bo  leans  away  from  the  observer, 
and  its  distance  is  measured  as  AC,  its  height  will  be  read  as  B'-iC  with 
an  error  of  — 16  per  cent,  but  if  this  distance  is  measured  to  the  point 
Co,  the  height  will  be  read  as  B2C2  with  an  error  of  —2  per  cent  as 
before.^ 

If  it  is  necessary  to  measure  leaning  trees,  this  can  be  done  by  taking 
a  position  at  right  angles  with  the  line  AC  in  Fig.  53,  or  at  right  angles 
with  the  vertical  plane  in  which  the  tree  lies.     The  ocular  measure- 

'  Some  New  Aspects  Regarding  the  Use  of  the  Forest  Service  Standard  Hyp- 
someter, Hermann  Krauch,  Journal  of  Forestry,  Vol.  XVI,  1918,  p.  772. 


246 


THE  MEASUREMENT  OF  STANDING  TREES 


/ 


/ 


ment  of  heights  largely  avoids  this  specific  error  since  the  eye 
allows  for  the  leaning  position  of  the  tree  while  the  instrument 
does  not. 

Where  total  heights  are  measured  to  the  tip  of  the  crown,  the 
greatest  accuracy  is  obtained  in  the  measurement  of  conical-crowned 
conifers.  Broad-  or  deliquescent-crowned  trees  are  difficult  to  measure 
accurately.  The  source  of  error  is  the  same  as  that  which  applies  to 
leaning  trees.  A  line  of  sight  AB,  in  order  to  be  directed  at  the  tip 
B,  must  penetrate  the  foliage  of  the  crown  while  if  directed  tangential- 

ly  to  the  edge 
of  this  crown, 
it  will  take 
the  position  of 
AB\.  The  error 
from  the  meas- 
urement of  broad- 
crowned  trees, 
unless  this  pre- 
caution is  ob- 
served, is  cumu- 
lative and  tends 
to  over-estimate 
their  heights. 

Merchantable 
heights  are  meas- 
ured  by  exactly 
the   same  princi- 
ples  as   are  ap- 
plied    to     total 
upon    broad-crowned    trees     may    be    obtained    more 
element   of  uncertainty  in   the   measurement  of   mer- 
is  not  height,   but   the  determination    of   the    point 
which    the   used    length  will    terminate,  that   is,  the 


/ 


/ 


y 


.#' 


./- 


Ci 


Co 


Fig.  53. — Errors  which  may  be  incurred  in  measuring  the 
height  of  a  leaning  tree.  To  avoid  error  the  measurement 
should  be  taken  at  right  angles  to  the  plane  in  which  the 
tree  falls. 


heights,    and 
exactly.     The 
chantable   bole 
on  the   bole    at 

merchantable  top  diameter  of  the  bole.  Merchantable  heights  may  be 
measured  in  16-foot  log  lengths  by  the  use  of  the  principle  in  Fig.  43. 
(Merritt  hypsometer,  §  195.)  This  same  principle  may  be  more  accu- 
rately applied  by  leaning  a  pole  of  known  length  against  the  tree  and 
then  noting  the  length  of  a  pencil  required  to  take  up  this  given  length  at 
the  distance  of  the  observer.  This  pencil  length  may  then  be  measured 
off  by  eye  on  the  remainder  of  the  tree  to  divide  it  up  into  logs. 

It  is  common  practice  amongst  timber  cruisers  to  measure  the 
total  or  merchantable  height  of  windfalls  as  a  check  on  ocular  timber 
estimating. 


MEASUREMENT  OF  UPPER  DIAMETERS.  ^  DENDROMETERS    247 


200.  The    Measurement    of    Upper    Diameters.     Dendrometers. 

Upper  diameters  of  standing  trees  must  be  measured,  first,  in  estimating 
timber  to  a  merchantable  top  diameter;  second,  to  determine  the  form 
quotient  of  the  tree,  where  form  classes  are  to  be  distinguished. 

In  timber  estimating,  ocular  methods  are  used  entirely,  and  the 
probable  upper  diameters  approximated  by  knowledge  of  rates  of  taper 
checked  by  the  measurement  of  diameters  on  the  boles  of  down  trees. 
But  for  the  measurements  required  to  determine  form  quotients,  it  is  not 
safe  to  depend  altogether  on  chance  windfalls,  nor  can  cutting  sample 
trees  be  resorted  to  on  account  of  the  time  and  expense  involved.  The 
eye  is  not  sufficiently  accurate  to  gage  diameters  at  upper  points,  hence 
these  measurements  for  form  quotient  must  be  taken  on  standing  trees 
by  instrumental  means. 

An  instrument  intended  to  measure  the  upper  diameters  of  stand- 
ing trees  is  termed  a  dendrom.eter. 

The  principle  of  the  dendrometer  is  that  of  similar  triangles;  but  in  this  case 
two  sets  of  triangles  are  used,  first,  those  required  in  determining  the  height  to  the 
point  to  be  measured, 
and  second,  those 
used  to  measure  the 
diameter  at  this  point 
by  comparison  with 
the  side  of  a  smaller 
triangle  on  the 
dendrometer.  These 
principles  are  illus- 
trated in  Fig.  54. 

In  determining  the 
form  quotient  for 
standing  timber, 
either  according  to 
Joason's  or  Schiffel's 
methods,  the  diam- 
eter at  the  middle 
point,  either  above 
D.B.H.  or  above  the  _^ 
stump  respectively,  ^ 
is  sought.  As  point- 
ed out,  the  absolute 
form  quotient  cannot 

be  determined  with  scientific  accuracy  from  measurements  taken  outside  the  bark 
or  on  standing  timber,  but  appro.ximate  results  can  be  obtained. 

The  triangles  whose  bases  are  respectively  B,  bi  and  60  are  similar,  and  the 
relation  between  B  and  either  61  or  bo  determines  the  diameter  at  B.  But  the 
points  61  and  62  are  not  the  same,  and  this  difference  distinguishes  two  different 
principles  used  in  constructing  dendrometers. 

When  the  distance  Ac  to  the  horizontal  scale  on  which  will  be  read  the  upper 
diameter  B,  is  fixed,  so  that  on  sighting  at  point  B  this  distance  coincides  with  62, 


54. — Principles  underlying    construction    of    dendrom- 
eters, as  illustrated  by  the  Biltmore  pachymeter. 


248  THE  MEASUREMENT  OF  STANDING  TREES 

as  it  does  on  most  dendrometers,  the  proportion  between  the  upper  diameter  B  and 
its  equivalent  C,  corresponding  to  c  on  the  instrument,  is  altered  since  the  side  ^46 
remains  of  the  same  length  and  coincides  with  Ab2  in  the  figure.  This  discrepancy 
increases  in  proportion  to  the  cotangent  of  the  angle  A  and  the  distance  read  on  the 
dendrometer  scale  at  62,  which  is  graduated  for  inches,  will  be  less  than  the  true 
diameter  B  by  just  the  amount  of  this  error.  The  use  of  all  dendrometers  built 
on  these  principles  requires  correction  by  a  table,  to  obtain  true  upper  diameter. 

This  difficulty  is  illustrated  by  a  dendrometer  attached  to  the  Barbow  cruising 
compass,  used  to  some  extent  on  the  Pacific  Coast.  The  dendrometer  on  this 
compass  was  a  brass  scale  1  inch  long,  finely  graduated  to  read  the  apparent  diameter 
in  inches  at  the  upper  end  of  the  desired  log,  when  held  exactly  1  foot  from  the 
eye  by  means  of  a  string.  But  the  true  diameter  had  then  to  be  looked  up  in  a 
table  furnished  with  the  compass.  The  correction  varied  with  the  angle  of  sight; 
that  is,  with  the  number  of  log  lengths  in  the  tree.  All  readings  were  made  at 
100  feet  from  base  of  tree. 

On  the  Pacific  Coast  a  second  plan  has  been  adopted,  that  of  making  the  length 
of  the  scale  6i  equal  to  the  diameter  B,  thus  substituting  two  parallel  lines  of  sight 
for  the  horizontal  triangles  shown,  and  reading  the  diameter  of  the  lower  side  of  a 
parallelogram  directly  in  terms  of  inches  of  diameter  at  B.  In  an  instrument 
invented  by  Judson  F.  Clark  and  C.  A.  Lyford,  a  telescopic  sight  moves  on  a  bar. 
In  one  invented  by  Donald  Bruce,  both  lines  of  sight  are  brought  into  the  same 
plane  by  means  of  two  reflecting  mirrors,  set  at  exact  angles  of  45  degrees. 

201.  The  Biltmore  Pachymeter.'  By  employing  the  second  principle,  in  which 
the  side  of  the  small  triangle  biC  remains  vertical,  the  diameter  indicated  at  bi 
on  the  hypsometer  remains  in  the  same  proportion  to  that  desired  at  B,  as  when 
the  reading  is  taken  at  position  C.  Since  the  point  opposite  c  may  be  taken  at 
the  base  of  the  tree,  regardless  of  whether  this  point  is  horizontally  opposite  the 
eye  or  above  or  below  it,  a  projection  of  the  diameter  B  upon  the  base  of  the  tree 
enables  it  to  be  directly  measured  on  the  tree,  or  on  a  scale  c  upon  the  instru- 
ment, graduated  for  the  distance  Ac.  This  principle  is  employed  by  an  instrument 
termed  the  "Biltmore  Pachymeter."  (Ref.  Forestry  Quarterly,  Vol.  IV,  1906, 
p.  8.)  A  slot,  the  two  edges  of  which  are  absolutely  parallel,  or  a  stick  or  cane 
of  which  the  same  is  true  is  suspended  in  a  vertical  position  in  front  of  the  eye. 
A  scale  marked  in  inches  is  held  by  an  assistant  tangentially  to  the  tree  trunk  at 
D.B.H.  The  diameter  at  any  desired  point  on  the  stem  is  obtained  by  finding  the 
distance  from  the  tree  at  which  the  diameter  of  the  slot  or  stick  exactly  obscures 
that  of  the  tree  at  the  desired  point,  when  the  width  corresponding  to  this  diam- 
eter will  be  indicated  by  the  intersections  of  these  edges  on  the  scale  below.  The 
instrument  and  its  projection  upon  the  tree  trunk  are  shown  in  Fig.  54. 

202.  The  d'Aboville  Method  for  Determining  Form  Quotients.  This  method 
depends  on  the  measurement  at  62,  but  is  simplified  by  using  a  horizontal  line  of 
sight  from  eye  to  tree,  and  an  angle  of  45  degrees  at  point  A,  in  which  case  the 
proportion  between  the  lines  AC  and  AB  in  Fig.  54  becomes  1.4,  and  the  diameter  at 
B  becomes  1.4^2.  To  make  this  measurement,  a  distance  is  found  which  is  just 
equal  to  the  length  of  the  bole  between  the  point  horizontally  opposite  the  eye,  as 
in  Fig.  54,  and  the  upper  point  to  be  measured. 

Substituting  d  and  D  for  diameter  at  |  height  and  D.B.H.  respectively,  the 

form  quotient  of  a  tree,  as  read  on  the  dendrometer,  is 

d 
/  =  -Xl,4. 

•  Pachymeter — an  instrument  for  measuring  small  thicknesses. — Century  Dic- 
tionary. 


THE  JONSON  FORM  POINT  METHOD  249 

The  instrument  consists  of  a  graduated  scale  or  straight-edge.  For  determining 
merely  the  form  quotient  the  actual  diameters  need  not  be  ascertained  but  only 
their  proportion  or  relation.  The  two  measurements  are  taken  by  eye,  holding  the 
horizontal  scale  at  arm's  length  (Ac  and  ^62)  for  each  reading.  The  principal 
error  to  be  guarded  against  is  failure  to  secure  the  horizontal  line  of  sight  and  the 
corresponding  distance,  which  will  result  in  correspondingly  large  errors  in  reading 
the  proportional  diameters.  Failure  to  select  the  right  point  on  the  tree,  provided 
a  definite  point  is  selected  and  the  method  otherwise  properly  applied,  incurs  only 
the  error  due  to  difference  in  taper  between  the  point  measured  and  the  point 
desired,  which  depends  on  rapidity  of  taper. 

This  simple  method  should  be  of  great  assistance  both  to  practical  woodsmen 
in  determining  upper  diameters,  and  to  foresters  desirous  of  testing  the  form  quotient 
of  trees  in  order  to  ascertain  the  appUcability  of  volume  tables  based  upon  principle 
of  form  factors. 

203.  The  Jonson  Form  Point  Method  of  Determining  Form  Classes.  In  con- 
nection with  his  studies  of  the  form  of  trees  and  form  quotients,  Tor  Jonson  has 
evolved  a  method  for  determining  the  form  class  of  standing  trees  without  the 
necessity  of  measuring  the  upper  diameter  or  the  form  quotient. 

This  method  consists  in  locating  a  point  on  the  stem  of  the  tree,  which  he  terms 
the  form  point.  The  percentage  relation  which  the  height  of  this  point  from  the 
stump  bears  to  the  total  height  of  the  tree,  he  claims,  bears  a  consistent  relation 
to  the  form  quotient,  and  by  means  of  a  table  showing  these  relations  the  form 
quotient  and  form  class  of  the  tree  may  be  determined. 

Mr.  Jonson  describes  the  method  as  follows: 

The  shape  and  position  of  the  crown  has  been  found  to  be  the  most  dependable 
and  useful  indication  of  different  tapers  and  form  classes.  This  is  connected  with 
the  bole's  function  to  carry  and  steady  the  crown,  especially  against  the  breaking 
forces  of  the  wind,  and  it  has  been  found  that  in  the  building  of  the  bole  only 
enough  material  is  used  to  make  it  equal  in  strength  to  the  force  of  the  winds.  It 
may  therefore  be  said  that  it  is  the  strength  of  the  winds  that  determines  the 
necessary  dimensions  of  the  trunk,  and  as  the  force  of  the  wind  is  generally  applied 
to  the  crown  of  the  tree,  it  will  be  found  that  its  weight,  shape  and  position  indirectly 
influence  the  size  and  taper  of  the  trunk. 

While  estimating,  the  D.B.H.  is  measured  with  caliper  and  the  taper  is  then 
determined  through  finding  by  ocular  means  the  form  point,  i.e.,  the  point  where 
the  pressure  of  the  wind  is  apparently  concentrated  which  is  usually  the  geomet- 
rical center  of  the  crown.  By  sighting  at  this  point  and  at  the  same  time  at  the 
base  and  tip  of  the  tree  over  a  stick,  approximately  30  cm.  long,  divided  into  10 
equal  parts  (Christen's  hypsometer),  the  height  of  the  form  point  can  be  easily 
found  expressed  in  per  cent  of  the  total  height.  This  form  point  can  then  be 
looked  up  in  the  table  giving  the  form  point  heights  which  are  characteristic  for 
each  form  class.  The  higher  the  crown  is  placed,  the  less  the  taper  and  the  more 
cyhndrical  the  form,  and  conversely,  the  lower  the  crown  extends,  the  more  rapid 
will  be  the  taper  and  the  poorer  the  form. 

WTien,  as  is  often  the  case,  the  estimating  is  based  on  diameter  outside  bark, 
the  difference  which  is  caused  by  variable  thickness  of  the  bark  must  be  taken 
into  consideration.  The  spruce,  fir  and  other  species  with  thin  even  bark  show 
no  difference  in  form  when  measured  inside  or  outside  bark,  for  which  reason  the 
given  normal  form  point  heights  give  the  form  with,  as  well  as  without,  the  bark 
for  these  trees. 

White  birch,  larch  and  others,  but  especially  the  pine,  show  great  reduction  in 
form  when  measui-ed  with  bark,  for  which  reason  the  form  quotient  outside  bark 


250 


THE  MEASUREMENT  OF  STANDING  TREES 


is  different  from  what  the  crown  normally  signifies.  On  this  account  special  tables 
have  been  made  up  for  use  with  outside  bark  measurements,  but,  as  the  Scotch  pine 
shows  many  different  types  of  bark,  four  tables  have  been  compiled  for  trees  whose 
bark  is  thin,  medium,  thick  and  very  thick. 

When  judging  the  location  of  the  form  point,  it  should  be  remembered  that  it 
is  at  the  base  of  the  branches  where  the  acting  forces  of  the  wind  are  transferred 
to  the  bole,  for  which  reason  deciduous  trees  with  branches  pointing  up  will  have 
the  form  point  not  in  the  center  of  the  crown  contour  but  as  much  lower  as  the 
bases  of  the  branches  lie  lower  than  the  foliage  on  which  the  wind  is  acting.  In 
estimating  trees  which  have  quickly  cleared  themselves  of  branches,  a  better  result 
will  be  obtained,  if  the  newly  shed  crown  be  imagined  reconstructed  before  the 
position  of  the  form  point  is  determined. 

Finally,  should  the  butt  sweUing  extend  so  high  as  to  influence  the  D.B.H., 
and  consequently  make  the  final  result  inaccurate,  it  will  be  satisfactory  for  prac- 
tical work  either  to  rovmd  the  diameter  off  downward  or  measure  the  diameter 
above  the  swelling;  for  scientific  work,  however,  the  form  class  should  be  lowered 
as  much  as  is  made  necessary  by  the  butt  swelling,  which  can  be  easily  found  through 
a  number  of  measurements  taken  above  and  below  B.H. 

In  extensive  timber  estimating  the  density  is  a  good  indication  of  the  general 
form  which  the  trees  ought  to  possess,  as  the  tree  grown  up  in  dense  stands  will 
have  a  clean  bole  and  high  crown,  while  on  the  contrary  the  tree  grown  in  the  open 
will  have  a  heavy,  low  crown  and  consequently  a  poor  bole  form. 


TABLE  XL 

Table  for  Determination  of  Form  Class  of  Trees  by  Means  of  Position  of 

Form  Point  ^ 


Height 

of 
tree 

in 
feet 


Form  Class 


0.50 


0.525 


0.55 


0.575 


0.60j0.625 


0.65 


;n  7nir 


0.675  0.7010.725 


0.7510.775 


0.80 


Form  point  height  in  per  cent  of  height  of  tree 


37.5 
1 35. 5 
'34.5 

34 

34 
34 
34 
34 


43.5 

47 

52 

57 

62 

69 

73 

79 

85 

92 

98 

40 

44 

49 

54 

59 

65 

70.5 

76.5 

82.5 

89 

95.5 

38 

43.5 

47.5 

52.5 

58 

63.5 

69 

75 

81 

87 

94 

38 

43 

47 

52 

57 

62 

68 

74.5 

80 

86 

93 

38 

42.5 

47 

52 

57 

62 

68 

74 

80 

86 

93 

38 

42 

47 

52 

57 

62 

68 

73.5 

80 

86 

92.5 

38 

42 

47 

52 

57 

62 

68 

73.5 

79.5 

86 

92 

38 

42 

47 

52 

57 

62 

68 

73 

79 

86 

92 

1  For  spruce  and  fir  in  Norway,  either  inside  or  outside  bark.  Adapted  from 
Mas.satabeller  for  Traduppskatnung.     Tor  Jonson,  Stockholm,  1918. 

The  prevailing  density  of  a  stand  causes  the  greater  number  of  the  trees  to  acquire 
a  certain  similarity  as  to  form,  and  only  a  very  small  number,  usually  the  smallest 
and  largest  trees,  differ  from  this  average  form  class.     Accordingly  it  is  often 


RULES  OF  THUMB  251 

204.  Rules  of  Thumb  for  Estimating  the  Contents  of  Standing  Trees. 

A  rule  of  thumb  represents  an  attempt  to  formulate  a  simple  rule  which 
can  be  memorized  and  by  the  use  of  which  the  contents  of  trees  of  any 
diameter  and  height  may  be  found.  Such  a  rule  would  enable  the 
cruiser  mentally  to  compute  the  volume  of  average  trees  without  looking 
them  up  in  a  table.  It  is  also  desired  as  a  substitute  for  a  universal 
volume  table  because  of  the  difficulty  of  finding  volmue  tables  for  the 
different  species. 

The  factors  of  variation  in  tree  form  are  exaggerated  by  application 
of  units  of  product  and  the  variation  in  board-foot  log  rules,  and  the 
further  differences  in  the  per  cent  of  total  contents  utilized  in  trees  of 
different  sizes  make  it  impossible  to  devise  rules  of  thumb  which  are 
as  accurate  as  good  volume  tables;  but  since  their  use  in  ocular  timber 
estimating  frequently  accompanies  methods  of  cruising  by  which  a 
close  degree  of  accuracy  is  not  attained,  a  slight  possibility  of  error 
in  application  is  not  considered  a  sufficient  drawback  to  offset  the 
advantage  of  simplicity.  They  are  especially  desired  in  judging  by 
eye  the  contents  of  single  trees. 

Rules  of  thumb  must  be  based  upon  either  the  cubic  or  board-foot  unit.  The 
simplest  forms  ignore  the  influence  of  height  and  are  therefore  inaccurate  except 
when  applied  to  trees  within  a  given  range  of  heights. 

The  effort  is  always  made  to  devise  rules  which  may  be  appUed  to  the  dimensions 
measured  by  the  eye;  that  is,  to  diameter  and  height.  Rules  which  require  the 
use  of  basal  area  call  for  tables. 

For  cubic  contents,  the  following  rules  of  thumb  will  serve  as  illustrations: 

1.  To  obtain  cubic  feet  multiply  the  basal  area  in  square  feet  by  the  height 
and  divide  by  2.  This  is  based  on  the  theory  that  the  cubic  form  factor  of  trees 
will  average  0.5  which  is  the  form  factor  for  a  paraboloid. 

2.  For  trees  averaging  80  to  100  feet  in  height,  with  a  form  factor  of  0.49,  the 
contents  in  cubic  feet  equals  the  radius  in  inches  squared  (B.  E.  Fernow).  For 
"average"  trees,  volume  in  cubic  feet  equals  one-fifth  of  the  diameter  squared 
(C.  A.  Schenck). 

Both  of  these  rules  of  thumb  are  good  only  for  trees  of  a  given  height  and  form 
factor.  They  are  similar  to  the  European  rule  of  thumb — volume  in  cubic  meters 
equals  the  diameter  squared  divided  by  1000.  In  this  rule,  D  is  measured  breast- 
high  in  centimeters.  This  rule  apphes  to  pine  30  meters  high,  beech,  oak  and 
spruce,  26  meters  high,  and  correction  factors  are  indicated  as  follows:  for 
each  additional  meter  of  length  above  or  below  these  heights,  for  pine,  a  3  per  cent 
correction;    for  beech,  5  per  cent;   for  spruce  and  fir,  3^  per  cent.     Hersche's  rule 

of  thumb  reads,  cubic  meters  =  D2 1 -  +  1  1,  using  meters.  This  applies  to  trees 
50  to  115  feet  in  height.  V^       / 

possible  to  estimate  the  whole  stand  in  the  same  form  class,  the  smaller  dimensions 
a  little  higher  and  the  larger  dimensions  somewhat  lower  than  the  average,  e.g., 
0.70  for  overtopped  trees,  0.675  for  intermediate  and  co-dominant  trees,  and  0.65 
for  dominant  trees  (§  171).  The  highest  and  lowest  form  classes  will  never  occur 
as  an  average,  but  only  for  .-ingle  trees. 


252  THE  MEASUREMENT  OF  STANDING  TREES 

Graves  gives  the  following  cubic  rule  of  thumb  for  white  pine; 

Square  the  breast-high  diameter  in  feet  and  multiply  by  30.  The  rule  gives 
approximately  correct  results  for  trees  10  to  14  inches  in  diameter  and  80  feet 
high,  16  to  20  inches  by  85  feet,  22  to  28  inches  by  90  feet,  and  30  to  36  inches  by 
95  feet.  Other  heights  require  a  correction  varying  between  5  and  6  per  cent, 
for  each  5  feet  of  length.  It  can  thus  be  seen  that  both  simplicity  and  accuracy  in 
these  rules  of  thumb  are  seldom  obtained  in  the  same  formula  without  considerable 
cumbersome  modification  and  it  would  seem  that  a  volume  table  could  be  referred 
to  almost  as  easily  and  give  as  accurate  results. 

The  use  of  rules  of  thumb  based  on  board  feet  is  primarily  caused  by  lack  of 
suitable  volume  tables.  This  is  illustrated  by  the  development  of  rules  of  thumb 
based  upon  the  Doyle  log  rule.  These  board-foot  rules  are  efforts  to  obtain  the 
total  board-foot  contents  of  the  trees  from  the  sum  of  the  contents  of  the  logs  which 
they  contain  and  were  usually  formulated  before  volume  tables  had  come  into  use. 

The  simplicity  of  the  formula  for  obtaining  the  contents  of  a  given  log  in  the 
Doyle  rule,  namely,  "subtract  4  inches  from  the  upper  diameter  inside  bark,  square 
the  remainder,  and  the  result  is  the  scaled  contents  of  a  log  16  feet  long"  (the  length 
used  in  estimating),  was  an  inducement  to  supplement  this  rule  so  as  to  obtain 
the  contents  of  the  average  log  in  a  given  tree.     There  are  two  rules  for  this. 

1.  Take  the  average  diameter  of  the  top  and  stump  inside  the  bark  for  the 
diameter  of  the  average  log.  Scale  this  and  multiply  by  the  number  of  16-foot 
logs  in  the  tree. 

2.  Multiply  the  diameter  at  breast-height  inside  the  bark  by  the  same  diameter 
minus  12.  Multiply  by  the  number  of  logs  in  the  tree.  This  gives  the  scale  of 
the  tree  (C.  A.  Schenck). 

Schenck  also  gives  a  rule  which  ignores  height,  as  follows:  For  "tall"  trees, 
volume  =  f  diameter  squared,  measured  at  breast-height. 

Efforts  to  formulate  general  rules  of  thumb,  not  based  on  the  Do3'le  rule  are 
illustrated  by  the  following  examples: 

1.  Subtract  60  from  the  square  of  the  estimated  diameter  at  the  middle  of  the 
merchantable  length  of  the  tree.  Multiply  by  0.8  and  the  result  is  the  contents 
in  board  feet  of  the  average  log  in  the  tree.  Multiply  by  the  number  of  16-foot 
logs  for  the  total  scale.     (Graves'  Mensuration,  p.  153.) 

2.  Average  the  base  diameter  of  the  tree  and  the  top  diameter  of  its  merchant- 
able timber.  Get  the  scale  of  a  log  of  that  diameter,  32  feet  long.  Multiply  by 
the  number  of  32-foot  logs  less  ^  log.     (Gary's  Manual  of  Northern  Woodsmen.) 

D'~XL 

3.  Board  feet  =  ^-—, 

60 

when  D  =  inches  and  L  =  feet. 

(A  formula  method  of  estimating  timVjer,  E.  I.  Terry,  Journal  of  Forestrj', 
Vol.  XVII,  No.  4,  p.  413.)  This  formula,  according  to  author,  requires  modification 
by  substitution  of  a  divisor  of 

70  for  trees  from  12  to  19  inches  D.B.H. 
60  for  trees  from  20  to  29  inches  D.B.H. 
55  for  trees  from  30  to  35  inches  D.B.H. 
50  for  all  trees  above  35  inches. 

4.  To  base  diameter,  add  one-half  of  base  diameter  and  divide  by  2;  multiply 
by  0.8,  square  and  divide  by  12.  The  result  is  the  number  of  feet  in  the  stick  per 
foot  of  its  length.  Three  to  5  per  cent  may  sometimes  be  added  for  contents  above 
the  point  stated. 


RULES  OF  THUMB  253 

There  are  two  steps  involved  in  these  rules  of  thumb  for  board  feet: 
First,  a  rule  or  formula  is  required,  which  gives  an  approximation  of  actual 
board-foot  contents  of  logs  of  different  sizes.     This  can  only  be  obtained  by  rules 
on  cubic  instead  of  board-foot  contents  (§39).     Taking  a  fixed  per  cent  of 

^0.6D\2 


the  contents  of  all  logs,  the  last  rule  above  quoted  reduces  to  I 1   . 

The  second  step  is  to  get  the  dimensions  of  an  average  log  in  a  tree,  thus  averaging 
large  and  small,  or  top,  butt  and  middle  logs  together.  Empirical  results  rather 
than  mathematical  soundness  has  u-sually  been  the  basis  of  all  such  rules  of  thumb. 

Practically  all  these  rules  of  thumb  for  board  feet  are  based  upon  the  log  unit, 
as  might  be  expected.  A  more  scientific  application  of  a  universal  rule  of  thumb 
is  that  devised  by  F.  R.  Mason  (Ref.  Rules  of  Thumb  for  Volume  Determination, 
Forestry  Quarterly,  Vol.  XIII,  1915,  p.  333).     This  rule  is  as  follows: 

5.  The  volume  of  a  tree  of  each  diameter  and  height  class  will  correspond 
closely  with  the  volume  as  obtained  by  averaging  the  scale  of  the  butt  and  top 
logs  and  multiplying  by  the  number  of  logs,  usmg  16  feet  as  the  standard  log  length. 

Mason  states  that  this  rule  has  been  in  use  by  Minnesota  cruisers.  Its  superior 
accuracy  is  based  upon  the  fact  that  it  conforms  to  the  form  quotient  of  the  tree 
as  well  as  to  its  diameter  and  height,  by  introducing  upper  diameters  at  two  points. 
For  Douglas  fir  this  rule  was  3  per  cent  below  actual  scale;  for  cedar,  above  24  inches, 
10  to  15  per  cent  high.  For  white  pine,  spruce,  yellow  pine,  larch,  lodgepole  pine 
and  fir,  average  results  were  within  5  or  6  per  cent  of  actual  volume  for  individual 
trees  of  all  sizes,  a  result  which  is  closer  than  niay  be  expected  in  the  use  of  average 
volume  tables  for  single  trees.  The  only  difference  between  this  rule  and  the  tally 
and  computation  of  each  log  in  the  tree  is  elimination  of  the  need  for  tallying  logs 
lying  between  butt  and  top.  The  size  of  the  top  log  is  constant  where  a  fixed  top 
diameter  is  used.  Mason  states  that  3^?^  is  the  approximate  board-foot  contents 
for  16-foot  logs  over  24  inches  in  diameter. 

6.  A  rule  given  by  J.  W.  Girard  is,  "add  6  inchas  to  the  D.B.H.,  divided  by  2 
and  use  this  result  as  the  diameter  for  the  average  log  in  the  tree.  Multiply  the 
scaled  volume  of  this  log  by  number  of  logs  for  the  tree  volume."  This  rule  holds 
good  for  white  pine  and  spruce  cut  to  6-inch  top  and  for  larch  cut  to  8-inch  top. 
For  Douglas  fir  cut  to  8-inch  top,  add  4  instead  of  6  inches.  For  lodgepole  cut  to 
6-inch  top,  add  5  inches.  For  yellow  pine  under  20  inches,  add  6  inches;  20  to  25 
inches,  add  8  inches;   26  inches  and  over,  add  10  inches. 

Any  rule  of  thumb  should  be  based  upon  the  log  rule  and  standard  of  utilization 
in  use.  Such  rules  are  largely  worked  out  as  a  matter  of  personal  efficiency  by 
individuals  and  should  be  tested  carefully  before  placing  too  much  rehance  upon 
them. 

References 

The  Biltmore  Stick  and  Its  Use  on  National  Forests,   A.  G.  Jackson,   Forestry 

Quarterly,  Vol.  IX,  1911,  p.  406. 
Notes  on  the  Biltmore  Stick,  Donald  Bruce,  Proc.  Soc.  Am.  Foresters,  Vol.  IX, 

1914,  p.  46. 
The  Biltmore  Stick  and  the  Point  of  Diameter  Measurements,  Donald  Bruce,  Proc. 

Soc.  Am.  Foresters,  Vol.  XI,  1916,  p.  226. 
A  Folding  Biltmore  Stick,  W.  B.  Barrows,  Journal  of  Forestry,  Vol.  XVI,  1918, 

p.  747. 
Relative  Accuracy  of  Cahpers  and  Steel  Tape,  Normal  W.  Sherer,  Proc,  Soc,  Am. 

Foresters,  Vol.  IX,  1914,  p.  102. 


254  THE  MEASUREMENT  OF  STANDING  TREES 

.\nother  Caliper  (Swedish  pole  and  hook  for  measuring  diameters  at  considerable 

height).     S.  T.  Dana,  Proc.  Soc.  Am.  Foresters,  Vol.  XI,  1916,  p.  337. 
Saving  Labor  in  Measuring  Heights,  S.  B.  Detwiler,  Forestry  Quarterly,  ^■ol.  XIII, 

1915,  p.  442. 
A  New  Hyp.someter,  H.  D.  Tiemann,  Forestry  Quarterly,  Vol.  II,  1904,  p.  145. 
Comparative   Test  of  the   Klaussner  and   Forest  Service  Standard   Hypsometers, 

Douglas  K.  Noyes,  Proc.  Soc.  Am.  Foresters,  Vol.  XI,  1916,  p.  417. 
Some  New  Aspects  Regarding  the  Use  of  the  Forest  Service  Standard  Plypsometer, 

Hermann  Krauch,  Journal  of  Forestry,  Vol.  XVI,  1918,  p.  772. 
A  Simple  H>T5Someter,  Vorkampff  Laue,  Forestry  Quarterly,  Vol.  Ill,  1905,  p.  195. 
A  New  Dendrometer,  Donald  Bruce,  University  of  California  Publications,  Vol.  Ill, 

No.  4,  Nov.,   1917,  pp.  55-<)l.     Review,  Journal  of  Forestry,  Vol.  XVI,  1918, 

p.  724. 
A  New  Dendrometer  or  Timber  Scale,  Judson  F.  Clark,  Forestry  Quarterly,  \o\.  XI, 

1913,  p.  467. 
The  Biltmore  Pachymeter,  Ralph  G.  Burton,  Forestry  Quarterly,  Vol.  IV,  1906,  p.  8. 
Determination  of  the  Middle  Diameter  of  Standing  Trees,  P.  d'Aboville.     Trans- 
lation, Journal  of  Forestry,  Vol.  XVII,  1919,  p.  802. 
Rules  of  Thumb  for  Volume  Determination,   F.   R.   Mason,   Forestry  Quarterly, 

Vol.  XIII,  1915,  p.  333. 
A  Home  Made  H\-psometer  (Winkler  tj-pe).     Construction   described   in   Farmers 

Bulletin  715,  1916,  p.  18. 


CHAPTER  XIX 

PRINCIPLES  UNDERLYING  THE  ESTIMATION  OF  STANDING 
TIMBER 

205.  Factors  Determining  the  Methods  Used  in  Timber  Estimating. 

There   are   five   basic   considerations  which   determine   the   conditions 
and  methods  to  be  used  in  estimating  timber.     These  are: 

1.  The  form  of  product  in  which  the  volume  of  the  timber  is  to 
be  estimated.  This  determines  the  unit  of  volume  to  be  used,  as  the 
piece  (poles,  railroad  ties),  the  board  foot  for  saw  timber,  and  the  cord 
for  bulk  products  (§§9-12). 

2.  The  economic  conditions,  customs  and  usages  governing  tht> 
business  of  logging  and  lumbering.  These  determine  the  basis  on 
which  standing  timber  is  to  be  sold  and  the  place  and  form  in  which 
it  is  to  be  measured.  The  three  considerations  which  affect  the  work 
are,  whether  the  basis  of  volume  measurements  is  to  be  the  contents 
of  logs  or  the  sawed  output  in  the  form  of  lumber,  what  log  rule  is  to 
be  used  in  scaling  the  logs,  and  the  practice  of  scaling  as  to  log  lengths, 
diameters  and  cull  as  affecting  the  scaled  contents  of  the  timber 
(§§  81-83). 

3.  The  character  of  the  demand  for  timber  products  and  the  result- 
ant closeness  of  utilization  of  the  trees  in  the  stand.  This  will  determine 
the  top  diameters  and  stump  heights  to  which  the  timber  must  be  esti- 
mated, and  the  minimum  D.B.H.  (diameter  limit)  of  trees  to  be  esti- 
mated as  part  of  the  merchantable  stand,  and  consequently  the  per  cent 
of  the  total  cubic  volume  of  the  stand  which  is  estimated  as  merchant- 
able (§23). 

4.  The  available  volume  tables,  their  reliability  and  basis  of  numbers, 
their  method  of  construction,  their  basis  of  diameter,  height  and  mer- 
chantable top  diameters  (§  124).     This  will  determine, 

(a)  Whether  to  dispense  with  a  volume  table  and  substitute  a 

log  rule,  tallying  the  contents  of  the  trees  in  the  form  of 
separate  logs  or  to  depend  upon  a  volume  table  for  entire 
trees. 

(b)  The  point  at  which  diameter  must  be  measured  in  timber 

estimated,  as  stump,  D.B.H. ,  or  top  of  first  log  inside 
bark. 

255 


256  ESTIMATION  OF  STANDING  TIMBER 

(c)  The   point   at  which   heights   are   taken — total   height   o  r 

merchantable  log  length. 

(d)  The  top  diameters  to  which  tree  must  be  estimated.    Diver- 

gence in  these  conditions  from  those  used  in  the  volume 
table  will  make  it  impossible  to  apply  the  same. 

5.  The  local  characteristics  of  the  timber  to  be  estimated  as  to  full- 
ness of  form  or  "  form  quotient,"  quality  and  defects.     This  determines, 

(a)  For  sound  trees,  the  applicability  of  existing  volume  tables 

without  modification  or  their  need  of  local  percentage 

corrections. 
(6)   For  the  defective  trees,  the  amount  of  deduction  for  defects 

and  losses  in  scale  to  be  made  from  the  standard  volume 

table. 

The  object  of  any  estimate  of  standing  timber  is  to  obtain  the  total 
volume  as  indicated  by  the  above  five  conditions  upon  the  entire  area 
of  a  specific  tract  of  land.     This  may  be  done  in  one  of  three  ways: 

By  direct  ocular  guess  or  appraisal. 

By  actual  estimate  or  measurement  of  the  volume  of  every  tree 

of  merchantable  size. 
By  measuring  or  estimating  a  part  of  the  timber  as  an  average 

of  the  whole. 

206.  Direct  Ocular  Estimate  of  Total  Volume  in  Stand.  The  direct 
estimation  or  guess  of  the  total  volume  of  a  tract  of  timber  can  have 
but  one  basis,  that  of  experience  in  cutting  tracts  of  similar  character. 
This  eliminates  all  doubtful  factors,  and  the  experience  thus  gained 
is  invaluable  as  a  standard  of  estimating. 

Skill  and  accuracy  in  this  method  depend  upon  the  uniformity  of 
the  stand,  and  the  ability  of  the  estimator  to  compare  this  uniform 
stand  with  those  of  similar  character  whose  yield  he  has  ascertained. 

As  the  area  of  timber  so  estimated  incr  ases,  its  variability  of 
stand  becomes  greater;  yet  the  necessity  for  obtaining  a  true  average 
of  these  variable  conditions  pers'sts.  Even  in  stands  as  large  as  40 
acres  it  becomes  very  difficult  even  with  the  closest  inspection  to  arrive 
at  the  average  stand  on  the  tract,  no  matter  how  skillful  the  cruiser  is 
for  smaller  and  more  uniform  areas.  With  increasing  size  of  area, 
accuracy  soon  becomes  utterly  impossible.  For  this  reason,  in  spite 
of  the  simplicity  of  the  plan  in  theory,  in  practice  cruisers  who  depend 
solely  upon  this  principle  are  apt  to  be  unreliable  and  inaccurate. 
Under  no  circumstances  can  this  method  be  applied  to  timber  with 
which  the  cruiser  is  unfamiliar.  It  therefore  limits  his  field  of  activity 
to  a  narrow  basis. 


ESTIMATING  A  PART  OF  THE  TIMBER 


257 


207.  Actual  Estimate  or  Measurement  of  the  Dimensions  of  Every 
Tree  of  Merchantable  Size.  This  is  known  as  a  100  per  cent  estimate 
and  differs  radically  from  the  total  ocular  estimate  of  stand  just 
described.  It  consists  of  recording  the  dimensions  of  each  log  on  the 
tract  in  case  no  volume  table  is  used,  or  with  a  volume  table,  the  dimen- 
sions of  every  tree  of  merchantable  size.  The  total  volume  is  then 
simply  a  matter  of  computation. 

The  trees  are  tallied  by  dots  and  lines,  in  blocks  of  ten,  as  indicated 
in  the  following  table,  which  shows  the  marks  corresponding  to  dif- 
ferent numbers: 


.1  n  n  0  M 


Species  -  Pine 


D.B.H. 

lloff 

2  logs 

2'/.IoKS 

3  logs 

etc. 

12 

13 

14 

.n 

15 

0 

16 

:  I 

r 

etc. 

-Method  of  tallying  trees  by  diameters 
and  log  lengths. 


When  diameter  alone  is  being  tallied,  a  single  column  giving  diameter 
classes  suffices  for  each  species.  Where  the  height,  either  total  or 
merchantable  is  also  recorded  for  each  tree  tallied,  each  species  will 
require  a  tally  similar  to 
that  shown  below. 

Where  several  species 
are  tallied  by  both  diameter 
and  height,  it  is  not  cus- 
tomary to  make  half-log 
divisions,  since  too  many 
columns  would  be  involved 
Where  the  top  diameter  of 
logs,  instead  of  D.B.H. ,  is  Fig.  55 
the  point  tallied,  the  same 
system  of  diameter  classes 

or  tallies  is  used.  It  is  possible  to  combine  this  tally  of  D.B.H.  for 
one  species  with  top  diameter  of  logs  inside  the  bark  for  others,  using 
the  same  horizontal  columns  for  diameter  in  each  case. 

208.  Estimating  a  Part  of  the  Timber  as  an  Average  of  the  Whole. 
Where  the  greatest  possible  accuracy  is  demanded,  it  is  obvious  that 
100  per  cent  of  the  trees  should  be  measured.  Only  in  extreme  cases 
can  this  be  done,  owing  to  the  excessive  cost.  The  process  of  measure- 
ment accomplishes  no  constructive  change  in  the  form  of  the  forest 
(§6)  as  does  logging  or  silviculture,  but  is  of  use  merely  in  the  orderly 
management  of  the  business  of  regulating  these  operations  as  to  location, 
quantity  and  time.  Efficiency  then  demands  the  reduction  of  the  cost 
of  obtaining  these  statistics  to  the  lowest  figure  which  will  suffice  for 
the  proper  conduct  of  the  business  and  avoid  loss  through  errors  in 
appraisals  of  quantities  and  values. 

With  timber  whose  average  value  per  tree  is  small,  the  cost  of  meas- 


258  ESTIMATION  OF  STANDING  TIMBER 

uring  each  tree  is  far  too  great  to  be  undertaken.  It  is  often  physically 
impossible  to  obtain  the  necessary  force  and  personnel  to  perform  the 
work  on  this  scale.  Finally,  the  time  required  is  too  long  since  the 
results  of  estimates,  especially  for  the  purpose  of  sale  are  usually  required 
within  a  limited  period.  For  these  reasons,  the  third  of  the  above 
methods,  by  which  the  principle  of  averages  is  utilized  as  a  means  of 
reducing  expense,  diminishing  the  number  of  persons  required  and 
shortening  the  time  demanded  for  completing  the  work,  is  almost 
universally  used  in  estimating  timber. 

The  use  of  this  principle  in  timber  estimating  does  not  differ  from 
that  applied  in  the  commercial  process  of  sampling  employed  in  mines 
or  in  grad'ng  wheat.  If  the  product  is  uniform,  a  single  sample  suffices, 
as  in  wheat,  but  if  variable,  as  in  ore,  far  greater  care  is  required  in 
order  that  the  samples  may  represent  the  average  value  for  the  entire 
body  to  be  tested.  The  advantage  in  timber  estimating  is  that  all 
of  the  timber  is  actually  visible  and  only  the  handicap  of  costs  and 
time  prevent  it  from  being  seen  and  measured. 

209.  The  Six  Classes  of  Averages  Employed  in  Timber  Estimating. 
There  are  six  classes  of  averages  employed  in  estimating  timber.  The 
first  three  differ  in  regard  to  the  methods  of  recording  the  dimensions 
of  trees.     These  methods  are  as  follows: 

1.  The  average  height  of  the  trees  of  each  separate  diameter  class 
is  obtained  For  this  purpose,  only  a  few  sample  heights  for  each 
separate  diameter  are  measured.  The  heights  so  measured  are  plotted 
on  cross-section  paper  on  which  diameter  is  the  determinate  variable 
plotted  on  the  horizontal  scale,  while  height  is  the  indeterminate  vari- 
able plotted  on  the  vertical  scale. 

An  illustration  of  a  curve  to  obtain  average  heights  based  on  diameter  is  shown 
in  Fig.  56.  The  trees  to  be  measured  for  height  must  be  selected  in  such  a  manner 
that  the  resultant  curve  will  give  the  true  average  heights  for  each  diameter  class 
for  the  entire  area  to  which  it  is  to  be  applied.  When  a  very  few  trees  are  taken, 
these  must  be  carefully  chosen  from  those  whose  crowns  are  of  average  height 
compared  with  the  remaining  stand.  This  is  best  accomplished  in  even-aged  stands. 
On  large  areas  and  in  many-aged  stands,  a  mechanical  distribution  of  trees  measured 
for  height  is  best,  in  order  to  secure  a  weighted  average  of  differences  caused  by 
variation  of  site  and  of  growth. 

In  plotting  the  data,  two  methods  are  shown.  By  the  first,  all  heights  are 
plotted  above  their  respective  diameters.  A  height  curve  may  thus  be  sketched 
by  eye  through  the  band  of  points  shown.  This  eliminates  mechanical  averaging. 
By  the  second  method,  the  average  height  is  calculated  for  the  trees  in  each  diameter 
class,  and  this  point  is  plotted  ® .  The  points  are  then  connected  by  straight 
lines,  their  weight  in  numbers  shown,  and  the  curve  drawn,  as  before,  guided  by 
the  original  data.^ 

'  In  the  first  system,  when  two  heights  fall  on  the  same  point,  the  number  is 
indicated  as  ^. 


AVERAGES  EMPLOYED  IN  TIMBER  ESTIMATING 


259 


A  combination  of  these  two  systems  may  be  used  as  follows:  First  plot  the 
points,  then  compute  the  mechanical  averages  from  the  plotted  data  by  using  the 
scale  as  follows:  For  the  9-inch  trees,  assume  the  40-foot  point  as  0.  The 
trees  are  then  entered  as  having  the  weights  0,  3,  S,  8;  total  19;  average  4.8  plotted 
as  5  above  the  40-foot  point,  or  an  average  height  of  45  feet.  This  method  com- 
bines the  advantage  of  visuahzing  the  data  to  indicate  abnormally  high  or  low 
trees,  with  a  slight  reduction  in  the  work  of  mechanical  averages. 

2.  Instead  of  tallying  the  diameters  of  all  the  trees,  they  are  merely 
counted,  but  a  certain  fixed  percentage  of  the  total  number  is  tallied 
for  diameter  (the  heights  are  either  tallied  individually  or  the  method 


70 

/ 

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il 

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f^ 

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<% 

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s 

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L^ 

30 

y 

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5        6        7        8        y       10       11       12      i;^       14       15      iQ      17       18       19 
D.B.H.  Inches 

Fig.  56. — Method  of  constructing  a  curve  of  height  based  on  diameter  at  B.H. 
White  Pine,  Milford,  Pike  Co.,  Pa. 


of  averages  described  above  is  applied).  The  volume  of  the  average 
tree  of  the  per  cent  tallied  is  used  to  find  the  average  volume  cf  the 
numbers  counted  but  not  measured. 

In  Southern  longleaf  pine,  it  is  possible  to  count  aU  of  the  trees  on  a  tract, 
and  to  tally  the  diameter  and  merchantable  height  of  one  tree  in  every  three  in 
such  a  way  that  the  trees  tallied  represent  the  mechanical  average  of  those  counted. 
When  the  volume  of  the  tallied  trees  is  computed,  it  represents  one-third  of  the 
volume  of  the  stand.  The  work  of  tallying  has  been  reduced  one-third  and  the 
accuracy  greatly  increased,  when  considered  with  reference  to  the  time  required  to 
complete  the  work. 

3.  None  of  the  trees  in  the  stand  is  tallied  for  either  diameter  or 
height.  The  trees  are  merely  counted  and  the  cruiser  then  decides 
upon  the  volume  which  will  be  contained  in  the  average  tree  of  the  stand. 
He  may  obtain  this  either  through  a  direct  guess  as  to  volume  or  through 


260  ESTIMATION  OF  STANDING  TIMBER 

the  selection  of  what  he  beUeves  to  be  a  tree  of  average  diameter  and 
height  whose  volume  he  then  ascertains.  There  are  two  modifications 
of  this  system,  dependent  upon  whether  the  unit  used  is  the  log  or 
the  tree.  When  the  log  unit  is  used,  the  cruiser  estimates  the  number 
of  logs  in  the  average  tree  and  the  contents  of  the  average  log  or  log 
run  (§  120). 

In  the  above  three  methods  of  averaging,  nothing  has  been  said 
about  the  question  of  area  covered.  The  averages  apply  to  that  portion 
of  the  area  on  which  the  timber  is  either  counted  or  in  addition  is  tallied 
for  dimensions.  This  may  be  100  per  cent  or  the  total  area.  Although 
it  may  not  be  possible  to  measure,  by  diameter  and  total  height,  each 
tree  on  the  entire  area,  yet  by  the  employment  of  one  of  these  three 
methods  of  averaging  the  contents,  all  of  the  trees  may  actually  be 
accounted  for. 

The  remaining  three  of  the  six  methods  of  employing  averages 
apply  to  tracts  whose  area  is  too  large  to  permit  of  100  per  cent  esti- 
mates, even  by  the  simplest  plan  of  counting  and  obtaining  the  average 
tree.  The  principle  here  is  to  estimate  the  stand  on  a  portion  of  the 
area  in  an  effort  to  derive  the  volume  of  the  stand  upon  the  remainder. 
The  systems  used  are  as  follows: 

4.  The  stand  per  acre  is  guessed  at  or  estimated  by  eye.  This  stand 
multiplied  by  the  area  in  acres  presumably  gives  the  total  stand  on  the 
tract.  This  is  merely  a  modification  of  the  method  of  total  ocular 
estimate,  in  which  the  problem  of  arriving  at  the  average  is  approached 
in  a  different  manner.  It  is  possible  for  a  skilled  estimator  to  guess 
closely  the  stand  on  a  given  acre,  but  the  difficulty  lies  in  either  finding 
a  specific  stand  whose  volume  per  acre  happens  to  agree  with  the  aver- 
age on  the  entire  tract  or  else  to  decide  from  the  inspection  of  given 
stands  how  much  the  actual  stand  per  acre  observed  on  specific  plots 
must  be  modified  in  order  to  obtain  the  true  average  for  the  entire 
tract  estimated.  The  probabilities  of  error  in  estimates  made  on  this 
basis  increase  with  the  size  and  diversity  of  the  stand  to  be  estimated. 

5.  The  dimensions  and  volume  of  the  trees  on  a  given  per  cent  of 
the  total  area  are  obtained  by  one  of  the  first  three  methods  and  the 
stand  thus  found  is  assumed  to  represent  the  average  stand  per  acre 
for  the  entire  tract.  This  requires,  first,  the  accurate  determination 
of  the  area  of  the  tract  and  of  the  area  covered  by  the  estimate,  and 
second,  the  location  of  this  latter  area  in  such  a  way  that  the  assumption 
that  it  represents  the  average  of  the  remainder  can  be  accepted  as 
approximately  correct. 

6.  The  same  principle  is  employed  as  described  under  5,  but  the 
assumption  that  the  per  cent  of  area  so  measured  will  give  an  accurate 
mechanical  average  applicable  to  the  remaining  tract  is  not  accepted. 
Instead,  the  remainder  of  the  area  is  inspected  by  the  method  of  ocular 


THE  CHOICE  OF  A  SYSTEM  FOR  TIMBER  ESTIMATING     261 

comparison.  None  of  the  trees  is  actually  measured  except  on  the 
per  cent  estimated.  Using  this  estimated  strip  as  a  standard,  the 
estimate  upon  the  remainder  is  taken  as  equaling,  exceeding  or  falling 
short  of  the  stand  per  acre  upon  the  estimated  strip,  and  its  volume 
is  obtained  by  applying  a  correction  to  this  estimated  stand  per  acre. 
210.  The  Choice  of  a  System  for  Timber  Estimating,  with  Relation 
to  Accuracy  of  Results.  All  systems  of  timber  estimating  involve  the 
choice,  first,  of  one  of  the  three  methods  for  determining  the  contents 
of  the  trees  and  second,  of  one  of  the  three  methods  of  covering  the  area. 
There  are  many  different  systems  of  timber  cruising,  involving  the 
possibility  of  an  endless  combination  of  these  six  elements  Each  of 
these  systems  represents  a  decision  as  to  the  per  cent  of  area  required 
to  get  the  average  stand  per  acre  for  the  total  area,  the  method  of  cover- 
ing the  area  to  obtain  this  per  cent,  and  the  question  as  to  acceptance 
or  modification  of  the  stand  per  acre  as  applicable  to  the  whole  tract; 
it  also  involves  the  further  reduction  in  the  work  of  measuring  dimen- 
sions to  get  the  volume  of  trees  by  substituting  averages  for  height, 
a  per  cent  of  total  tallies  for  total  tallies  and  average  volumes  for 
individual  volumes.  These  two  groups  of  factors  are  closely  inter- 
related. For  instance,  where  the  per  cent  of  area  covered  is  reduced 
to  a  low  figure,  the  area  which  is  actually  estimated  must  be  covered 
thoroughly  by  careful  measurement  of  distances  and  widths  of  strips, 
the  diameter  of  every  tree  should  be  measured  or  tallied,  and  each  tree 
may  be  tallied  for  height,  especially  if  merchantable  heights  are  used. 
Where,  on  the  other  hand,  all  of  the  area  is  covered,  it  may  be  sufficient 
merely  to  count  the  trees,  substituting  the  method  of  an  average  tree 
or  log  for  the  more  detailed  and  time-consuming  method  of  measuring 
each  diameter.  The  gain  in  accuracy  in  one  of  these  factors  may  be 
offset  against  possible  inaccuracy  in  another,  the  sum  of  the  factors 
being  determined  by  the  total  cost  of  the  method.  These  points  may 
be  briefly  summed  up  as  follows: 

Area — 

Full  estimate,  100  per  cent. 
As  modified  by  averages. 

Sample  plots  taken  as  the  average. 
A  given  per  cent  accepted  as  the  average. 

A  given  per  cent  estimated  as  a  basis  for  obtaining  the  remainder  by  compari- 
son and  correction. 
Trees- 
Full  estimate,  100  per  cent  tallied  for  both  diameters  and  height. 
As  modified  by  averages. 

Average  height  obtained  from  sample  measurements. 

Volurne  of  average  tree  obtained  from  tally  of  dimensions  of  a  fixed  per  cent 

of  the  total  stand. 
Volume  of  average  tree  obtained  by  jnpj)rction,  from  SMmple  tree,  or  average 
tree  on  sample  plots. 


262  ESTIMATION  OF  STANDING  TIMBER 

Both  the  degree  of  accuracy  obtained  and  the  expense  of  estimating 
the  timber  are  reduced: 

By  the  reduction  of  the  per  cent  of  area  covered. 

By  substituting  tree  counts  for  measurements  of  dimensions  and 
averages  for  totals. 

By  substituting  ocular  measurements  of  dimensions  for  instru- 
mental measurements. 

By  substituting  pacing  for  chained  or  measured  distances. 

As  an  offset  to  the  loss  of  absolute  accuracy  by  the  substitution  of 
these  laws  of  averages  and  reduction  of  detail,  the  relative  accuracy 
or  efficiency  of  the  application  of  the  cheaper  methods  can  be  enormously 
increased  by  the  development  of  technical  skill,  experience  and  judg- 
ment, so  much  so  that  the  old-time  timber  cruiser  depended  upon  these 
factors  both  for  his  reputation  and  the  reliability  of  his  estimates. 
This  relative  accuracy  is  increased: 

By  the  choice  of  methods  and  care  in  location  by  which  partial 
areas  are  secured  in  such  a  manner  as  to  insure  the  highest  probability 
of  average  volumes.  This  is  similar  to  the  methods  used  in  sampling 
ore. 

By  the  development  of  skill  and  accuracy  in  the  use  of  pacing 
and  in  the  use  of  the  eye  for  measuring  diameters,  heights  and  width 
of  strips  or  plots. 

By  the  ability  to  apply  the  methods  of  tallying  a  fixed  per  cent  of 
the  stands  or  selecting  average  trees  in  such  a  manner  that  the  true 
average  volume  of  the  total  number  or  count  is  obtained. 

By  painstaking  observance  of  obtainable  standards  of  accuracy  in 
the  use  of  instruments  for  measuring  distances,  diameters  and  heights, 
and  in  proper  record  or  tally. 

By  individual  training  and  ability  to  make  the  proper  discounts 
for  defects. 

By  the  careful  checking  of  the  reliability  of  volume  tables  used, 
and  the  correlation  of  field  methods  with  the  conditions  for  which  they 
were  constructed. 

Finally,  by  correlating  all  of  the  above  factors  with  the  actual  con- 
ditions of  the  tract  or  stand  to  be  estimated,  which  in  themselves  will 
determined  the  degree  of  accuracy  required  in  each  step  as  above 
outlined. 

211.  Relation  between  Size  of  Area  Units  and  Per  Cent  of  Area  to 
be  Estimated.  There  are  two  elements  to  l)e  considered  in  arriving 
at  accurate  averages  in  estimating  a  given  tract.  First,  the  problem 
of  distributing  the  samples  throughout  the  area  in  order  to  obtain  the 
greatest  probability  of  true  average;  second,  the  uniformity  of  the  stand 


SIZE  OF  AREA  AND  PER  CENT  OF  AREA  ESTIMATED         263 

itself  as  increasing  or  decreasing  the  probability  of  accuracy  for  a  given 
method  of  sampling. 

The  first  of  these  problems  is  influenced  b}^  the  size  of  the  tract. 
In  any  method  of  estimating  based  upon  measuring  a  part  of  the  area, 
the  system  employed  must  be  that  of  strips  or  plots  spaced  at  regular 
intervals.  Otherwise  the  element  of  judgment  in  selection  introduces 
a  difficult  factor  which  will  improve  the  average  obtained  only  when 
accompanied  by  considerable  individual  skill.  With  plots  or  strips 
at  fixed  intervals,  the  number  of  such  strips  depends  upon  the  dimensions 
of  the  tract. 

The  choice  between  plots  and  strips  does  not  affect  this  principle. 
Plots,  when  substituted  for  strips  and  taken  along  compass  courses  at 
regular  mechanical  intervals,  serve  to  reduce  the  per  cent  of  total 
area  covered.  Since  the  distribution  of  the  sample  areas  is  more  evenly 
diffused  on  the  basis  of  the  per  cent  covered,  by  plots,  than  it  is  by 
strips,  the  loss  in  accuracy  by  substituting  plots  for  strips  is  not  in 
proportion  to  the  reduction  in  per  cent  of  area  covered,  but  is  consider- 
ably less,  thus  resulting  in  a  material  saving  where  the  use  of  plots 
permits  of  the  reduction  in  size  of  crew  (§  224). 

The  size  of  the  separate  units  of  area  on  which  accurate  estimates 
are  desired — as  for  instance,  when  owners  require  the  estimates  sepa- 
rately by  "  forties  "  (§  8),  is  the  basis  for  determining  the  effect  of  the 
spacing  of  these  strips.  If  the  estimate  must  be  accurate  only  for  the 
entire  tract,  a  quite  different  problem  is  presented  from  that  when  the 
same  degree  of  accuracy  is  required  for  smaller  subdivisions.  Assuming 
that  the  tract  is  in  the  form  of  a  square,  the  coefficient  of  accuracy  bears 
a  close  relation  to  the  number  of  strips  run  across  this  area,  rather 
than  to  the  distance  between  these  strips.  This  may  be  expressed  as 
follows: 

The  per  cent  covered  by  strips  wiU  be  the  product  of  the  number 
of  strips  and  width  of  each  strip,  divided  by  width  of  the  area.  With 
strips  of  a  uniform  width,  e.g.,  8  rods  or  132  feet,  run  at  intervals  of 
i  mile,  the  per  cent  of  area  covered  is  A  or  10  per  cent,  whether  the  tract 
be  40  acres,  1  square  mile  or  25  square  miles.  But  the  probability  of 
accuracy  in  securing  an  average  stand  is  not  in  the  same  proportion 
for  each  tract,  but  increases  with  the  size  of  the  tract.  The  reason  is 
that,  regarded  as  a  unit,  the  larger  tract  is  more  uniformly  sampled, 
and  with  reference  to  its  total  area,  the  strips  or  plots  are  more 
thoroughly  distributed  than  on  the  smaller  areas.  The  relative  accu- 
racy is  m  proportion  to  the  distribution  of  the  sampled  or  estimated 
strips  with  respect  to  this  total  unit,  which  for  large  tracts  tends  to 
reduce  the  per  cent  of  area  required  to  obtain  a  given  standard  of  accu- 
racy. 


264 


ESTIMATION  OF  STANDING  TIMBER 


Standard  distances  between  strips  or  plots  are  80  rods,  or  once 
across  a  forty  for  very  extensive  work  of  low  accuracy;  40  rods,  or 
twice  across  a  forty  for  work  of  average  accuracy;  20  rods,  or  four 
times  across  a  forty  for  work  approaching  a  50  per  cent  estimate; 
10  rods,  or  eight  times  across  a  forty,  which  with  a  10-rod  strip 
permits  100  per  cent  of  the  timber  is  to  be  measured. 

The  first  problem  then,  in  estimating  a  tract,  is  to  decide  upon  the 
proper  per  cent  of  the  area  which  must  be  covered  to  secure  the  desired 
standard  of  accuracy,  and  this  per  cent  will  be  a  direct  function  of  the 
size  of  the  smallest  unit  of  area  upon  which  a  separate  estimate  is 
required  (Fig.  57). 


25  Square  Miles 


h  Sq.Mile 


1 — r 

I       I 
l_i 


1 !  i  i  i  J  i  1 

1 

ii 

11 

ii 

'  1 '  1 '  1 1 

liiiiil 

'  1 ' ' '  1 
'''I'll 

;  1  i  j  1 1  i 

ill 

iiii  i! 

1 1 1 1 1 1 1 

iliiiii, 

1 II 

Fig.  57. — Influence  of  size  of  tract  upon  probable  error  in  obtaining  average  volume 
per  acre,  by  running  strips  40  rods  apart  in  each  instance.  Dotted  lines 
indicate  location  of  strips. 


Narrow  strips  spaced  at  one  of  these  standard  intervals  are  commonly 
used  for  large  tracts.  Upon  small  tracts,  the  necessity  for  increasing 
the  per  cent  of  area  covered,  as  a  substitute  for  increasing  the  number 
of  strips  run,  takes  the  form  of  widening  the  strip.  This  is  usually 
accompanied  by  a  modification  of  the  method  of  tallying  the  trees 
and  the  substitution  of  a  count  for  the  measurement  of  every  diameter. 
For  small  areas  as  low  as  40  acres,  this  frequently  takes  the  form  of  a 
100  per  cent  estimate,  the  strips  being  so  arranged  that  they  cover  the 
entire  area,  and  where  the  value  of  the  timber  and  its  size  is  such  that 
accuracy  is  desired  for  each  forty,  100  per  cent  of  the  entire  tract  is 
covered,  no  matter  what  its  total  size. 

The  relations  between  the  distance  apart  of  strips  or  plots,  width 
or  size  of  these  strips  or  plots,  and  resultant  per  cent  of  area  covered, 
to  the  size  of  the  unit  of  area  to  be  estimated,  is  the  most  practical 


UNIFORMITY  OF  STAND  AS  AFFECTING  METHODS  265 

problem  of  timber  cruising  upon  whose  solution  depends  the  attain- 
ment of  the  desired  standard  of  efficiency  secured  by  properly  relating 
costs  to  accuracy  of  results. 

212.  Degree  of  Uniformity  of  Stand  as  Affecting  Methods  Employed. 
The  second  factor  affecting  the  probability  of  accuracy  in  obtaining 
the  average  stand  per  acre  is  the  character  of  the  stand  as  affecting  its 
uniformity.  Uniformity  depends,  first,  upon  the  range  of  sizes  both 
as  to  diameter  and  height  of  the  trees  which  compose  the  stand;  second, 
on  the  regularity  or  evenness  of  their  distribution  or  the  variation  in 
the  density  of  the  stand  over  the  area.  The  greater  the  extremes, 
both  in  sizes  and  density,  the  more  difficult  the  attainment  of  a  correct 
average  stand  by  a  measurement  of  a  part  of  the  area,  and  the  greater 
the  necessity  of  increasing  either  the  number  of  strips  or  the  per  cent 
of  area  covered  in  each  strip  to  get  a  larger  total  per  cent  of  area  in 
obtaining  the  average. 

Age  of  timber  increases  both  the  range  of  sizes  and  the  variation 
in  density.  Old  timber  is  never  as  evenly  distributed  as  a  young  stand, 
owing  to  the  progressive  losses  from  natural  causes.  Mixed  forests, 
composed  of  several  species,  are  more  difficult  to  average  than  pure 
forests  of  a  single  or  of  two  or  three  similar  species.  There  is  greater 
irregularity  both  in  size  and  distribution  in  the  mixed  forest.  The 
greatest  u-regularities  for  a  given  tract  are  caused  by  differences  in 
topography  and  soil,  or  site  conditions,  which  are  reflected  in  the  char- 
acter of  the  stand.  In  mountainous  topography,  the  entire  forest 
changes  from  bottom  to  lower  slope  and  from  lower  slope  to  upper  slope. 
In  more  level  topography,  the  type  changes  as  abruptly  and  completely 
on  the  basis  of  the  moisture  content  of  the  soil  from  swamp  to  drained 
bottom,  from  drained  bottom  to  dry  upland.  Any  system  of  timber 
estimating  must  be  planned  to  secure: 

1.  The  separation  of  areas  which  differ  radically  from  each  other, 
but  which  within  themselves  are  fairly  uniform.  These  areas  conform 
with  the  types  of  forest  cover. 

2.  An  arrangement  of  the  strips  such  as  to  secure  the  greatest  pos- 
sible accuracy  in  sampling,  which  is  done  by  crossing  these  variations 
of  density,  type  and  form,  at  right  angles  with  their  longest  dimen- 
sions of  area,  as  far  as  possible  (§§  219  and  228) 

The  degree  of  detail  and  cost  of  the  work  as  reflected  either  in  an 
increased  per  cent  of  area  or  number  of  strips  or  an  increased  per  cent 
of  trees  tallied  for  dimensions,  either  diameter  or  height,  will  thus  be 
increased  in  proportion  as 

The  size  of  the  unit  diminishes. 
The  size  of  the  timber  increases. 


266  ESTIMATION  OF  STANDING  TIMBER 

The  variety  of  the  timber  increases. 

The  topography  is  more  mountainous  or  varied,  resulting  in  a 

greater  diversity  of  types. 
The  number  of  products  required  increases. 

Finally  the  degree  of  accuracy  required,  other  things  being  equal, 
will  depend  upon  the  stumpage  value  of  the  products  to  be  estimated, 
as  influenced,  first,  by  the  character  of  the  timber  itself,  and  second, 
by  the  unit  price  of  the  product.  In  the  earlier  days  crude  and  inaccu- 
rate methods  of  timber  estimating  were  justified  by  the  low  price 
per  acre  and  per  thousand  feet  at  which  stumpage  changed  hands. 
With  record  stumpage  prices  running  up  to  S27  per  thousand  feet  for 
white  pine  in  state  auctions  in  Minnesota,  in  1920,  a  degree  of  accuracy 
is  justified  which  would  not  be  thought  of  by  old-time  timber  cruisers. 


CHAPTER  XX 
METHODS  OF  TIMBER  ESTIMATING 

213.  The  Importance  of  Area  Determination  in  Timber  Estimating. 
Except  in  a  few  instances  where  every  tree  on  a  tract  is  separately 
measured,  all  methods  of  timber  estimating  depend  upon  the  principle 
of  applying  the  results  obtained  on  part  of  an  area  to  the  entire  area, 
or  on  small  portions  of  an  area  to  larger  subdivisions.  Any  error  in 
determining  the  total  area  included  within  the  boundaries  of  a  tract, 
or  the  correct  area  of  any  subdivision  made  within  it,  will  incur  a  cor- 
responding error  in  applying  the  results  of  the  estimated  portion  to  the 
whole.  The  separation  of  timbered  from  non-timbered  areas  is  an 
example.  If  the  average  stand  of  the  timbered  portion  is  correctly 
found,  but  its  area  is  estimated  to  be  10  per  cent  greater  than  it  actually 
is,  an  error  of  plus  10  per  cent  is  incurred  in  the  estimate.  Correct 
determination  of  areas  of  the  tract  and  its  timbered  subdivisions  is 
the  first  consideration  in  the  field  work  of  timber  estimating  and  counts 
for  fully  half  in  the  total  scale  of  accuracy. 

The  first  essential  is  to  locate  and  determine  definitely  the  boundaries 
of  the  area  to  be  estimated.  Where  the  tract  lies  in  regions  subdivided 
by  a  rectangular  system  of  government  surveys  this  is  not  ordinarily 
difficult.  The  area  may  be  approximately  located  with  sufficient 
exactness  for  the  work.  Even  here  it  is  necessary  to  identify  the 
section  corners  and  sometimes  to  re-run  the  lines  if  time  permits.  In 
other  regions  where  the  land  surveys  follow  an  irregular  pattern,  the 
identification  of  the  corners  and  lines  is  best  accomplished  by  the  aid 
of  some  local  resident  who  is  familiar  with  these  bounds.  The  retrac- 
ing and  mapping  of  the  boundaries  of  a  property  is  an  essential  step 
in  management,  but  its  cost  is  not  properly  chargeable  against  the  item 
of  timber  estimating  alone. 

If  methods  are  used  by  which  100  per  cent  of  the  timber  is  estimated, 
the  total  stand  can  be  obtained  independent  of  the  actual  area  or  shape 
of  the  tract  provided  only  that  all  of  the  trees  upon  it  are  counted  and 
their  contents  determined.  When  for  a  100  per  cent  estimate  is  sub- 
stituted an  estimate  covering  only  a  part  of  the  tract,  the  cruiser  requires 
a  knowledge  of  its  shape  and  size.  In  the  rectangular  system  of  surveys 
most  of  the  subdivisions  are  square  and  the  smallest  unit  commonly 

267 


268  METHODS  OF  TIMBER  ESTIMATING 

used  contains  40  acres.  Even  here  fractional  lots  lying  along  the  north 
and  west  boundaries  of  a  township  or  adjoining  meandered  streams 
and  lakes  call  for  a  plot  which  shows  their  dimensions.  With  these 
rectangular  areas  it  is  a  simple  matter  to  obtain  a  definite  per  cent  of 
the  total  by  running  strips  of  a  given  width. 

On  irregular  tracts,  a  map  showing  the  boundaries  and  area  is 
required  to  enable  the  cruiser  to  determine,  first,  in  what  direction  and 
relation  to  lay  out  his  lines  or  strips,  and  second,  to  compute  the  exact 
per  cent  of  the  total.  This  desired  per  cent  is  approximated  and  the 
exact  relation  secured  is  determined  after  the  lines  are  run. 

214.  The  Forest  Survey  as  Distinguished  from  Timber  Estimating. 
Timber  estimating  may  be  undertaken  for  the  sole  purpose  of  determin- 
ing the  volume  of  timber  on  a  tract,  but  as  commonly  carried  out,  this 
requires  the  running  of  numerous  definitely  located  compass  courses, 
gridironing  the  area,  which  gives  an  opportunity  for  the  collection 
of  a  large  amount  of  additional  data  required  in  its  permanent  manage- 
ment and  in  the  logging  of  the  area.  The  collection  of  this  additional 
data,  together  with  the  timber  estimate,  constitute  what  is  termed  a 
forest  survey.  Even  the  crudest  work  of  timber  cruisers  embraces 
some  elements  of  a  forest  survey.     The  features  of  such  a  survey  are: 

1.  A  map  showing  the  topography  of  the  area  either  by  hachures 
or  contours,  giving  streams  and  ridges  and  other  important  features 
which  influence  logging  and  management. 

2.  A  map  showing  the  character  of  the  forest  cover,  classified  as  to 

(a)  Timber  types,  corresponding  with  divisions  made  in  the 
stand  in  timber  estimating  and  showing  blank  areas,  such 
as  water,  barren,  cultivated  or  grass-land. 

(Jo)  Divisions  due  to  age  of  the  timber  such  as  burns,  re-stocked 
or  barren,  reproduction  or  immature  timl)er,  older  age 
classes. 

3.  Soil  maps,  locating  land  of  agricultural  value  and  land  fit  only 
for  forest  purposes. 

Under  timber  estimating  proper,  the  forest  survey  makes  an  inven- 
tory showing  both  the  quantity  and  quality  of  timber  by  different 
products,  grades  and  sizes  as  required  for  the  purpose  of  valuing  the 
tract  as  follows: 

1.  Quantity  or  volume. 

(a)  Separately  by  species. 

(6)   Separately  by  units  of  merchantable  volume,  as  board  feet, 

poles,  cords, 
(c)   Separately  by  character,  as  live  or  dead  timber,  sound  or 

cull,  and  giving  the  net  volume  after  deductions  for  cull. 


TIMBER  APPRAISAL  269 

2.  A  statement  of  amount  and  character  of  damage  present  due 
to  rot  and  other  defects  such  as  shake,  fire  damage  to  standing  timber, 
the  presence  of  insect  damage,  windfall. 

3.  The  quality  and  sizes  of  the  timber  under  the  items;  average 
diameters,  average  merchantable  length  in  logs,  form  of  bole  as  to 
straightness,  taper  and  clearness  and  finally  the  grades  present,  classi- 
fied either  as  log  grades  or  as  grades  of  lumber. 

The  third  class  of  data  is  that  needed  for  permanent  forest  manage- 
ment for  the  production  of  timber  by  growth.  These  data  are  fre- 
quently omitted  or  overlooked  in  a  timber  survey,  first,  by  old  cruisers 
who  have  not  been  trained  to  collect  them;  second,  by  foresters  who 
have  failed  to  formulate  a  definite  plan  for  their  proper  collection  in 
anticipation  of  the  need  for  its  use.     These  data  fall  under: 

1.  Age  classes  in  the  merchantable  timber,  either  by  area  (maps), 
or  by  size  or  diameter  (stand  tables  of  diameter  classes),  or  both. 

2.  Age  classes  in  immature  timber  either  by  areas  as  mapped,  by 
per  cent  of  area  occupied  or  by  tree  counts;  the  ages  and  sizes  of  these 
age  classes,  their  condition,  thrift  and  the  chances  of  survival. 

In  addition,  a  forest  survey  may  include  data  on  all  other  resources 
of  the  forest  such  as  forage  for  grazing,  while  under  timber  it  should 
determine  the  areas  included  within  different  site  classes  (§  227). 
Forest  surveys  include  all  data  of  every  kind  necessary  for  the  making 
of  a  working  plan  for  the  management  of  the  area  for  permanent  forest 
production. 

215.  Timber  Appraisal  as  Distinguished  from  Forest  Survey.  The 
forest  survey  as  described  above  is  the  preliminary  step  in  the  appraisal 
of  the  value  of  timber  stumpage.  This  appraisal  constitutes  a  separate 
operation,  although  the  survey  and  the  appraisal  are  so  closely  bound 
together  that  they  are  frequently  performed  by  the  same  man.  They 
must  not  be  confused,  however,  for  a  timber  appraisal  is  not  a  part  of 
Forest  Mensuration,  but  belongs  under  the  separate  subject.  Forest 
Valuation  (§5).  It  may  begin  where  the  timber  survey  leaves  off, 
using  the  data  acquired  by  this  survey.  Separate  parties  may  conduct 
the  timber  survey  and  the  timber  appraisal  with  satisfactory^  results. 

A  timber  appraisal  covers  the  following  points: 

1.  Logging  conditions  summarized  for  each  logging  unit,  under 
topogxaphy,  slopes,  surface,  rock,  brush  and  character  of  bottom  as 
affecting  logging.  Transportation  possibilities,  availability  of  streams 
for  log  driving,  routes  for  roads,  flume  or  railroads,  methods  best  adapted 
for  skidding  and  hauling  the  timber  and  the  costs  of  these  processes. 

2.  Costs  of  forestry  such  as  the  per  cent  of  the  stand  to  leave  for 
seed  or  second  cut,  the  cost  of  brush  disposal  and  other  protective 
measures. 


270  METHODS  OF  TIMBER  ESTIMATING 

3.  Economic  conditions,  markets  and  prices  for  lumber. 

4.  General  appraisal,  cost  of  milling,  cost  of  logging,  cost  of  trans- 
portation, profits  required. 

5.  Specific  appraisal,  the  direct  cost  of  logging  the  specific  body 
of  timber  and  the  resultant  stumpage  value  of  this  unit. 

A  clear-cut  distinction  between  the  work  of  timber  estimating  and 
of  timber  appraisal  will  prevent  the  mistake  so  often  made  of  burden- 
ing the  timber  estimating  crew  with  the  work  of  recording  in  great 
detail  items  of  cover,  surface,  brush,  etc.,  which  instead  should  be  sum- 
marized for  an  entire  unit  by  the  person  who  appraises  the  value  of  the 
timber  and  sizes  up  logging  conditions.  It  is  seldom  that  the  two  jobs 
can  be  effectively  combined  in  the  same  party  or  individual.  The 
work  of  timber  estimating  requires  routine  and  concentration  on  the 
details  of  the  job.  The  actual  appraisal,  even  if  the  same  party  makes 
it,  should  follow  rather  than  accompany  the  estimate  and  should  be 
based  first,  upon  the  data  on  topography  as  shown  by  the  map  and 
second,  upon  the  data  on  volumes  as  shown  in  the  estimate. 

216.  Forest  Surveying  as  a  Part  of  the  Forest  Survey.  A  forest 
survey  as  above  outlined  includes  the  work  of  forest  surveying  or  the 
determination  of  the  boundaries  and  area  and  the  mapping  of  the  topog- 
raphy of  a  forest  tract.  This  subject  is  not  a  part  of  Forest  Mensu- 
ration, but  must  be  treated  separately.  Since  the  gridironing  of  the 
tract  requires  the  measurement  of  distance  and  direction  and  the  plotting 
of  these  lines  will  give  the  framework  of  a  map,  it  follows  that  the  work 
of  making  a  topographic  map  which  may  employ  the  same  general 
methods  of  examination  for  the  area,  can  be  advantageously  combined 
with  the  work  of  timber  estimating.  Timber  cruisers  usually  prepare 
a  crude  map  showing  the  intersection  of  streams  and  the  position  of 
ridges  and  other  topographic  features  of  importance.  The  prepara- 
tion of  a  map  based  upon  basal  elevations  and  giving  contours  is  a 
development  of  the  timber  survey  introduced  by  foresters  and  adds 
greatly  to  the  efficiency  of  the  survey.  Bj-  combining  this  map-making 
with  the  entirely  separate  operation  of  estimating,  a  crew  of  two  men 
can  complete  both  operations  with  a  very  slight  increase  in  expense, 
not  comparable  with  the  cost  of  doing  each  piece  of  work  separately. 

At  the  same  time  the  preparation  of  the  type  or  timber-cover  map 
can  proceed,  and  upon  this  in  many  instances  depends  the  accuracy 
of  the  timber  estimate  itself  (§  225).^ 

1  The  detailed  methods  of  Forest  Surveying  employed  in  a  forest  survey  cannot 
be  discussed  in  a  text  on  Forest  Mensuration  without  exceeding  the  limits  of  the 
volume.  Any  summary  of  a  system  of  forest  survey  must  include  a  description 
of  the  methods  of  surveying  and  topographic  mapping  which  are  to  be  used.  The 
various  methods  of  survey  must  be  co-ordinated  with  the  methods  of  cruising  and 
with  the  cost  and  relative  accuracy  of  the  work  desired,  both  for  the  survey  and 
the  estimate. 


THE  CULL  FACTOR,  OR  DEDUCTIONS  FOR  DEFECTS  271 

217.  The  Cull  Factor,  or  Deductions  for  Defects.  Most  timber 
estimating  for  board-foot  contents  of  stands  is  based  on  the  amount 
which  the  logs  will  scale  (§  116).  Since  a  sound  scale  of  logs  requires 
deductions  for  defects  which  will  not  make  sound  boards,  the  timber 
estimator  must  make  the  same  deductions  in  the  standing  trees.  This 
deduction  from  total  sound  scale  is  independent  of  any  separation 
of  the  timber  into  grades  or  quality,  which  calls  for  additional  special 
attention.  Deductions  from  full  sound  scale  of  standing  timber  are 
made  either  by  the  log  unit  or  by  the  tree  unit  on  the  basis  of  the  judg- 
ment and  experience  of  the  cruiser.  Where  the  estimate  is  made  by 
logs,  only  sound  logs  are  tallied.  Culled  logs  are  dropped  from  the 
tally  altogether  and  trees  which  contain  defective  portions  are  scaled 
by  shortening  the  length  or  decreasing  the  size  of  the  logs  tallied  so 
as  to  represent  only  their  net  sound  volume.  Where  it  is  impossible 
or  inaccurate  to  use  this  method  of  omission,  a  straight  percentage 
deduction  for  cull  is  either  substituted  for  the  method  of  dropping 
or  reducing  logs  or  is  subtracted  after  all  of  the  clearly  visible  defect 
has  been  deducted. 

Tree  units  are  handled  in  the  same  manner.  Trees  so  defective 
that  they  are  practically  cull  are  not  tallied  at  all,  but  in  species  where 
few,  if  any,  trees  are  cull  and  the  defect  constitutes  a  portion  of  a  large 
per  cent  of  the  logs  and  is  not  easily  deducted,  cruisers  deduct  a  straight 
per  cent  from  the  total  sound  scale  of  the  trees  tallied.  Usually  a  com- 
bination of  these  methods  is  necessary  since  the  per  cent  deducted 
represents  more  accurately  the  loss  in  the  sound  scale  of  logs  actually 
siwed  and  taken  to  the  mill,  whUe  a  considerable  additional  cull  is 
found  in  logs  and  trees  not  utilized  at  all. 

Foresters,  in  making  a  tally  of  diameters  and  heights,  customarily 
tally  all  trees,  regardless  of  their  condition,  omitting  only  dead  timber 
which  is  unmerchantable,  and  then  apply  to  the  total  volume  a  per- 
centage deduction  for  total  cull,  which  will  cover  both  that  portion 
left  in  the  woods  and  that  lost  in  sawing. 

218.  Total,  or  100  Per  Cent  Estimates.  To  completely  cover  a 
small  area,  it  is  only  necessary  to  avoid  duplicating  the  count  or  measure- 
ment of  the  individual  trees.  This  may  be  done  by  the  use  of  a  bark 
blazer  or  scratcher,  or  by  tagging  the  trees,  a  method  employed  in  India 
where  labor  is  cheap. 

Trees  may  be  given  a  light  ])ark  blaze.  In  working  over  a  tract 
in  this  manner,  the  blaze  is  placed  upon  the  same  side  of  all  trees,  facing 
the  direction  towards  which  the  measurement  is  proceeding.  Where 
topographic  features  are  present  on  small  areas,  duplication  may  be 
avoided  by  covering  sections  bounded  by  these  natural  features  without 
the  necessity  of  spotting  the  trees. 


272  METHODS  OF  TIMBER  ESTIMATING 

On  larger  areas,  where  it  would  be  impossible  to  keep  track  of  the 
individual  trees,  parallel  strips  may  be  run.  The  trees  on  the  outer 
edge  of  a  strip  can  be  blazed  facing  the  strip  which  has  not  yet  been 
measured,  and  in  this  way  the  entire  tract  covered  with  a  minimum 
of  effort.  In  dense  swamps  men  may  be  employed  to  hew  parallel 
lanes  through  the  underbrush;  the  cruiser  then  estimates  all  trees 
between  these  lanes. 

It  is  possible  to  dispense  with  all  methods  of  marking  the  trees 
provided  sufficient  care  is  taken,  first,  in  running  the  strips  accurately 
as  to  direction  so  that  they  lie  parallel  and  at  fixed  distances  apart, 
and  second,  by  estimating  or  measuring  the  trees  on  strips  so  placed 
that  they  cover  the  entire  area;  i.e.,  strips  whose  borders  are  contiguous. 
There  is  danger  of  overlapping  or  duplication  by  this  method,  and  if 
it  is  the  intention  to  run  a  100  per  cent  estimate,  a  slightly  greater 
accuracy  can  be  insured  by  blazing.  This  ocular  method,  however, 
is  commonly  employed  as  a  substitute  for  blazing. 

A  modification  of  this  method  of  completely  covering  the  area  by 
strips,  is  the  laying  out  of  rectangular  plots  whose  dimensions  are  such 
as  to  cover  the  area  without  overlapping.  These  plots  are  estimated 
consecutively  and  may  be  of  any  convenient  width  and  length.  As 
an  example,  a  method  given  in  Graves'  Mensuration,  page  196,  consists 
in  laying  out  two  tiers  of  plots,  each  40  rods  wide  and  16  rods  across. 
Ten  of  these  plots  give  the  area  of  40  acres.  The  cruiser  proceeds  20 
rods  from  the  corner  of  the  forty,  and  then  crosses  the  center  of  the 
first  tier  of  five  plots,  returning  through  the  center  of  the  second  tier. 

To  get  the  contents  of  the  trees  on  areas  100  per  cent  of  which  is 
estimated,  the  following  systems  may  be  used: 

1.  Tally  the  merchantable  contents  of  each  tree  directly.  This 
is  estimated  by  eye,  or  from  a  universal  volume  table  which  may  be 
printed  on  a  Biltmore  stick,  or  any  other  convenient  form. 

2.  Tally  the  upper  diameter,  inside  bark,  of  each  log  in  the  tree, 
or  tally  the  upper  diameter  of  the  butt  log  and  top  log  (see  Rule  of 
Thumb  by  F.  R.  Mason,  §  204) .  The  contents  are  then  computed 
from  a  log  rule. 

3.  Tally  the  diameter  and  merchantable  height  in  16-  or  32-foot 
logs  or  half-logs  of  every  tree.  The  contents  are  then  computed  from 
a  volume  table  based  on  similar  dimensions. 

4.  Tally  the  diameter  only,  of  eveiy  tree,  either  by  eye  or  by  the 
use  of  calipers.  Measure,  by  a  hypsometer,  several  sample  trees  of 
each  diameter  to  give  a  curve  of  average  height  on  diameter.  The 
contents  of  the  trees  are  then  computed  from  a  volume  table  based 
on  diameter  and  height.  The  heights  measured  may  be  either  merchant- 
able or  total,  but  are  usually  the  latter.     In  this  method,  types  or  areas 


ESTIMATES  COVERING  PART  OF  TOTAL  AREA  273 

which  differ  in  average  height  and  diameter  must  be  estimated  sepa- 
rately. 

5.  Count  all  the  trees  on  the  area  and  tally  a  fixed  percentage  such 
as  1  in  either  3,  4  or  5,  whose  volumes  are  found  as  by  method  4  above. 

6.  Count  all  the  trees  on  the  area  and  determine  their  volume  by 
arriving  at  the  contents  of  an  average  tree.     This  may  be  done: 

By  guessing  at  the  average  contents. 

By  selecting  a  tree  of  average  diameter  and  height  and  determin- 
ing its  contents  by  the  use  of  volume  table. 

By  determining  the  number  of  logs  per  tree  or  average  mer- 
chantable height  expressed  in  logs,  thus  getting  the  total 
number  of  logs  on  the  area  and  then  guessing  at  the  con- 
tents of  the  average  log  or  number  of  logs  per  thousand. 

Method  6  may  be  applied  to  all  of  the  timber  considered  as  one 
class,  or  the  timber  may  be  separated  into  two  or  possibly  three  dif- 
ferent classes,  corresponding  with  marked  differences  in  size  and  char- 
acter. 

219.  Estimates  Covering  a  Part  of  the  Total  Area.  The  Strip 
Method.  There  are  two  methods  generally  employed  to  estimate  a 
portion  of  the  area,  the  strip  method  and  the  plot  method.  The  strip 
method  adopts  the  principle  of  endeavoring  to  obtain  the  average 
stand  per  acre  for  the  whole  area,  from  the  portion  estimated  by  the 
running  of  strips  parallel  or  in  a  given  direction  and  spaced  at  mechanic- 
ally regular  intervals.  By  this  means  it  is  sought  to  eliminate  judg- 
ment or  choice  in  the  obtaining  of  the  required  average. 

This  average  is  still  further  improved  by  the  choice  of  direction  of 
running  these  strips.  The  effect  of  differences  in  elevation  and  in  drain- 
age or  soil  moisture  is  to  produce  differences  in  the  density  and  character 
of  the  forest  corresponding  with  these  changes.  The  belts  of  forest 
which  have  comparatively  uniform  stands  usually  run  parallel  with 
contour  lines  and  at  right  angles  to  the  direction  of  slope.  A  basic 
principle  of  strip  estimating  is  therefore  to  cross  these  belts  at  right 
angles  or  proceed  directly  up  and  down  slopes  or  directly  across  the 
larger  stream  or  drainage  bottoms  as  far  as  possible,  and  to  avoid 
traveling  along  contour  lines  or  bottoms  and  in  general  along  the  long 
axis  of  belts  of  timber.  If  this  fundamental  principle  is  neglected, 
very  large  errors  may  be  incurred  in  applying  the  average  estimate 
so  obtained  to  the  larger  area. 

In  rectangular  surveys,  it  is  customaiy  to  run  the  strips  in  one  of 
two  cardinal  directions,  and  the  choice  is  therefore  narrowed  down  to 
either  north  and  south,  or  east  and  west.  In  irregular  surveys,  or 
where  the  topography  is  so  mountainous  that  the  estimate  will  be  made 


274 


METHODS  OF  TIMBER  ESTIMATING 


by  topographic  blocks  and  units,  rather  than  by  forties  or  legal  sub- 
divisions, the  S3'stem  of  strips  will  he  planned  with  reference  to  base 
lines  run  along  the  main  bottoms  and  streams,  from  which,  at  regular 
intervals,  the  strips  will  be  run  directly  up  the  slopes  and  as  nearly 
parallel  to  each  other  as  possible.  The  strips  in  each  separate  unit 
may,  therefore,  have  a  different  direction. 

220.  Factors  Determining  the  Width  of  Strips.  The  standard  widths 
of  strips  used  in  timljcr  estimating  are  six  in  number  and  their  dimen- 
sions are  given  in  the  following  table: 

TABLE  XLI 
Relation  of  Width  and  Number  of  Strips  to  Area  Co\t:red 


w 

iDTH  OF  Strips 

Area  covered  by 

one  strip  per  forty 

acres  or  four  per 

mile. 

Strips  per  \  mile 
to  cover  entire 

1 

area. 

Feet 

Rods    1 

1 

Chains 

Per  cent 

Number 

33 

2      ! 

h 

2h 

40 

66 

4 

1 

5 

20 

110 

61 

If 

8^ 

12 

132 

8 

2 

10 

10 

165 

10 

2i 

121 

8 

330 

20 

5 

25 

4 

On  rectangular  surveys,  to  compute  this  per  cent  of  total  area 
covered  by  the  strips,  multiply  the  number  of  strips  run  per  forty 
or  one-fourth  mile  square,  by  the  width  of  the  strip  in  rods,  and  divide 
by  80  rods.  These  two  factors,  number  and  width  of  strips,  are  not 
reciprocals  since  each  has  a  distinct  function  to  perform.  The  number 
of  strips  per  forty  increases  directly  the  probability  of  accuracy 
in  securing  an  average  stand  or  proper  sampling  of  the  timber  on  the 
area  (§  211).  The  width  of  the  strip  affects  this  average  to  a  lesser 
degree.  Its  principal  function  is  to  enable  the  cruiser  to  determine 
accurately  the  dimensions  and  volume  of  the  trees  which  stand  upon 
the  strip  estimated,  and  the  factors  which  affect  his  ability  to  obtain 
this  accuracy  will  determine  the  width  of  strip  without  respect  to  its 
effect  upon  the  total  area  covered.  If  narrow  strips  must  be  run  in 
order  to  get  accurate  estimates  of  timl)er  on  the  strip,  and  it  is  necessary 
to  increase  the  per  cent  of  area,  the  number  of  strips  will  have  to  be 
increased  rather  than  the  width  of  the  strip. 

An  example  of  the  relations  between  these  two  factors  is  cited  by  Austin  Gary, 
Manual  for  Northern  Woodsmen,  where  a  system  on  the  Pacific  Coast  of  using  two 


FACTORS  DETERMINING  WIDTH  OF  STRIPS  275 

strips  per  forty,  each  10  rods  wide,  covering  25  per  cent  of  the  area  was  abandoned 
in  favor  of  the  use  of  a  narrower  strip  65  rods  wide  to  increase  the  accuracy  of  the 
estimate  on  the  strip.  The  number  of  strips  was  then  doubled,  or  four  strips  run 
per  forty,  and  the  total  per  cent  of  the  area  estimated  was  thus  increased  from 
25  per  cent  to  33|  per  cent.  If,  instead,  the  number  of  strips  had  been  kept  the 
same,  but  the  width  of  each  strip  increased  to  20  rods,  a  lesser  degree  of  accuracy 
would  have  been  attained  in  spite  of  an  increase  to  50  per  cent  of  the  area  covered. 

In  determining  the  number  of  strips  required  for  a  forest  survey, 
the  character  of  the  topographic  map  desired  must  be  considered  with 
reference  to  the  topography.  Lines  run  |-mile  apart  will  give  onlj'  a 
rough  scale  map  in  bold  mountainous  topography.  Lines  placed  at 
j-mile  intervals  in  mountainous  slopes  with  large  features,  are  sufficient 
for  an  accurate  topographic  map  with  a  large  contour  interval  of  from 
50  to  100  feet.  On  all  flat  or  gently  rolling  forested  slopes  with  no 
outlook,  cut  up  by  drainage  or  interspersed  with  swamps,  it  is  impos- 
sible to  make  an  accurate  topographic  map  with  proper  contour  interval 
of  from  10  to  20  feet  and  show  all  details  of  drainage  and  slope,  unless 
lines  are  run  at  |-mile  intervals,  but  this  interval  is  sufficient  for  all 
maps  on  the  ordinary  scale  of  from  2  to  4  inches  per  mile.  Only  for 
a  much  greater  detail  will  lines  be  required  at  less  than  "this  interval. 

The  influence  of  the  forest  cover  upon  the  number  of  strips  required 
for  accuracy  increases  with  the  two  factors,  density  of  the  forest  cover 
and  variation  of  the  timber,  whether  caused  either  b}'  age,  size  or  diver- 
sity of  species.  Finally,  the  increasing  value  of  the  timber  from  any 
cause,  whether  through  quality  or  unit  price,  will  require  an  increase 
in  the  per  cent  of  area  covered,  which  means  a  greater  number  and 
more  closely  spaced  strips. 

These  conditions  frequently  require  a  full  or  100  per  cent  estimate 
by  forties,  the  best  examples  of  which  are  the  heavy  stands  of  rapidly 
increasing  value  in  the  Pacific  Coast  States,  or  stands  of  large  mature 
hardwoods  with  great  variety  in  size  and  value. 

The  width  of  strips  is  determined  by  the  accuracy  with  which  this 
width  can  be  measured  by  the  eye  and  the  dimensions  of  all  the  trees 
standing  thereon  ascertained,  or  the  timber  upon  it  measured  and 
counted.  This  width  is  diminished  directly  by  the  amount  of  brush 
and  undergrowth  which  obstructs  the  vision.  In  brushy  country,  strips 
seldom  exceed  from  4  to  6|  rods.  The  width  of  a  strip  is  also  diminished 
by  deoreasing  size  and  increasing  number  of  trees  on  the  strip.  In 
young  timber,  with  many  stems  per  acre,  a  greater  degree  of  accuracy 
is  obtained  on  a  4-rod' strip  accurately  measured  and  counted  than 
upon  a  strip  of  twice  the  width.  Conversely,  open  and  large  timber 
with  fewer  and  more  scattered  trees  and  an  unobstructed  view  not 
only  permits  a  wider  strip  to  be  measured  accurately,  but  requires  an 


276  METHODS  OF  TIIMBER  ESTIMATING 

increase  in  the  per  cent  of  area,  which  is  easily  obtained  by  increasing 
the  width  of  the  strip  without  an  appreciable  increase  in  the  cost.  This 
is  independent  of  the  need  for  running  more  strips  per  acre,  by  which 
the  per  cent  is  still  further  increased.  With  unobstructed  vision,  a 
wide  strip  may  be  estimated  with  almost  as  great  accuracy  as  a  narrow 
strip,  since  the  error  may  be  in  proportion  to  the  total  width  without 
affecting  the  percentage  of  error  in  the  estimate. 

With  increasing  openness  and  irregularity  of  timber,  strips  may 
give  way  altogether  to  a  total  count  of  timber  on  an  entire  forty, 
since  no  system  of  partial  or  sample  estimates  can  be  depended  upon  to 
secure  an  average  or  a  correct  total. 

The  method  of  determining  the  volume  of  the  trees  on  the  strip 
affects  the  width  of  strip  which  can  be  used  accurately.  Where  trees 
are  counted,  without  measuring  the  diameter  of  each  tree,  nearly 
double  the  width  of  strip  can  be  used  because  trees  can  be  seen  for 
this  additional  distance  while  it  is  less  possible  to  judge  their  diameters 
accurately.  Upon  a  calipered  strip,  the  additional  width  sometimes 
slows  up  the  work  and  introduces  a  greater  per  cent  of  error. 

The  counting  of  trees  in  open  country  is  so  simple  a  matter  that 
cruisers  accustomed  to  estimating  such  species  as  longleaf  pine  in  the 
South  have  usually  abandoned  the  strip  method  altogether.  Guided 
by  the  compassman,  they  cross  a  forty  about  twice,  pursuing  a 
snake's  course  back  and  forth,  and  attempting  to  see  and  roughly  to 
count  all  of  the  trees  on  the  forty. 

221.  Method  of  Running  Strip  Surveys.  Record  of  Timber. 
Strips  are  universally  run  with  the  compass.  A  hand  compass  is  com- 
monly used  by  cruisers  working  in  dense,  swampy  or  brushy  country, 
as  it  is  more  quickly  read  and  increases  the  number  of  sights  possible 
without  delaying  the  work.  For  ordinary  accurate  surveying,  in  which 
a  topographic  map  is  made,  the  use  of  a  staff  compass  adds  to  the  accu- 
racy of  the  direction  of  the  strips,  and  is  commonly  employed  (Fig. 
58).  In  the  use  of  either  hand  or  staff  compasses,  it  is  a  great  advan- 
tage to  be  able  to  turn  off  the  declination  of  the  needle  on  a  movable 
arc  with  a  vernier  so  that  a  cardinal  direction  is  indicated  by  the  sights. 
This  is  especially  true  in  the  Pacific  Northwest,  where  variations  up  to 
25  degrees  are  encountered. 

The  size  of  the  field  party  for  strip  estimating  depends  upon  the 
methods  used  in  measuring  and  recording  the  timber.  Wliere  the 
diameters  of  each  tree  are  measured  either  with  the  calipers  or  Bilt- 
more  stick,  the  party  will  consist  of  three  or  four  men  to  best  advantage. 
One  man  runs  the  compass  and  makes  the  topographic  and  type  maps. 
A  second  man  tallies  the  diameters;  the  thjrd  and  fourth  work,  one 
on  each  side,  calipering  trees.     Heights  are  usually  taken  at  regular 


METHOD  OF  RUNNING  STRIP  SURVEYS 


277 


intervals  so  as  to  be  distributed  uniformly  over  the  area.  Consider- 
able errors  may  be  incurred  in  bunching  sample  heights  in  timber  which 
may  be  too  tall  or  too  short 
for  the  average  of  the  stand. 

Where  diameters  and  mer- 
chantable heights  are  meas- 
ured by  the  eye,  the  party  is 
usually  reduced  to  two  men, 
one  for  the  compass  and  map, 
the  other  to  record  the  dimen- 
sions of  the  trees  which  he 
estimates.  It  was  a  common 
practice  in  the  Lake  States 
in  earlier  days,  for  timber 
cruisers  to  work  alone  without 
the  assistance  of  a  compass- 
man.  The  system  of  counting 
timber  and  recording  merely 
the  average  dimensions  and 
volume  enabled  a  man  to  run 
his  own  compass,  keep  track 
of  his  paces,  and  at  the  same 
time  count  the  trees. 

The  record  kept  by  cruis- 
ers on  strip  estimating  con- 
sists  primarily   of  a  tally  of 

the  trees  by  diameter,  height,  or  volumes  direct;  second,  of  the 
cull,  per  cent;  third,  notes  on  damage  to  the  stand;  fourth, 
quahty  of  timber  and  grades;  fifth,  young  timber  and  reproduction; 
sixth,  soil  and  ground  cover.  A  report  or  summary  sheet  for  each  sepa- 
rate unit,  usually  by  forties,  is  worked  out.  The  following  headings 
are  submitted  as  samples  (p.  278) : 

In  the  Appalachian  region  upwards  of  twenty  species  and  a  variety  of  products 
may  be  estimated.  For  the  hardwoods,  volume  tables  based  upon  diameter  and 
merchantable  log  lengths  are  used.  It  has  been  found  necessary  to  have  available 
a  table  for  one-  and  two-log  trees  to  avoid  errors  in  inaccurately  applying  small  top 
diameters  for  these  trees  rather  than  the  actual  merchantable  top.  '  Cull  is  deducted 
from  each  tree  by  reducing  the  D.B.H.  or  number  of  logs.  An  additional  per  cent 
is  deducted  for  unseen  defects.  The  tally  is  coordinated  with  existing  volume 
tables  to  secure  a  record  of  lumber,  cordwood  (principally  acid  wood),  poles,  ties, 
posts,  or  other  products.     An  example  of  the  tally  form  used  is  shown  on  p.  279. 


Fig.  58. — Staff  compass. 


278 


METHODS  OF  TIMBER  ESTIMATING 


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280 


METHODS  OF  TIMBER  ESTIMATING 


REVERSE  SIDE  OF  BLANK 
Forest  types,  Lower  slope 
Age  classes,     1-60 
Condition  of  timber,     Immature 

Thrifty 95     per  cent 

Mature. .  .' 2    per  cent 

Decadent 3     per  cent 

Fire  killed. per  cent;    damaged,     5     per  cent 

Insect  killed per  cent ;   damaged,     -    per  cent 

Other  killed per  cent;   damaged,     2    per  cent 

Name  of  disease.     Bark  disease 

Species  affected,     Chestnut 

Quality  of  timber  (give  by  log  grade;  percentage  of  tall,  medium  or  .s7ior<  clear  boles; 
or  number  of  clear  logs  of  stated  minimum  length  and  diameter) : 

80%  tall;  15%  medium;  5%  short 


Logging  factors: 

Undergrowth;  light-medium-dense,      Light 

Windfall;  light-medium-dense.     None 

Bowlders  and  broken  rock;  numerous;  occasional;  absent.  Absent 

Other  factors.  Easy  gradient.     Logging  conditions  ideal  as   skid    and    wagon 
roads  can  be  constructed  anywhere 

Replacement:  Species  Per  cent 

No   replacement,   

Ground  one-third  stocked, 

Ground  two-thirds  stocked, 

Ground  fully  slocked.  Chestnut,   50%;    white,    5%,   red,   5%, 
black,   20%,  and  chestnut  oaks,   10%;    white,   1%, 
pitch,  2%,  and  scrub  pines,  2%;  gum,  2%;  sourwood, 
1%,  and  maple,  2% 100% 

The  stand  shows  an  absence  of  poplar  due  to  grazing 

Additional  Notes:  This  is  a  stand  which  was  cut  over  for  charcoal  during  the  war 
and  since  then  was  culled  for  chestnut  ties  and  poles.  Bark  infested  chestnuts 
should  be  cut  as  well  as  suppressed  chestnut  for  extractwood.  The  few  mature 
"wolf"  trees  left  from  former  cuttings  should  be  removed  as  well  as  some  of 
the  scarlet  and  black  oaks  where  the  stand  is  too  dense.  Rernoval  of  the 
latter  can  be  made  for  ties.  The  dead  and  down  timber  from  the  laps  in  the 
tie  and  pole  cuttings  should  be  removed  for  extractwood 


TYING  IN  THE  STRIPS.     THE  BASE  LINE  281 

Explanation  of  Blank,  by  Supervisor  J.  H.Fahrenbach. 

All  saw  timber  is  tallied  by  the  number  of  16-foot  logs  in  each  tree.  If  a  tree 
happens  to  have  odd  lengths  "  we  give  and  take." 

Under  chestnut  all  trees  to  be  removed  for  extract  wood  are  tallied  in  the  "  0  " 
column.  All  trees  to  be  left  are  tallied  in  the  one-log  column,  even  though  they 
are  not  large  enough  to  make  one  16-foot  log  as  is  the  case  in  trees  under  10  inches 
D.B.H.  Street  railway  ties  (6  by  6  inches  by  8  feet)  are  tallied  in  trees  which 
have  reached  their  maximum  value  for  hewn  ties.  Standard  gage  ties  are  usually 
sawed  in  saw  timber  operations,  and  are  tallied  as  saw  timber.  Poles  are  tallied 
by  diameter  class.  In  this  way  we  are  able  to  approximate  the  number  of  25-foot, 
30-foot,  35-foot,  etc.,  poles. 

Chestnut  oak  and  hemlock  trees,  suitable  for  bark  alone,  are  tallied  in  the  "  0  " 
column.  In  figuring  the  estimate  for  bark  the  number  of  trees  tallied  as  saw  timber 
must  also  be  included.  It  sometimes  happens  that  we  also  have  a  market  for  black 
oak  bark,  and  in  this  event  a  "  0  "  column  must  be  entered  under  mixed  oak. 

Poplar  and  scrub  pine  pulp  wood  are  entered  in  the  "0  "  column. 

We  class  black,  scarlet,  pin  and  Spanish  oak  under  mixed  oak.  If  a  "  0  "  column 
is  added,  it  is  understood  that  black-oak  bark  is  to  be  entered.  Under  mixed-oak 
ties  red-oak  ties  are  included. 

Pitch,  short-leaf  and  table-mountain  pine  are  tallied  under  yellow  pine. 

If  there  is  a  market  for  locust-tree  nails  they  are  tallied  in  the  one-  and  two-log 
columns  for  the  larger  locast  trees  and  the  smaller  trees  are  tallied  as  posts,  using 
as  a  basis  a  post  4  inches  in  diameter  and  7^  feet  long. 

Under  others  are  tallied  beech,  birch,  gum,  maple,  sourwood  and  sycamore. 

If  there  should  be  other  valuable  species  for  which  provision  has  not  been  made 
in  the  headings  the  diameter  and  number  of  logs  in  each  tree  are  given  at  the  bottom 
of  the  Form.     This  includes  walnut,  ash  and  wild  cherry. 

If  there  is  a  market  for  fuel  wood,  provision  must  be  made  for  a  "  0  "  column  for 
all  those  species  which  cannot  be  utilized  for  either  bark,  pulp  or  extract  wood. 
All  the  oaks  can  be  thrown  together  in  one  heading,  the  pine  in  one  heading  and  the 
remainder  of  the  species,  except  hickory,  in  another  heading. 

222.  Tying  in  the  Strips.  The  Base  Line.  In  laying  out  and 
recording  the  strips  run  in  estimating,  independent  of  the  question 
of  topographic  mapping,  it  is  necessary  to  tie  in  each  strip  to  a  known 
point  at  each  end,  so  that  its  position  and  the  error  incurred  in  running 
it  in  both  distance  and  direction  may  be  determined.  For  this 
purpose,  and  also  to  form  the  basis  of  a  map  when  one  is  constructed, 
a  base  line  is  first  surveyed  along  the  route  from  which  the  strip  will 
be  later  laid  out.  The  strip,  whether  rectangular  or  irregular  areas 
are  being  estimated,  will  start  as  nearly  at  right  angles  as  possible  from 
points  on  this  base  line,  and  will  either  be  tied  in  to  a  second  base  line 
approximately  parallel  to  the  first,  or  by  offsets  will  be  run  back  at  the 
proper  interval  and  tied  in  to  the  original  base  line. 

In  laying  out  this  base  line,  therefore,  stations  or  measurements 
are  established  at  the  exact  points  and  intervals  from  which  these  strips 
must  later  be  initiated  and  tied  in.  Methods  of  survey  and  establish- 
ment of  base  lines  fall  under  the  subject  of  Forest  Surveying.     The 


282  METHODS  OF  TIMBER  ESTIMATING 

base  line  is  a  primary  feature  of  the  forest  survey.  Where  a  land  survey 
exists  which  is  accurate  and  easily  traced,  or  where  such  a  survey  is 
retraced,  it  may  serve  as  a  base  line. 

Where  the  area  is  small,  and  a  survey  and  map  exists,  the  corners 
and  known  or  located  points  on  the  boundaries  of  the  tract  are  sub- 
stituted for  a  base  line  as  points  from  which  to  initiate  strip  surveys. 
The  same  rules  apply  as  to  the  necessity  of  tying  in  each  strip  on  its 
completion  to  some  known  point  on  the  map,  in  order  to  check  errors 
in  the  survey  which  would  affect  the  areas  determined. 

In  running  the  strip,  the  estimator  is  dependent  upon  the  compass- 
man  for  the  distances  from  which  the  areas  are  determined  and  the 
estimate  separated  by  40-acre  tracts.  Errors  in  measuring  this  dis- 
tance will  cause  the  cruiser  to  misplace  timber,  thus  altering  the  accuracy 
of  the  individual  estimates  per  forty.  Where  types  or  differences  in 
stand  are  separated  in  estimating,  the  distance  across  each  separate 
type,  as  kept  by  the  compassman,  will  determine  the  area  and  con- 
sequently the  accuracy  of  the  estimate  within  the  type.  If  errors  are 
incurred,  their  character  and  extent  is  revealed  by  tying  in  to  known 
points,  which  enables  the  construction  of  a  correct  map  and  the  correc- 
tion of  the  estimates. 

In  running  estimates  over  separate  forties,  it  is  customary  to  run 
strips  1  mile  in  length,  cruising  a  tier  of  4  forties  before  returning. 
Where  one  strip  per  forty  is  run,  the  estimate  for  the  forty  is  completed 
at  the  end  of  80  rods.  Where  two  or  more  strips  are  run  per  forty, 
the  tally  of  the  timber  on  each  forty  is  separated  for  each  strip  as  indi- 
.cated  to  the  cruiser  by  the  compassman,  and  is  not  completed  until 
the  last  strip  on  each  forty  is  run.  The  results  for  each  strip  on  the 
same  forty  are  usually  tallied  together  on  the  same  sheet,  and  care 
must  be  exercised  not  to  misplace  or  mix  up  these  tallies. 

223.  Systems  of  Strip  Estimating  in  Use.  Examples  of  systems  of 
estimating  in  which  the  various  factors  itemized  above  are  harmonized 
to  meet  a  given  set  of  conditions,  are  given  below: 

Forest  Service  Standard  Valtiation  Survey.  This  system  was  used  almost  uni- 
versally by  the  Forest  Service  and  with  minor  modifications  is  still  a  standard  method 
used  on  national  forests.     Its  characteristics  are: 

Width  of  strip 4  rods  or  1  chain 

Number  of  strips  per  forty 1  to  2 

Per  cent  of  area  estimated, 5  to  10 

Measurement  of  distances By  chain  or  tape 

Measurement  of  trees,  diameters By  calipers  or  Biltmore  stick  or  ocular 

Heights Sample  heights  by  hypsometer 

Forest  types Separated    and     coordinated    with     a\ciaj.,c 

heights 

Cull  factor Estimated  by  a  total  per  cent 

Corrections    from    strip     estimate    for 
average  stand None 


SYSTEMS  OF  STRIP  ESTIMATING  IN  USE  283 

In  this  system,  as  indicated  in  the  last  item,  no  effort  was  made  to  modify  the 
average  stand  per  acre  obtained  from  the  strip  in  order  to  get  a  more  correct  total  for 
the  area.  The  employment  of  inexperienced  men  made  necessary  the  use  of  instru- 
ments for  diameter  and  height  measurement,  and  the  rigid  elimination  of  the  element 
of  judgment  on  every  point  possible.  Where  the  unit  of  area  was  large,  from  1 
square  mile  up,  this  method  gave  excellent  results,  since  the  mechanical  average  for 
areas  of  this  size  is  quite  dependable  on  the  basis  of  a  5  to  10  per  cent  estimate. 
The  errors  possible  could  be  easily  avoided  by  conscientious  effort.  These  errors 
consisted  of  too  wide  or  narrow  a  strip,  diameters  measured  too  low,  average  heights 
measured  too  high,  dead  trees  calipered  for  live  ones.  When  applied  to  large  timber 
in  units  of  40  acres  or  less,  these  mechanical  results  cannot  be  depended  upon. 

Lake  States  Cruisers'  Method 

Width  of  strip 8  to  10  rods — 2  to  2^  chains 

Number  of  strips  per  forty 1  to  2 

Per  cent  of  area  estimated 10  to  25 

Measurement  of  distances By  pacing 

Measurement  of  trees Counted 

Heights Average  number  of  16-foot  logs  per  tree 

Volume From  number  of  logs  on  tract  and  log  run,  or 

contents  of  average  log 

Forest  types Timber  of  different  age  classes  and  quality 

separated 

Cull  factor Usually  by  per  cent  deduction  from  total  esti- 
mate 

Corrections    from    strip    estimate    for 

average  stand Close  inspection  of  remaining  area  and  modifi- 
cation of  average  whenever  necessary  to 
obtain  correct  total 

Of  late,  timber  cruisers  in  these  states  have  been  adopting  the  use  of  volume 
tables,  but  in  many  instances  these  tables  are  based  upon  stump  diameter  inside 
the  bark  which  makes  them  less  consistent  and  accurate  than  if  based  on  D.B.H. 
The  more  modern  cruisers  are  adopting  the  use  of  standard  volume  tables  constructed 
by  regular  methods  and  differentiated  by  D.B.H.  and  height. 

Southern  Timber  Cruisers'  Methods 

Width  of  strip A  strong  tendency  to  substitute  ocular  esti- 
mate, based  on  the  stand  per  acre,  for  the 
running  of  strips.  Great  carelessness  in 
methods  until  recently 

Measurement  of  distances Paced  by  a  compassman,  the  cruiser  usually 

riding  a  horse.  Consequently  estimates  fre- 
quently stopped  at  the  edges  of  swamps 

Measurement  of  trees Cruiser  gets  located  by  compassman,  but  does 

not  follow  the  strip.  Trees  are  counted  on 
acre  plots 

Volume  of  average  tree Guessed  at,  using  rule  of  thumb  based  on 

Doyle  rule.  Trees  on  entire  forty  may  be 
counted  to  check  results  of  plots  and  get 
reduction  factor 


284  METHODS  OF  TIMBER  ESTIMATING 

Forest  types Accuracy  of  the  better  class  of  cruisers  greatly 

increased  by  careful  elimination  of  blank 
areas  and  containing  net  area  of  timber  to 
which  reduction  factor  from  stand  per  acre 
is  applied  for  total 

Cull  factor Usually  neglected  on  account  of  deficiencies  in 

Doyle  scale 

Corrections    from    strip    estimate    for 

average  stand This  is  based  on  general  inspection  and  count- 
ing since  no  systematic  strips  are  run 

Many  Southern  cruisers  have  adopted  more  systematic  methods  of  late. 

Yale  Forest  School  Method  in  Southern  Pine. 

Width  of  strip 10  rods — 2|  chains 

Number  of  strips  per  forty 2 

Per  cent  of  area  estimated 25 

Measurement  of  distances By  pacing 

Measurement  of  trees Count  of  the  trees  on  the  strip,  tally  of  one- 
third  to  one-fifth  of  the  timber  by  mechan- 
ical selection  to  avoid  choice. 

Diameters Tallied  by  eye 

Merchantable  height Tallied  by  eye  in  16-foot  logs  and  half-logs  of 

all  trees  whose  diameters  are  tallied 

Volume  on  strip From  volume  table  for  trees  talhed  multiplied 

by  3,  4  or  5,  according  to  per  cent  talhed 

Forest  types Areas  not  stocked  with  merchantable  timber 

eliminated  by  mapping.  Net  area  of  timber 
obtained.  Types  not  usually  separate 
within  a  forty  except  on  the  map 

Cull  factor By  per  cent  of  total  estimate 

Correction  from  strip  estimate  for  aver- 
age stand Careful  inspection  at  stated  intervals  of  stand 

on   remainder   of   forty.     Comparison    by 

weighted  volumes  with    stand    estimated. 

^^'cighted  correction  factor  applied  to  area 

*  estimated    to    obtain    proper    stand    per 

forty 

Horseshoe  Method.  This  is  a  modification  of  the  strip  method,  by  which  two 
strips  are  practically  combined  in  one  by  running  a  horseshoe  or  angular  course 
through  the  forty  as  shown  in  Fig.  59.  This  results,  first,  in  a  saving  of  time,  cut- 
ting down  a  certain  amount  of  travel  from  one  strip  to  another;  second,  in  a  better 
inspection  of  the  timber  and,  it  is  thought,  in  a  better  average,  since  the  strips  run 
in  both  cardinal  directions.  This  method  was  employed  extensively  by  a  firm  of 
Southern  timber  cruisers,  who  used  a  10-rod  strip,  thus  running  25  per  cent  of  the 


Pacific  Coast  Method. 

Width  of  strip 10  rods,  or  2\  chains 

Number  of  strips  per  forty 4 

Per  cent  of  area  estimated 50 

Measurement  of  distances By  pacing 


METHODS  DEPENDENT  ON  THE  USE  OF  PLOTS 


285 


Measurement  of  trees The  volume  of  each  tree  recorded  directly, 

based  upon  the  universal  volume  tables 

Forest  types Not  necessary  to  regard  them 

Cull  factor Deductions    made    for    each    tree   when    its 

volume  is  ascertained 

Correction  from  strip  estimate  for  aver- 
age stand By  running  50  per  cent,  corrections  are  usually 

avoided.  Where  inspection  reveals  the 
necessity,  modifications  are  made  in  the 
total  estimate 

Separate  record  under  this  system  may  be  made  of  the  board-foot 
contents  and  of  other  products,  such  as  poles.  The  estimate  is  fre- 
quently increased 
to  100  per  cent. 

These  examples 
are  cited  merely  to 
show  the  various 
combinations  of  ele- 
ments which  go  to 
make  up  a  system 
of  timber  estimat- 
ing.    The  securing 

of  accuracy  consists      i 

in     adapting      the  Fig.  59 

number  and  width 

of     strips    to    the 

local     conditions    described    ! 

estimated    and,    second,    size 

estimated 


r 

-n 

r 

-1 

1 
1 
1 
1 

1 

L. 

-1 

Horseshoe  method  of  strip   estimating, 
of  compassman  shown  by  dotted  line. 


Route 


to  be 
to  be 
instru- 


s,  first,  character  of  timber 
of  the  smallest  unit  of  area 
The  details  of  measurement,  whether  by  eye  or 
ment,  for  distance  or  for  tree  dimensions,  must  be  coordinated  with 
the  volume  table  and  with  the  skill  and  personal  ability  of  the  individ- 
uals employed  in  the  work.  The  saving  in  time  by  the  substitution 
of  the  eye  and  of  ocular  judgment  requires  dependence  upon  personal 
skill.  Where  cruisers  with  sufficient  experience  are  unobtainable, 
accurate  results  may  still  be  obtained  by  mechanical  measurements, 
carefully  supervised  and  conscientiously  applied. 

224.  Methods  Dependent  on  the  Use  of  Plots  Systematically 
Spaced.  In  the  use  of  plots  in  timber  estimating,  the  method  employed 
depends  upon  whether  the  principle  of  mechanical  arrangement  or 
spacing  is  to  be  observed,  in  order  to  obtain  an  average  stand,  free 
from  the  element  of  personal  judgment,  or  whether  instead,  plots  are 
to  be  selected  by  the  use  of  judgment  in  an  effort  to  obtain  thereby 
an  average  stand  which  will  apply  to  the  area  as  a  whole.  By  the 
first  principle,  the  plot  method,  so-called,  is  merely  a  modification  of 


286 


METHODS  OF  TIMBER  ESTIMATING 


the  strip  method.  Compass  strips  are  run  at  the  usual  intervals, 
but  instead  of  a  continuous  belt  or  ribbon  of  area  being  covered,  this  is 
broken  or  separated  into  plots  at  fixed  or  stated  intervals  along  the  line. 

These  plots  may  be  rectangular,  but  the  use  of  such  plots  is  not 
common.  In  the  measurement  of  rectangular  plots,  a  crew  is  usually 
employed,  and  this  same  crew  can  probably  run  out  the  entire  strip 
with  better  results.  Rectangular  plots  for  the  measurement  of  young 
growth  and  reproduction,  which  is  desired  only  on  a  small  per  cent 
of  the  area,  are  frequently  used  in  conjunction  with  a  strip  for  the 
merchantable  timber. 

The  common  form  of  plots  is  circular  to  enable  one  man  to  work 
to  advantage  without  the  assistance  of  a  compassman.  By  dividing 
the  functions  of  pacing  and  compass  work  from  those  of  estimating 
and  recording  the  diameters  and  heights  of  timber,  the  mind  is  kept 
free  for  concentration  on  each  task  in  turn.  A  crew  of  two  men  is 
sometimes  used  for  circular  plot  estimating  with  the  same  advantage 
to  the  timber  cruiser,  who  can  inspect  the  stand  for  defect  and  quality 
between  the  estimation  of  the  volumes  of  his  plots.  The  coromon 
size  of  plots  is  as  follows: 

TABLE  XLII 
Sizes  of  Circular  Plots 


Size  of 
plot. 

Acres 

Radius. 
Feet 

Diameter 

Feet 

Rods 

h 

1 

59 

83 

118 

118 
166 
236 

7.15 
10.0 
14.3 

The  relation  of  these  plots  to  the  per  cent  of  area  covered  is  given 

below. 

TABLE  XLIII 
Relation  between  Plots  and  Area  Covered 


Size  of  plot. 

Shortest 
distance 
between 
centers. 

Rods 

Plots  for  \ 
mile  of 
strip 

Total  area 

included  in 

plots. 

Acres 

Per  Cent  of  40  Acres 
Included  in  Running 

Acres 

1  strip 

2  strips 

\ 
\ 

1 

8 
10 
16 

10 
8 
5 

2i 

4 

5 

6i 
10 
121 

12^ 

20 

25 

METHODS  DEPENDENT  ON  THE  USE  OF  PLOTS  287 

Great  care  must  be  taken  in  the  use  of  circular  plots  to  obtain  the 
width  of  the  plot  correctly.  An  error  in  this  factor  is  more  serious  than 
that  on  a  strip,  since  it  affects  the  entire  boundary.  The  same  principle 
as  to  size  and  number  of  plots  and  per  cent  of  area  covered  applies 
to  these  methods  as  to  strip  estimating.  In  dense  brush  and  with  small 
timber,  the  common  size  is  one-fourth  acre,  while  plots  1  acre  in  size 
are  required  for  old  and  large  trees.  The  amount  of  timber  on  each 
plot  is  obtained  by  the  use  of  the  same  variety  of  methods  as  for  strips. 

Examples.     Spruce  in  the  Northeast  on  large  tracts. 

Size  of  plot 5  acre 

Number  of  strips  per  forty 1 

Distance  between  plots  on  strip 20  rods — 5  chains 

Per  cent  of  area  covered 2^ 

Measurement  of  distances By  pacing 

Measurement  of  trees D.B.H.,  calipered  or  tallied  by  eye 

Heights A  few  sample  heights  taken  on  each  plot  for 

curve  of  height  on  diameter 

Types Separated  in  mapping 

Cull By  per  cent  applied  to  total  estimate 

Correction  of  estimates  to  get  average .  None 

Large  Timber  on  the  Pacific  Coast. 

Number  of  strips  per  forty 1  to  2 

Size  of  plots 1  acre 

Number  of  plots  per  strip 5 

Per  cent  of  area 12^  to  25 

Measurement  of  distance By  pacing 

Measurement  of  trees  on  plot Average  tree  selected  for  each  species.  Diam- 
eter at  stump  inside  bark  and  at  top 
measured.  Average  of  these  diameters 
taken  as  diameter  of  the  average  log 

Volume Obtained  by  rule  of  thumb   (§  214).     (Any 

of  the  three  standard  methods  for  obtaining 
the  contents  of  trees  on  a  plot  or  area  apply 
to  this  method.) 

Types Blank  areas  eliminated  and  stand  obtained  for 

average  acre 

Cull By  a  per  cent  of  the  total  estimate 

Correction  factor  to  the  estimate Obtained  by  general  observation  and  com- 
parison with  stands  on  the  plots 


CHAPTER  XXI 

METHODS   OF  IMPROVING  THE  ACCURACY   OF  TIMBER 
ESTIMATES 

225.  The  Use  of  Forest  Types  in  Estimating.  T\Tien  only  a  part 
of  the  area  of  a  tract  is  covered  in  estimating,  the  accuracy  of  the 
resultant  estimate  depends  upon  the  success  with  which  the  actual 
average  stand  per  acre  has  been  obtained.  Although  the  per  cent  of 
area  taken  has  been  properly  chosen  to  fit  the  topographic  conditions 
and  character  of  the  timber  and  although  the  measurement  of  the  timber 
upon  this  area  and  the  width  of  the  strips  has  been  accurately  carried 
out,  so  that  no  avoidable  error  remains  in  the  work  done,  yet  the  esti- 
mate may  stUl  be  in  error  by  the  failure  to  secure  the  same  proportion 
of  the  different  types  and  variations  of  stand  on  the  strips  as  exist  on 
the  area  as  a  whole.  On  account  of  the  prohibitive  expense  of  running 
a  sufficient  per  cent  of  the  area  to  get  this  average  mechanically,  a 
margin  of  error  in  timber  estimating  is  permitted,  and  is  gaged  by  the 
value  of  the  timber  and  the  purpose  of  the  estimate.  Any  modification 
which  will  secure  the  required  degree  of  accuracy  and  at  the  same  time 
avoid  incurring  an  um-easonable  expense  wUl  necessarily  become  a 
part  of  the  system  employed. 

The  more  uniform  the  stand  as  to  sizes  and  density  of  stocking,  the 
better  the  averages.  This  applies  to  the  use  of  all  six  of  the  classes  of 
averages  cited  in  §  209. 

For  the  purpose  of  securing  a  greater  degree  of  uniformity  in  the 
stand  on  those  subdivisions  of  total  area  to  which  the  estimates  obtained 
on  strips  or  plots  are  applied,  the  distinction  of  forest  cover  types  is 
indispensable.  A  forest  type  includes  all  stands  of  similar  character 
as  regards  composition  and  development  due  to  given  physical  and 
biological  factors,  by  which  they  may  be  differentiated  from  other 
groups  of  stands.  A  cover  type  is  the  forest  type  now  occupying  the 
ground,  whether  this  be  temporary  or  permanent.  Timber  estimating 
concerns  itself  only  with  the  existing  forest  cover. 

The  factors  which  are  reduced  to  greater  uniformity  by  the  sepa- 
ration of  forest  types  in  estimating  are  composition  of  stand  as  to  species, 
and  consequent  relative  per  cent  of  total  volume  of  stand  represented 
by  the  different  species,  a  vital  consideration  in  thnber  estimating.     This 

288 


THE  USE  OF  FOREST  TYPES  IN  ESTIMATING  289 

factor  has  an  influence  upon  the  total  volume  of  the  stand,  as  well  as 
its  average  height,  though  both  of  these  are  influenced  even  more  pro- 
foundly by  differences  in  quality  of  site  within  the  same  cover  type. 

These  differences  in  type  msiy  be  caused  by  altitude,  slope,  moist- 
ure and  depth  of  soil.  By  separating  the  total  into  sub-areas,  a  far 
greater  uniformity  of  size  and  density  of  the  timber  in  these  sub- 
divisions may  be  obtained,  first  by  securing  a  more  uniform  mixture 
of  species  in  the  per  cents  of  the  different  species  represented  in  the 
stand;  second,  by  reducing  differences  in  the  density  of  stocking  per 
acre;  third,  by  securing  more  uniform  sizes  both  in  height  and  diameter, 
and  a  smaller  range.  The  subdivision  of  an  area  into  a  number  of 
smaller  units  is  a  means  of  avoiding  the  necessity  for  securing  a  weighted 
average  of  these  factors  in  order  to  get  the  average  acre.  Doubling  the 
number  of  strips  would  probably  secure  the  same  result,  but  the  expense 
of  separation  of  the  estimate  into  two  or  more  types  is  much  less  than 
this  increase  in  field  work. 

The  only  increased  expense  of  separating  types  consists  of  the 
increase  in  computations  required  by  separating  the  areas  and  the 
precaution  required  in  changing  the  tally  sheet  on  entering  the  type. 
Proper  coordination  between  the  compassman  who  maps  the  area 
and  the  estimator  who  records  the  timber  is  necessary. 

Where  areas  as  small  as  40  acres  are  mapped  and  a  large  per  cent 
taken,  distinctions  between  the  two  types  of  timber  are  not  often  made 
by  old  woodsmen.  The  total  volume  of  each  species  is  obtained  with- 
out separate  computations  of  area. 

But  the  principle  of  type  separations  is  universally  applied  in  sepa- 
rating areas  which  do  not  contain  merchantable  timber  from  those  which 
do.  Blank  areas  caused  by  cultivation,  burns,  swamps,  or  unmerchant- 
able reproduction  must  be  subtracted  from  the  total  timbered  area 
under  any  system  which  permits  the  completion  of  a  cover  map.  The 
arbitrary  inclusion  of  these  unstocked  areas  makes  it  practically  impos- 
sible to  obtain  an  average  stand  on  the  remainder.  In  theory  the  same 
law  of  averages  applies  even  in  this  case  and  with  a  sufficient  number 
of  strips  which  cross  blank  areas  in  such  a  way  that  a  per  cent  of  the 
blanks  is  taken  as  the  merchantable  stand,  no  error  would  be  incurred 
in  the  average.  But  the  extreme  danger  of  obtaining  a  different  per 
cent  from  that  on  the  whole  tract,  and  the  comparative  simplicity 
of  mapping  out  these  blanks  to  obtain  net  timbered  area,  makes  this 
method  universal  wherever  the  number  of  strips  per  forty  or  |-mile 
amounts  to  at  least  two,  and  possible  even  when  but  one  strip  is  run. 
This  correction  requires,  first,  the  area  of  the  type  whether  timbered 
or  blank,  from  a  map;  second,  the  area  covered  by  the  strip  in  esti- 
mating.    The  latter  expressed  in  acres  is  computed  by  multiplying 


290 


IMPROVING  THE  ACCURACY  OF  TIMBER  ESTIMATES 


Fig.  60. — Polar  planimeter. 


length  of  strip  by  its  width.  The  most  convenient  units  are  rods, 
since  160  square  rods  equals  1  acre,  or  chains,  10  square  chains  to  1 
acre.  Distance  in  chains  on  strip  required  for  1  acre  may  be  computed 
for  each  width  of  strip  and  the  area  of  the  strip  obtained  by  dividing 
its  length  by  this  factor. 

226.  Method  of  Separating  Areas  of  Different  Types.     To  determine 

the  total  area  of 
the  type  accurately 
from  a  map,  a  plan- 
imeter may  be  used. 
By  the  use  of 
this  instrument  a 
direct  reading  on 
the  map  is  obtained 
in  square  inches 
of  the  area  whose 
boundary  is  traced 
by  the  needle,  moving  clockwise.  The  stationary  pin  is  placed  outside 
of  the  area  to  be  traced.  When  placed  within  the  area  so  that  the 
movable  pin  finally  encircles  the  pivot  before  returning  to  its  point  of 
origin,  a  deduction  or  correction  must  be  made  in  the  indicated  area,  the 
size  of  which  depends  upon  the  make  of  instrument  used. 

The  equivalent  in  acres  for  square  inches,  as  determined  by  scale 
of  the  map,  gives  the  acreage.  Lacking  a  planimeter,  the  area  of  types 
can  be  computed  by  the  method  of  approximation  through  triangles 
or  the  sum  of  small  squares.  For  the  latter  purpose  a  map  should  be 
plotted  on  fine  cross-section  paper. 
The  area  of  these  types  is  required 
only  to  a  reasonable  degree  of 
accuracy  since  the  determination 
of  their  field  boundaries  is  a 
matter  of  inspection  and  sketching 
and  the  total  area  of  the  tract  is 
not  involved. 

As  an  illustration  of  the  effect  of 
using  type  areas  in  estimating,  the  follow- 
ing example  may  be  cited:  Area  of 
tract,  200  acres,  divided  into  two  types 
containing  100  acres  each.  The  stand 
on  the  first  type  is  30,000  Vjoard  feet  per 
acre,  and  on  the  second  10,000  board  feet. 
The  total   stand   is   therefore  4  million 

board  feet.      Twenty-five  per  cent  of  this  area  or  50  acres  is  to  be  covered  by 
strips.     The  result  of  the  cruise  is  shown  in  Fig.  61. 


Type  II 


Fig.  61. — Relation  of  areas  of  types  to 
strips  in  timber  estimating. 


SITE  CLASSES  AND  AVERAGE  HEIGHTS  OF  TIMBER  291 

The  result  of  running  the  five  strips  at  regular  intervals  is  to  include  within 
type  I,  30  acres,  which  at  30,000  board  feet  per  acre  would  give  900,000  board  feet. 
In  type  II,  20  acres  was  included  which  at  10,000  board  feet  gives  200,000  board 
feet,  a  total  for  the  50  acres  run,  of  1,100,000  board  feet.  As  this  is  25  per  cent  of 
the  area,  the  required  factor  for  the  tract  without  subdivision  into  types  would 
be  a  multiple  of  4,  giving  an  estimate  of  4,400,000  board  feet,  an  error  of  +10  per 
cent  caused  not  by  errors  in  the  strip  but  by  failure  to  get  the  weighted  average 
stand  from  the  strips  run. 

But  if  while  running  these  same  strips  the  tally  sheet  had  been  changed  wherever 
the  strip  passed  from  one  of  these  types  to  the  other,  and  both  the  map  of  the  area 
and  the  corresponding  estimate  of  the  timber,  or  tally,  had  thus  been  separated 
into  two  areas,  corresponding  with  each  of  the  two  types,  the  computed  estimate 
would  show  that  while  on  30  acres  900,000  board  feet  was  tallied  the  average  acre 
for  type  I  is  30,000  board  feet,  but  instead  of  this  applying  to  three-fifths  of  the  total 
area,  it  applies  only  to  the  actual  area  shown  to  be  in  the  type,  or  one-half  of  the  total, 
which  is  100  acres,  totaling  3,000,000  board  feet.  The  less  fully-stocked  type  in 
the  same  way  is  shown  to  contain  1,000,000  board  feet  or  a  correct  total  for  the  tract 
of  4,000,000  board  feet.  The  10  per  cent  error  incurred  in  the  first  method  is  elimi- 
nated. The  accuracy  of  this  area  correction  obviously  depends  first  upon  ability 
to  obtain  by  sketch  a  correct  map  of  the  actual  areas  of  the  different  types,  and 
second,  to  convert  this  area  from  the  map  into  acres  by  use  of  the  proper  methods 
of  map  reading  as  explained  in  this  paragraph. 

This  system  of  type  divisions  is  of  especial  value  in  mountainous  regions  where 
sharp  distinctions  can  be  drawn  between  t3T3es  coinciding  with  great  differences 
in  the  average  density,  volume,  size  and  value  of  the  timber.  Under  such  circum- 
stances the  more  valuable  types  would  require  a  greater  per  cent  of  the  total  area 
to  be  estimated,  to  obtain  the  same  basis  of  accuracy  as  could  be  secured  for  the 
less  densely  stocked  and  less  valuable  tracts  %vith  a  smaller  per  cent.  The  type 
divisions  also  are  more  conveniently  made  in  large  or  irregular  areas  than  where 
estimates  are  separated  by  rectangular  tracts  of  40  acres. 

227.  Site  Classes  and  Average  Heights  of  Timber.  Differences 
in  the  quality  of  the  site  on  which  timber  is  growing  cause  very  great 
differences  in  total  volume  per  acre,  and  in  the  total  heights  of  the 
trees  and  stands.  To  quite  an  extent  these  differences  are  closely 
correlated  with  changes  in  cover  types,  different  types  being  found 
on  wet  soils,  fresh  well-drained  soils,  and  dry,  shallow  soils.  But  it 
often  happens  that  the  same  type  of  forest  cover  will  extend  without 
appreciable  changes  in  composition  over  a  range  of  site  quality  so  great 
that  it  becomes  necessary  to  subdivide  the  area  within  the  type  into 
from  two  to  three  site  classes,  ranging  from  good  to  poor.  This  is 
made  necessary  by  the  effect  of  site  upon  the  height  of  the  trees  in  the 
stand,  on  account  of  the  methods  usually  required,  of  selecting  sample 
trees  to  measure  for  height. 

Heights  constitute  an  extremely  variable  factor  in  timber  estimating. 
Not  only  do  total  heights  range  through  limits  of  at  least  100  per  cent 
for  the  same  diameter,  but  merchantable  heights,  especially  in  old  hard- 
woods, vary  still  more  widely.  Just  as,  in  a  100  per  cent  estimate, 
the  necessity  for  averages  is  eliminated,  so  when  the  height  of  every 


292 


IMPROVING  THE  ACCURACY  OF  TIMBER  ESTIMATES 


tree  in  a  stand  is  tallied  there  is  no  necessity  for  average  heights.  Only 
when  merchantable  log  lengths  are  used  as  the  basis  for  height  will  the 
height  of  every  tree  measured  for  diameter  be  tallied.  Where  total 
height  is  used,  far  greater  accuracy  can  be  obtained  by  the  measure- 
ment of  a  few  trees  with  a  hypsometer  than  by  attempting  to  guess 
by  eye  the  height  of  each  tree. 

In  a  large  tract  with  varying  site  qualities,  the  securing  of  the  average 
height  for  each  diameter  class  from  a  range  of  heights  of  100  per  cent 
would  require  the  selection  of  heights  on  the  basis  of  the  principle  of 
a  weighted  average.  If  exactly  the  same  proportion,  as  for  instance, 
1  per  cent,  of  the  heights  for  each  diameter  were  obtained  from  large, 
medium  and  short  trees  as  existed  in  the  original  stand  on  the  entire 
tract,  the  height  curve  could  then  be  applied  to  the  tract  as  a  whole. 
Any  failure  to  secure  this  weighted  average  would  result  in  a  curve 
giving  too  high  or  too  low  an  average  for  the  timber  as  a  whole. 

The  difficulty  of  securing  a  weighted  average  is  eliminated  if  the 
tract  can  be  divided  into  two  or  three  site  quahties,  separated  as  dis- 
tinct units  in  the  field  in  estimating.  On  each  of  these  separate  sites 
the  heights  conform  to  a  much  closer  range  for  the  same  diameter  than 
for  the  entire  area,  and  a  few  selected  trees  for  each  class  will  give  a 
dependable  height  curve  (§  209)  from  which  the  volumes  in  each 
diameter  class  may  be  accurately  computed. 

228.  Methods  of  Estimating  which  Utilize  Types  and  Site  Classes; 
Corrections  for  Area.  An  example  of  the  application  of  these  principles 
is  found  in  the  standard  methods  of  timber  cruising  adopted  by  the 
Forest  Service  in  the  Appalachian  region.  Four  types  are  used,  termed 
cove,  lower  slope,  upper  slope  and  ridge.  The  variations  in  the  per 
cent  of  estimate  required  are  shown  in  the  following  table : 

TABLE  XLIV 
Per  Cent  of  Total,  Area  Required  in  Estimating 


Total  Area  Estimated 

Area 
of 

estimate 

Average 

Heavily 

Lightly 

unit. 

of  all  types. 

timbered 

timbered 

tj^es. 

types. 

Acres. 

Per  cent 

Per  cent 

Per  cent 

0-  100 

50-100 

50-100 

50  -100 

100-  .500 

25-  50 

25-100 

10  -  25 

.500-1000 

10-  15 

20-  50 

5-10 

1000-5000 

5-  10 

1.5-  25 

21-     5 

5000  + 

3-    5 

10-  25 

U-    2i 
J 

THE  USE  OF  CORRECTION  FACTORS  FOR  VOLUME 


293 


Fif 


The  problem  of  combining  a  large  per  cent  of  area  on  a  heavily 
timbered  type,  as  the  cove  type,  with  a  small  per  cent  elsewhere,  has 
been  solved  here  by  running  strips  across  the  entire  area,  embracing 
the  minimmn  per  cent.  Where  these  strips  cross  the  cove  types,  points 
are  marked  on  the  ground  which  serve  to  tie  in  the  strips  run  through 
the  coves.  Where  100  per  cent  is  not  estimated,  a  plan  of  running 
strips  in  a  zigzag  course  from  one  boundary  to  the  others  of  the,  type 
through  these  coves  has  been  adopted.  The  more  acute  the  angle 
between  two   courses  and  the 

more  nearly  parallel  the  result-       ^skt^t^^^^-T'""'""^"'^       1^^^^-v 
ant  strips,  the  greater  the  per       ~'~~' 
cent  of  the  type  included. 

229.  The  Use  of  Correction 
Factors  for  Volume.  The  pur- 
pose of  all  estimates  is  to  secure 
the  actual  volume  of  timber  on 
the  entire  tract  as  accurately 
and  inexpensively  as  possible. 
In  systems  of  covering  partial 
areas,  even  after  the  probable 
error  has  been  reduced  by  adopt- 
ing subdivisions  based  on  type 
or  forest  cover  and  site,  there 
remains  a  final  possibility  that 
the  average  stand  per  acre  wit  hin 

the  type  differs  from  that  secured  by  the  methods  employed.^  The  older 
and  more  diversified  a  stand,  the  greater  will  be  its  irregularity  of  stocking, 
and  the  greater  the  necessity  for  accuracy.  Can  this  accuracy  be  still 
further  improved?  A  correction  of  an  average,  mechanically  obtained, 
rests  upon  the  assumption  of  definite  knowledge  that  this  average  is 
wrong,  and  the  ability  to  determine  approximately  how  much  it  is  in 
error.  Since  the  timber  on  the  area  lying  outside  the  measured  and 
estimated  strips  is  neither  counted  nor  measured,  the  impression  that 
the  average  is  wrong  depends  upon  the  ability  of  the  cruiser  to  estimate 
or  size  up  timber  by  the  eye  and  to  compare  it  ocularly  as  a  whole  with 
the  stand  upon  the  strip  which  he  has  measured.  This  comparison 
is  useless  unless  enough  of  the  remaining  timber  can  be  seen  so  that 
it  is  practically  certain  that  the  average  stand  on  the  whole  remaining 
area  is  greater  or  less  than  that  measured  on  the  strips.  Where  strips 
are  narrow  and  run  at  wide  intervals,  it  is  impossible  to  arrive  at  this 
judgment  and  no  reliable  correction  can  be  made  by  eye. 

1  Errors  in  Estimating  Timber,  Louis  Margolin,  Forestry  Quarterly,  Vol.  XII, 
1914,  p.  167. 


62. — Method  of  running  strips  to  cover 
an  additional  20  per  cent  of  area  in  heavily 
timbered  t\T3e,  on  basis  of  original  5  per 
cent  estimate  for  entire  area.  Strips  8  rods 
wide. 


294         IMPROVING  THE  ACCURACY  OF  TIMBER  ESTIMATES 

But  where  strips  are  run  at  intervals  of  |  mile  and  the  timber  is 
open  and  large,  and  especially  in  coniferous  stands  which  have  a  fair 
degree  of  uniformity  of  sizes,  although  varying  materially  in  density, 
it  is  possible  to  view  the  remaining  timber  without  counting  it  or  caliper- 
ing.  If  there  were  tmie  for  additional  measurements,  these  would  be 
made.  The  application  of  a  correction  factor  is  based  on  the  assumption 
that  the  per  cent  actually  measured  is  the  maximum  possible  under 
the  luniting  conditions.  Where  an  error  would  evidently  be  incuned 
unless  the  mechanical  average  is  corrected,  this  correction  should  alwaj  s 
be  made. 

The  method  of  applying  this  sort  of  a  correction  in  the  past  has 
been  as  unsystematic  as  the  ocular  estimation  of  timber  itself.  The 
estimate  from  sample  plots  or  strips  was  arbitrarily  raised  or  lowered 
according  to  unpressions  obtained  by  the  cruiser.  This  system  may 
be  greatly  improved  and  a  much  higher  per  cent  of  accuracy  obtained 
by  observing  the  following  principles: 

1.  The  comparison  sought  is  not  an  absolute  estimate  of  the  volume 
per  acre  on  the  remaining  area,  but  a  percentage  relation  between  this 
stand  and  the  strip  which  is  measured,  by  which  the  estimate  on  this 
remaining  area  may  be  obtained  by  increasing  or  diminishing  that  on  the 
strip. 

2.  The  correction  is  an  average  for  the  whole  area  to  be  corrected, 
in  the  form  of  a  per  cent  of  total  volume.  Single  observations  must 
therefore  be  carefully  weighted  to  obtain  average  results. 

3.  The  correction  actually  applies  only  to  the  area  lying  outside 
the  strip  and  not  measured.  If  applied  to  the  entire  area  of  the  unit, 
the  estimate  on  the  strip  itvself  is  arbitarily  raised  by  the  same  per- 
centage as  applied  to  the  residual  area  and  this  factor  cannot  be  neglected 
in  arriving  at  the  proper  per  cent. 

To  illustrate  the  last  point,  assume  that  50  per  cent  of  a  tract  has 
been  estimated.  By  observation,  the  correction  factor  on  the  remainder 
is  assumed  as  + 10  per  cent.  The  estimate  is  100,000  board  feet  on  the 
strip.  The  correct  estimate  on  the  remaining  area  is  therefore  110,000 
board  feet  and  the  total,  210,000  board  feet.  If  10  per  cent  is  applied 
to  the  results  obtained  for  the  forty,  the  process  would  be,  10Q,000 
times  2  gives  the  uncorrected  estimate  for  the  area,  or  200,000  board 
feet.  A  correction  of  10  per  cent  gives  220,000  board  feet,  which  is 
an  error  of  4.8  per  cent  in  the  estimate.^ 

•  This  multiple,  which  in  this  illustration  is  2,  is  sometimes  termed  the  correction 
factor,  but  assumes  no  correction.  It  is  merely  the  extension  of  the  mechanical 
average  over  the  entire  area.  For  a  25  per  cent  estimate,  the  multiple  is  4;  for 
20  per  cent,  it  is  5,  etc.  A  method  of  applying  the  correction  factor  is  in  use,  by  which 
this  multiple  is  raised  or  lowered.  Where  the  multiple  is  4,  a  +25  per  cent  correc- 
tion calls  for  5;    +12^  per  cent  requires  4^,  etc. 


THE  USE  OF  CORRECTION  FACTORS  FOR  VOLUME  295 

Since  this  error  consists  in  applying  the  per  cent  erroneously  to  the 
area  estimated  within  the  strip,  it  diminishes  with  the  per  cent  covered 
by  the  strip;  e.g.,  should  25  per  cent  of  the  above  tract  be  estimated 
and  found  to  contain  50,000  board  feet,  and  the  correction  factor  be 
actually  10  per  cent,  the  remaining  area,  which  if  uncorrected  would 
have  a  stand  of  150,000  board  feet,  has  actually  10  per  cent  more  than 
this  or  165,000  board  feet  or  a  total  for  the  tract,  of  215,000  board  feet. 
But  applying  10  per  cent  to  the  entire  tract  indicates  a  total  stand  of 
220,000  board  feet  or  an  error  of  +2.4  per  cent.  But  with  the  decrease 
in  the  per  cent  tallied,  the  probability  of  obtaining  a  close  observation 
of  the  remainder  and  applying  a  correct  per  cent  also  diminishes  so 
that  if  a  correction  factor  is  used  at  all,  there  is  less  need  for  modifying 
the  per  cent.  The  conclusion  is  that  when,  on  account  of  measuring 
a  large  per  cent  of  the  area,  it  is  possible  successfully  to  use  a  correction 
factor  as  applied  to  the  remainder,  there  is  all  the  greater  necessity 
for  making  a  correct  application  of  this  factor. 

To  determine  the  actual  correction  from  a  per  cent  obtained  by 
weighted  observations,  two  methods  may  be  used.  The  first  of  these 
methods  applies  to  irregular  areas  where  the  per  cent  estimated  is  not 
uniform,  that  is,  in  areas  estimated  by  the  separation  of  types.  The 
steps  are  as  follows: 

1.  Reduce  the  stand  on  strip  to  stand  per  acre. 

2.  Apply  the  per  cent  correction  to  this  stand  per  acre. 

3.  Calculate  the  stand  separately  for  the  area  not  estimated,  using 
the  corrected  average  stand. 

4.  Add  together  the  estimates  on  and  off  the  strip  for  the  total; 
e.g.,  on  100  acres,  17  per  cent  is  estimated  and  the  remaining  83  acres 
is  judged  to  run  10  per  cent  heavier  than  the  strip.  The  tally  on  the 
strip  is  170,000  board  feet,  averaging  10,000  board  feet  per  acre.  The 
10  per  cent  correction  gives  11,000  board  feet  per  acre  off  the  strip,  or 
a  total  estimate  off  strip  of  913,000  board  feet.  The  total,  both  on 
and  off  strip  is  1,083,000  board  feet. 

The  second  procedure  may  be  applied  when  the  per  cent  estimated 
is  uniform  and  type  or  area  correction  seldom  applied.  The  rule  is, 
reduce  the  correction  -per  cent  by  the  proportion  which  the  area  estimated 
in  the  strip  bears  to  the  total  area.  E.g.,  where  the  strips  cover  one-half 
the  area  or  50  per  cent,  a  correction  factor  of  10  per  cent  applies  to  the 
other  50  per  cent  or  one-half.  Then,  . 50 X.  10  =.05.  A  5  per  cent  cor- 
rection can  be  apphed  to  the  total  normal  estimate.  Where  25  per  cent 
is  estimated  and  a  10  per  cent  correction  is  found,  this  applies  only 
to  three-quarters  of  the  area;  .75X.10  is  .075.  The  correction  factor 
of  7|  per  cent  may  then  be  applied  to  the  total  area.  It  makes  no  dif- 
ference whether  a  correction  of  10  per  cent  is  applied  to  75  per  cent 


296         IMPROVING  THE  ACCURACY  OF  TIMBER  ESTIMATES 


of  the  area  or  75  per  cent  of  a  correction  of  10  per  cent  is  applied  to  the 
whole  area. 

Since  the  greatest  danger  in  applying  corrections  to  mechanical 
averages  lies  in  failure  to  obtain  a  proper  weighted  average,  and  since 
it  is  better  to  let  these  mechanical  averages  stand  rather  than  to  intro- 
duce an  unknown  factor,  dependent  merely  upon  a  guess,  observations 
intended  to  demonstrate  the  need  for  a  correction  factor  must  be  made 
as  systematically  as  the  strips  themselves  are  run.  Fixed  points  should 
be  chosen  at  definite  intervals  along  the  strips  at  which  to  take  these 
observations.  These  may  be  taken  for  instance  at  points  20  rods  apart 
on  the  strip.  At  these  points,  the  areas  on  either  side  of  the  strip 
should  be  compared  with  the  stand  upon  the  strip. 

The  final  result  is  expressed  in  terms  of  a  per  cent,  but  if  each  sepa- 
rate observation  of  a  series  is  so  expressed,  the  resultant  per  cent  will 
not  be  weighted  by  the  volumes  to  which  its  components  apply;  e.g., 
two  successive  observations  may  give  the  following  result : 


Stand  on  strip 

Correction  per 
cent 

Weighted  volume 
correction 

10,000 
5,000 

Average  of  2  plots 

+  10 
-10 

0 

+1000 
-  500 

+  250 

The  actual  correction  factor  is  +2|  per  cent  instead  of  zero. 

This  principle  of  weighting  the  observations  by  volume  is  very 
simply  applied.  It  consists  of  entering  for  each  observation,  not  the 
per  cent  of  comparison,  but  a  comparison  based  on  an  ocular  estimate 
of  the  stand  per  acre.  The  estimator  puts  down  in  two  parallel  columns, 
first  the  stand  per  acre  estimated  to  be  on  the  strip  at  that  point,  second, 
the  stand  per  acre  estimated  to  be  on  the  remaining  area.  In  arriving 
at  this  he  includes  as  large  an  area  as  comes  under  his  observation 
both  on  and  off  the  strip.  For  double  observations,  i.e.,  taken  on  both 
sides  of  the  strip,  it  is  necessary  to  record  the  stand  on  the  strip  twice, 
once  for  each  observation  off  strip. 

On  the  completion  of  the  unit,  these  stands  on  and  off  strip  are 
totaled.  By  dividing  the  total  off  strip  by  the  total  on  strip,  the  true 
weighted  volume  correction  factor  is  obtained. 

This  factor  is  a  percentage  relation  and  therefore  does  not  require 
that  the  ocular  estimates  per  acre  on  which  it  is  based  be  correct,  pro- 
vided they  are  in  the  proper  proportion.  Each  ocular  guess  may  be  25 
per  cent  too  low,  yet  the  resultant  correction  factor  will  he,  identical 


METHODS  DEPENDENT  ON  USE  OF  PLOTS  297 

with  that  obtained  if  the  ocular  guess  in  each  case  were  correct.  This 
increases  the  probabihty  of  accuracy  in  applying  the  method.  Actual 
tests  of  this  principle  have  shown  that  where  the  average  stand  per  acre 
off  the  strip  differs  as  much  as  from  10  to  15  per  cent  from  that  on  the 
the  strip,  under  conditions  permitting  the  inspection  or  actual  seeing 
of  the  greater  part  of  the  timber,  it  is  possible  to  reduce  the  error  incurred 
by  the  mechanical  average  by  at  least  one-half,  provided  the  cruisers 
have  some  training  and  skill  in  application  of  the  principle  of  ocular 
estimating. 

230.  Methods  Dependent  on  the  Use  of  Plots  Arbitrarily  Located. 
In  discussing  the  methods  of  estimating  by  means  of  sample  plots, 
only  the  systematic  or  strip  method  of  arrangement  has  been  described. 
A  second  plan  is  to  locate  these  plots  arbitrarily  by  selection  based  upon 
individual  judgment,  the  purpose  being  to  get  the  total  estimate  by 
means  of  a  few  typical  plots  and  greatly  cut  down  the  work  required 
in  systematic  measurements.  As  in  the  strip  systems,  one  of  two  things 
is  done;  either  the  plots  which  are  measured  are  taken  to  represent 
the  average  stand  per  acre  for  the  larger  area  of  which  they  are  a  sample, 
or  these  plots  are  merely  the  basis  of  arriving  at  the  stand  by  sub- 
sequent application  of  a  correction  factor. 

The  first  plan  can  be  used  only  in  conjunction  with  the  area  or  type 
method  in  order  to  eliminate,  as  far  as  possible,  variations  in  the  stand 
by  separating  uniform  and  comparatively  small  areas.  In  this  case, 
sample  plots  selected  with  care  after  a  thorough  inspection  may  be 
relied  upon  within  reasonable  limits  of  accuracy.  By  the  second  method, 
the  plots  chosen  are  seldom  rehed  upon  without  further  close  inspec- 
tion of  the  stand.  Cruisers  using  this  method  employ  these  plot 
measm-ements  in  order  to  establish  in  their  minds  the  volume  of  typical 
stands  having  a  definite  density  and  appearance.  Once  fixed,  this 
standard  is  used  as  a  basis  with  which  to  compare  the  average  stand 
on  the  area  by  exactly  the  same  methods  as  were  described  under  the 
correction  factor  in  the  strip  method.  The  plots  are  merely  much 
smaller  and  have  more  definite  standards  than  the  strips,  and  their 
application  to  the  larger  area  is  more  difficult.  The  use  of  these  plots  is 
still  further  restricted,  with  improved  accuracy,  when  they  are  intended 
merely  to  determine  the  volume  of  the  average  tree  of  certain  classes 
of  timber,  and  the  estimate  on  the  remaining  area  is  determined  by  a 
tree  count  covering  practically  100  per  cent. 

Various  combinations  of  the  above  plans  are  used,  especially  in  the 
South,  by  cruisers  working  in  pine  in  an  effort  to  cover  the  ground 
accurately  with  a  minimum  of  time  and  expense. 

231.  Estimating  the  Quality  of  Standing  Timber.  An  estimate  of 
standing  timber  is  in  effect  an  inventory  of  raw  materials  intended 


298        IMPROVING  THE  ACCURACY  OF  TIMBER  ESTIMATES 

to  establish  the  total  value  of  the  stock  on  hand.  It  is  not  sufficient 
to  know  the  quantity  of  wood  in  the  forest  in  terms  of  board  feet  or 
cubic  feet.  The  estimation  of  poles,  ties  and  other  piece  products 
by  sizes  and  grades  illustrates  this  need.  An  inventory  requires  a 
statement  of  the  total  quantity  of  each  class  of  product,  and  of  each 
grade  or  quality  within  that  class,  which  has  a  different  unit  price  or 
value. 

Lumber  grades  differ  enormously  in  value  (§  352),  and  the  quantity 
of  separate  grades  of  lumber  which  may  be  sawed  from  trees  of  different 
ages  and  sizes  differs  as  widely  as  their  values.  The  estimation  of  the 
amount  of  the  different  standard  grades  of  lumber  in  standing  timber 
is  as  essential  in  determining  its  value  as  the  measurement  of  the  total 
quantity  in  board  feet.  The  neglect  or  inability  of  many  foresters, 
whose  training  was  along  lines  of  mechanical  estimating  (§  223)  to 
determine  the  amount  of  the  product  by  grades  has  done  much  to 
withhold  a  recognition  among  practical  cruisers  of  the  great  services 
rendered  the  profession  of  cruising  by  foresters  in  contributing  volume 
tables  and  in  systematizing  the  making  of  topographic  maps. 

What  is  wanted  is  the  estimation  of  the  total  quantity  of  timber 
on  a  tract,  separated  into  the  amount  of  each  of  several  standard  grades, 
covering  the  range  of  the  products  and  sufficient  to  include  practically 
the  entire  cut  and  to  determine  its  average  value  on  the  stump.  This 
problem  is  closely  related  to  that  of  discounting  for  defects  in  that  both 
require  a  close  observation  of  the  character  of  the  standing  timber 
rather  than  its  mere  dimensions. 

All  defects  which  reduce  the  value  of  sawed  lumber  reduce  its  grade. 
When  these  defects  are  of  a  character  to  reduce  the  grade  below  a  certain 
standard  (§  358,  Appendix  A),  the  material  is  no  longer  scaled  under 
the  rule  of  sound  scale.  It  may  still  be  sawed  and  sold  as  lumber. 
But  when  it  ceases  to  hold  together  as  boards  it  is  cull. 

The  deduction  of  a  per  cent  of  the  total  estimate  for  defects  brings 
the  estimate  into  conformity  with  the  quantitative  "  sound  "  scale. 
The  further  separation  into  grades  of  the  sound  portion  of  the  timber 
which  will  be  scaled  and  estimated,  recognizes  the  influence  of  defects, 
chiefly  knots,  but  including  other  classes,  such  as  wormholes,  sound 
stain,  and  twisted  grain,  which  lower  the  grades  and  nature  of  the 
log  contents  (§  352,  Appendix  A). 

To  determine  grades,  a  knowledge  of  the  results  of  sawing  and  the 
study  of  logs  as  they  are  opened  up  and  graded  into  products  on  the 
sorting  table  is  far  more  valuable  than  the  experience  gained  in  studying 
the  apparent  defects  of  standing  timber.  This  knowledge  must  then 
be  supplemented  by  a  knowledge  of  the  growth  of  trees  in  stands. 
Open-grown  trees,  although  large,  are  of  low  quality  due  to  the  presence 


METHOD  OF  MILL  RUN  APPLIED  TO  THE  STAND  299 

of  knots,  while  trees  grown  in  dense  stands  have  a  higher  per  cent  of 
upper  grades  due  to  the  history  of  their  development.  The  skill  required 
in  judging  the  per  cent  of  grades  in  standing  timber  is  based  directly 
on  these  two  sources  of  information  and  is  not  a  matter  of  guess  work. 

232.  Method  of  Mill  Run  Applied  to  the  Stand.  Data  on  grades 
produced  in  sawing  takes  two  forms;  the  total  output  by  grades  for 
mills  sawing  in  a  given  region  and  character  of  timber,  and  the  specific 
contents  of  logs  of  different  sizes  and  quahty,  as  determined  by  mill- 
scale  studies  (§361,  Appendix  A).  This  corresponds  with  two  dif- 
ferent methods  of  applying  the  information  on  grades  to  the  standing 
timber,  namely,  application  to  the  stand  as  a  unit,  and  application 
to  the  tree  or  log  units. 

In  applying  mill-run  grade  per  cents  to  the  stand,  the  total  estimate 
in  board  feet  is  arbitrarily  divided  into  the  different  grades  which  it 
will  probably  yield,  by  per  cents  of  this  total.  This  method  corresponds 
with  that  of  ocular  estimate  of  a  stand  (§  206)  and  its  results  are  about 
equally  unreliable.  The  basis  is  the  sawed  output  by  grades  from  mills 
in  the  vicinity.  These  per  cents  so  obtained  will  apply  to  the  timber 
in  question,  only  if  it  happens  to  average  the  same  in  quality  as  that 
sawed,  which  assumption,  considering  the  great  variation  in  standing 
timber,  is  wholly  untrustworthy.  This  means  that  the  per  cents  of 
grade  must  be  modified  as  the  timber  is  better  or  poorer  than  that 
sawed,  which  requires  a  knowledge  of  the  standing  timber  previous 
to  sawing, 

233.  Method  of  Graded  Volume  Tables  Applied  to  the  Tree.  Evi- 
dently, a  better  basis  is  required  and,  just  as  in  timber  estimating  for 
volume,  this  must  be  found  in  the  use  of  the  tree  unit  or  the  log  unit, 
by  which  the  varying  quality  of  the  timber  can  be  standardized. 

The  tree  unit  has  not  proved  a  satisfactory  basis  for  grading,  though 
it  is  possible  to  use  it.  The  basis  is  graded  volume  tables  (§  165)  which 
show  the  per  cent  of  standard  grades  in  trees  of  different  diameters, 
preferably  in  the  form  of  per  cents  of  contents. 

These  per  cents  could  be  applied  to  the  trees  in  each  diameter  class 
and  the  total  estimate  divided  in  this  way  into  the  component  grades. 

The  objection  to  this  method  is  that  it  is  not  sufficiently  elastic 
to  take  care  of  the  great  range  of  quality  in  trees  of  the  same  diameters. 
A  given  graded  table  will  hold  good  only  for  timber  of  a  certain  character; 
if  more  open-grown,  shorter  boiled  or  limbier,  or  otherwise  different, 
the  volume  table  is  not  applicable.  The  method  is  probably  better 
than  the  ocular  guess,  but  is  equally  subject  to  large  corrections  in  the 
field. 

234.  Method  of  Graded  Log  Rules  Applied  to  the  Log.  The  third 
method  employs  the  log  as  the  basis  of  grades,  and  applies  this  basis 


300         IMPROVING  THE  ACCURACY  OF  TIMBER  ESTIMATES 

to  the  standing  timber.  The  graded  log  table  (§  74)  appears  to 
satisf}'  the  requirements  of  the  problem.  Log  grades  are  such  as  can 
be  recognized  in  standing  trees,  on  the  basis  of  diameter,  surface  appear- 
ance, presence  of  knots  or  limbs,  and  character  of  the  tree  and  the  stand 
in  which  it  is  growing.  In  turn,  these  log  grades  can  be  anah'zed  by 
mill-scale  studies,  so  that  the  average  per  cent  of  grades  of  timber  in 
each  log  grade  is  known.  Since  three  grades  are  usually  made  in  valu- 
able species,  and  at  least  two  for  the  less  valuable,  trees  of  the  same 
D.B.H.  can  easily  be  thrown  into  the  lumber  grades  corresponding 
with  differences  in  their  character,  by  recording  the  logs  which  they 
contain  as  grades  No.  1,  2  or  3.  By  contrast,  if  graded  volume  tables 
are  used,  ordinarily  only  one  classification  is  available  for  the  tree — 
that  corresponding  with  the  table. 

The  final  problem  is  the  application  of  these  graded  log  tables  to 
the  standing  timber,  in  a  manner  to  conform  to  the  methods  used  in 
timber  estimating.  Cruisers  who  use  the  method  of  selecting  an  aver- 
age tree  (§  209)  usually  analyze  this  tree  by  the  use  of  the  log  grades, 
or  directly  by  per  cents,  into  the  grades  of  lumber  which  they  believe 
it  will  cut,  and  apply  these  per  cents  to  the  remainder  of  the  stand. 
This  is  a  crude  method. 

Where  the  method  of  tallying  the  diameter  of  every  log  (§  119)  is 
used,  each  log  can  be  tallied  under  its  proper  log  grade.  The  total 
volume  in  each  log  grade  is  thus  obtained  directly.  Where  timber 
is  sold  as  logs,  it  is  unnecessary  to  go  beyond  this  point. 

But  where  the  sawed  product  determines  stumpage  value,  these 
log  grades  are  merely  the  basis  of  application  to  the  standing  trees  of 
the  grades  of  lumber  which  they  probably  contain,  and  the  contents 
of  the  log  grades,  in  lumber  of  each  grade,  w  ill  be  computed  for  the 
estimate. 

235.  Combination  Method  Based  on  Sample  Plots  and  Log  Tally. 
Where  the  tree  tally  and  volume  tables  are  used  in  estimating  (§  121), 
the  application  of  the  log-grade  unit  to  each  tree  is  not  possible,  since 
it  would  mean  a  shift  to  the  tally  of  logs  and  not  trees.  Here  a  com- 
bination method  is  necessitated,  based  on  the  principle  that  grades 
or  quality  of  timber  can  be  determined  by  the  measurement  of  a  much 
smaller  per  cent  of  the  total  volume  than  is  required  for  volume  estimate. 

The  method  is  to  lay  out  sample  or  representative  areas  in  the  form 
of  strips  crossing  the  tj^pes  as  for  timber  estimating  (§  209)  and  com- 
prising a  per  cent  of  the  area  estimated,  sufficient  in  the  judgment  of 
the  cruiser  to  obtain  the  average  quality  sought.  On  these  areas, 
every  log  in  each  tree  is  totaled  by  upper  diameter,  in  the  log  grade 
in  which  it  belongs.  Instead  of  guessing  at  these  upper  diameters, 
taper  tables  based  on  D.B.H.  (§  167)  and  total,  or  merchantable,  heights, 


LIMITS  OF  ACCURACY  IN  TIMBER  ESTIMATING  301 

possible  if  the  latter  are  cut  to  a  fixed  diameter,  or  if  made  to  conform 
to  average  utilization,  are  used  to  get  these  diameters;  e.g.,  for  a  tree 
38  inches  D.B.H.  containing  eight  logs,  the  upper  diameters  are 
respectively,  from  the  table,  32,  30,  28,  25,  22,  18,  14,  and  10  inches, 
and  are  so  recorded,  each  log  under  its  proper  log  grade.  (See  §  207 
for  form  of  tally.) 

The  determination  of  the  number  of  board  feet  of  each  standard 
grade  in  logs  of  each  diameter  and  grade,  and  the  total  scale  for  each 
lumber  grade,  is  based  on  the  contents  given  for  these  log  grades  from 
mill-scale  studies  of  log  contents.  The  purpose  is  to  obtain  the  per 
cent  of  each  grade,  regarding  the  total  contents  of  the  logs  tallied  as 
100  per  cent,  and  then  to  apply  these  per  cents  to  the  volume  estimated 
for  the  tract.  These  per  cents  can  be  obtained  more  accurately  if  over- 
run is  included  in  logs  of  each  separate  size  (§46).  The  mill-scale 
study  will  show  the  amount  of  over-run  in  logs  of  different  diameters 
and  standard  lengths.  The  scaled  volume  of  these  logs  should  then  be 
increased  by  this  per  cent  of  over-run,  before  the  division  into  lumber 
grades  is  made.  On  the  total  sawed  contents  thus  obtained,  the  per 
cent  of  each  grade  is  based. ^ 

Even  if  considerably  in  error,  the  value  of  an  estimate  expressed 
by  grades  of  lumber  is  much  greater  than  one  which  entirely  ignores 
the  quality  and  consequently  the  relative  stumpage  value  of  the  tract. 

In  the  absence  of  specific  information  on  grades,  a  record  of  the  sizes 
of  the  trees,  their  clearness  of  bole,  and  the  density  of  the  stand  may 
furnish  a  basis  for  approximating  the  probable  grades. 

236.  Limits  of  Accuracy  in  Timber  Estimating.  Purely  ocular 
estimates  vary  in  accuracy  up  to  errors  of  100  per  cent,  dependent 
upon  how  far  the  method  is  stretched  from  its  original  limitations. 
This  does  not  include  errors  due  to  inexperience,  inefficiency  or  careless- 
ness. 

In  mechanical  methods  of  measurements,  serious  errors  may  occur 
in  computations.  Such  errors,  of  course,  are  inexcusable,  but  their 
avoidance  requii-es  careful  checking.  The  mechanical  errors  due  to 
the  operation  of  the  law  of  averages  have  been  pointed  out  as  a  function 
of  the  factors  influencing  these  averages,  the  chief  of  which  is  the  size 
of  the  area  unit. 

The  degree  of  accuracy  must  be  based  upon  the  standard  of  utiliz- 
ation. It  is  entirely  unfair  to  judge  the  accuracy  of  estimates  based 
upon  one  standard  against  the  results  of  sawing  attained  by  the  appli- 
cation of  an  entirely  different  standard.  Where  the  standard  is  the 
same  in  both  cases,  the  present  demands  of  timber  estimating  require 

1  The  details  of  this  method  are  taken  from  the  article  by  Swift  Berry,  Journal 
of  Forestry,  Vol.  XV,  1917,  p.  438. 


302         IMPROVING  THE  ACCURACY  OF  TIMBER  ESTIMATES 

an  accuracy  of  within  10  per  cent.  The  error  should  be  conservative 
rather  than  an  over-estimate  if  possible.  Greater  errors  than  10  per 
cent  may  be  caused  by  differences  in  scaling  practice  alone,  or  in  the 
length  of  logs  cut,  or  the  thickness  of  lumber  sawed. 

237.  The  Cost  of  Estimating  Timber.  No  figures  will  be  given  for 
the  costs  of  various  methods  of  timber  estimating.  These  must  be 
determined  locally.     The  elements  of  cost  are: 

1.  The  size  of  the  crew  and  the  wages  paid  each  memljer;  the 
character  of  supervision,  such  as  the  combining  of  several  crews  under 
one  supervisor;  and  the  employment  of  a  cook. 

2.  Accessibility  of  the  tract  as  affecting  transportation  of  men  and 
of  supplies,  especially  of  food.  The  means  of  transportation,  such  as 
pack  versus  wagon  haul. 

3.  Cost  of  location  of  boundaries  and  surveys  and  cost  of  establish- 
ment of  base  lines  from  which  strip  surveys  are  to  be  run.  This  is  a 
function  of  the  size  of  the  tract  and  the  character  of  the  boundary  survey 
and  monuments  already  established. 

4.  The  number  of  strips  or  miles  of  line  to  be  run  per  unit  of  area. 
The  cost  is  not  exactly  proportional  to  the  miles  run  since  certain 
items  such  as  travel  to  and  from  work  and  from  one  strip  to  another, 
cost  of  computing  the  estimate,  and  cost  of  mapping  in  the  office,  increase 
in  a  lesser  ratio.  Doubling  the  number  of  strips  increases  the  cost  from 
50  to  80  per  cent,  dependent  upon  the  saving  in  these  items. 

5.  The  rapidity  of  traverse  or  number  of  miles  of  line  which  may  be 
run  per  day.  A  standard  day's  work  varies  directly  with  topography 
and  brush,  and  with  the  amount  of  detailed  work  required  in  the  actual 
estimate  along  the  strip,  as  determined  by  the  number  of  products, 
the  number  of  species,  the  number  of  trees  and  the  details  of  record 
required.  In  very  brushy  and  mountainous  or  precipitous  country 
with  a  variety  of  species,  1  mile  per  day  may  be  all  that  is  possible, 
varying  up  to  2  miles.  An  average  day's  work  in  fairly  open  country 
varies  from  2  to  4  miles;  on  level  open  land  with  sparse  timber  and  no 
brush,  4  to  8  miles  may  be  made. 

6.  The  character  of  the  topographic  map  required.  To  a  certain 
extent,  a  detailed  topographic  map  appreciably  slows  up  the  work. 
It  is  the  object  of  a  forest  survey  to  require  only  that  degree  of  accuracy 
and  detail  which  will  not  add  appreciably  to  the  cost  by  delaying  the 
party. 

7.  Computation  or  office  work  required.  By  practical  cruisers,  this 
is  almost  eliminated  through  the  methods  employed.  Methods  of 
tallying  dimensions  and  the  use  of  volume  tables  increase  this  addi- 
tional expense. 

8.  Holidays,  sickness  and  lost  time.     Only  the  number  of  hours 


TRAINING  REQUIRED  TO  PRODUCE  TIMBER  CRUISERS       303 

on  the  actual  work  of  running  lines  and  estimating  can  be  considered 
as  the  basis  of  costs.  All  lost  time  for  any  other  cause  adds  to  the 
costs  per  hour  of  work. 

9.  Personal  efficiency.  The  training  and  personal  efficiency  of  the 
men  employed  may  make  from  25  to  50  per  cent  difference  in  the  actual 
cost  of  the  work,  but  its  principal  effect  is  in  greatly  increasing  the 
relative  accuracy  of  the  estimate. 

Cost  of  estimating  should  be  computed  as  follows: 

Total  cost  itemized  under  salaries,  and  cost  of  supplies,  transporta- 
tion and  subsistence. 

Cost  reduced  to  the  cost  per  hour  of  actual  work  by  dividing  this 
total  by  the  number  of  hours  employed  in  estimating.  These  costs 
can  be  separated  into  field  work  and  office  work,  including  mapping." 
The  costs  can  then  be  expressed  as  cost  per  unit  of  area  or  per  acre 
and  finally  as  cost  per  unit  of  product,  as  per  thousand  feet  or  per 
cord.  This  is  the  final  test  of  cost.  The  cost  should  then  be  compared 
with  the  stumpage  value  per  unit.  If  possible  it  should  not  exceed 
1  per  cent  of  this  value. 

238.  Methods  of  Training  Required  to  Produce  Efficient  Timber 
Cruisers.  Mechanicjil  methods  of  timber  estimating,  dependent  upon 
the  measurement  of  diameters  and  heights  with  instruments,  and  secur- 
ing the  mechanical  average  stand  per  acre  by  strips,  do  not  require 
anything  more  than  conscientious  work  and  care  in  details.  Skill  and 
training  enter  with  the  application  of  the  laws  of  averages,  even  for  the 
construction  of  height  curves.  The  demand  for  training  is  increased 
by  the  use  of  ocular  methods  of  measurement  and  reaches  its  maximum 
in  the  application  of  cull  for  defects  and  in  judging  the  quality  of  timber. 
Aside  from  Tamiliarity  with  cull  and  grades,  there  are  no  principles  of 
timber  estimating  that  cannot  be  learned  in  a  month's  intensive  train- 
ing. The  common  impression  that  it  takes  several  years  to  develop 
ability  as  a  timber  cruiser  is  based  upon  the  unscientific  methods 
employed  in  training  these  men.  They  usually  acquire  their  skill  by 
a  maximum  of  hard  work  in  the  woods,  with  a  minimum  of  accurate 
comparisons  of  the  estimated  volumes  with  an  actual  cut.  Even  in 
the  matter  of  judging  defect,  the  basic  training  should  not  be  in  the 
woods,  but  in  the  mill  and  in  scaling.  It  is  comparatively  easy  to  recog- 
nize the  signs  of  defect  in  standing  timber,  but  much  more  difficult  to 
judge  of  the  amount  of  cull  which  it  causes.  In  actual  training  of 
timber  cruisers  it  has  been  found  that  ability  to  secure  accurate  esti- 
mates is  greatest  in  men  who  have  best  developed  their  mental  faculties 
by  education,  close  observation,  memory  and  systematic  coordination. 
This  same  combination  of  qualities  is  desirable  for  success  in  any  line. 
Many  cruisers  lack  this  ability  and  remain  permanently  inefficient  tO 


304 


IMPROVING  THE  ACCURACY  OF  TIMBER  ESTIMATES 


a  marked  degree.  The  only  reason  that  such  individuals  have  in  the 
past  continued  to  practice  timber  cruising  as  a  profession  is  the  almost 
complete  absence  of  a  reliable  check  on  their  results  for  years  at  a 
stretch,  and  the  comparative  indifference  of  purchasers  to  the  accuracy 
of  estimates  due  to  a  rising  market  and  a  plentiful  lumber  supply. 

Standing  timber  cannot  be  "  measured."  There  is  always  a  residual 
error  in  the  closest  work.  Hence  the  use  of  the  term  "  estimates." 
Although  the  only  basic  check  on  estimates  is  the  measurement  of  the 
timber  after  it  is  cut,  yet  it  is  possible,  by  the  use  of  intensive  methods, 
to  measure  plots  of  standing  timber  so  closely  that  they  will  serve  as 
checks  on  individual  estimators. 

An  example  of  this  check  is  cited  below  in  the  case  of  a  Minnesota  lumber  com- 
pany, which  in  1907  required  each  of  its  timber  cruisers  to  estimate  an  area  which 
had  previously  been  carefully  calipered  and  measured  with  a  volume  table  and  was 
afterwards  cut  and  checked  out  with  these  measurements.  The  results  speak  for 
themselves.     These  men  were  given  all  the  time  they  desired  to  make  this  estimate. 

TABLE  XLV 

Comparative  Estimates  on  a  Tract  of  40  Acres 
Board  Feet 


Calipered, 

and 

measured 

by  volume 

table. 

Defects 

deducted 

Estimators,  by  Individual  Methods 

No.  1* 

No.  2 

No.  3 

No.  4 

White  pine 

Norway  pine 

Spruce 

Tamarack 

Jack  pine 

Balsam 

250,800 
4,120 
9,870 
35,480 
730 
2,220 
9,910 

220,000 
23,000 

300,000 
45,000 

400,000 

35,000 
3,000 

130,000 

10,000 
10,000 
15,000 

Total 

313,130 

243,000 

345,000 

438,000 

165,000 

White  pine  t                       

No.  5 

No.  6 

No.  7 

No  8 

199,000 

175,000 

125,000 

115,000 

Number  of  cruiser.  t  No  other  species  estimated  by  these  four  cruisers. 


TRAINING  REQUIRED  TO  PRODUCE  TIMBER  CRUISERS      305 

The  tract,  when  cut,  scaled  by  Scribner  Decimal  C  log  rule  314,350  board  feet, 
an  error  of  A  of  1  per  cent. 

The  best  system  of  training  men  for  timber  estimating  is  by  the  use  of  sample 
plots  on  which  the  diameter  and  merchantable  heights  in  log  lengths  of  each  tree 
are  estimated  by  the  eye  and  checked  against  the  records.  On  these  same  plots, 
each  of  the  six  classes  of  averages  (§  209)  can  then  be  tested  and  their  application 
mastered.  Each  day's  training  can  be  checked  against  the  measured  volume  of 
the  plot  that  night  and  not  only  the  total  error  in  per  cent  but  the  exact  cause  of 
this  error  ascertained.  On  this  basis,  the  progress  of  training  is  rapid  and  the 
cruiser  is  advanced  in  a  short  time  more  than  would  be  possible  in  several  years  of 
estimating  without  these  checks.  The  following  outline  wUl  illustrate  the  possi- 
bilities: 

1.  Plots  of  20  acres,  40  by  80  rods,  are  laid  out  with  compass.  The  boundaries 
are  marked  by  blazing  the  trees  facing  each  of  the  four  sides  on  the  face  towards  the 
plot.  Stakes  are  set  on  all  four  sides  at  distances  of  20  rods  apart.  Two  plots  are 
laid  out  adjoining  each  other,  together  comprising  40  acres. 

2.  Every  tree  on  the  plot  is  calipered  at  B.H.  in  two  directions,  the  average 
being  taken  to  the  nearest  even  inch  and  the  bark  blazed  to  prevent  duplication. 
The  blazes  are  made  facing  the  portion  or  strip  not  yet  measured.  A  crew  of  one 
tally  man  and  two  caliper  men  are  used  and  all  trees  above  a  fixed  diameter  are  taken, 
corresponding  with  the  minimum  exploitable  diameter  class. 

3.  The  merchantable  heights  to  the  nearest  8-foot  length  or  half-log  are  measured 
by  two  or  three  additional  men  with  Faustmann  hypsometers.  From  30  to  40  per 
cent  of  all  heights  can  be  measured  during  calipering  in  this  way.  Height  men 
work  with  the  diameter  crew  taking  the  diameter  as  measured,  pacing  for  distance 
from  the  tree  and  recording  heights  based  on  diameter.  Forty  to  sixty  heights 
per  hour  can  be  recorded  by  each  man.  Upper  diameters  or  merchantable  lengths 
are  based  upon  the  practice  of  sawing  as  applied  to  the  species  measured,  provided 
this  is  the  basis  on  which  the  volume  table  was  constructed. 

4.  The  determination  of  the  merchantable  height  of  every  tree  from  that  of  30  to 
40  per  cent  of  the  trees  is  made  separately  for  each  diameter  class.  The  heights 
tallied  within  the  diameter  class  are  taken  to  indicate  the  percentage  or  proportion 
of  the  different  height  classes  existing  in  this  diameter  class  and  the  total  number 
of  trees  are  then  distributed  according  to  the  same  proportion.  As  the  result  required 
is  a  proper  distribution  for  the  plot  as  a  whole,  and  not  for  each  diameter  separately, 
this  method  gives  a  sufficient  degree  of  accuracy. 

5.  The  record  for  the  plot  will  show  the  following  data:  total  estimate  in  board 
feet,  total  number  of  trees,  average  stand  per  acre,  volume  of  average  tree,  volume 
of  average  log  or  log  run  per  thousand  board  feet,  exact  number  of  trees  in  each 
diameter  class,  exact  number  of  trees  in  each  log  and  half-log  height  class  independent 
of  diameter. 

The  exact  number  of  trees  in  each  separate  diameter  and  height  class  is  the 
basis  for  the  last  two  summaries ;  but  the  summaries  rather  than  the  detailed  class- 
ification are  made  the  basis  of  the  estimating,  i.e.,  the  tally  is  totaled  for  each 
diameter  class,  and  in  turn,  is  totaled  for  each  height  class  irrespective  of  diameter. 

For  each  day's  work  the  cruiser  hands  in  a  report  on  the  first  five  of  the  above 
seven  items  and  brings  in  his  notebook  in  which  he  has  totaled  the  number  of  trees 
for  each  diameter  class  and  each  height  class  separately.  His  accuracy  is  computed 
as  a  per  cent  of  the  total  stand  on  the  plot.  The  error  in  per  cent  is  recorded.  The 
sources  of  error  are  then  examined.     These  are  four  in  number. 

1.  The  width  of  the  strip  may  be  too  great  or  too  small.  This  is  shown  by  an 
error  in  the  number  of  trees  tallied. 


306         IMPROVING  THE  ACCURACY  OF  TIMBER  ESTIMATES 

2.  The  trees  may  not  be  counted  accurately.  This  error  is  identical  with  the 
first,  but  usually  shows  up  as  a  deficiency  of  small  timber  near  the  minimum  diameter 
tallied. 

3.  The  diameter  of  the  trees  may  be  over-  or  under-estimated  either  as  a  whole, 
or  in  certain  classes.  There  is  a  strong  tendency  to  bunch  diameters  towards  a  tree 
whose  size  seems  to  be  the  standard  in  the  cruiser's  mind.  This  results  in  over- 
estimate of  small  trees  and  under-estimate  of  trees  of  larger  diameters. 

4.  The  heights  may  be  over-  or  under-estimated.  When  this  happens  it  shows 
up  consistently  for  the  whole  tract,  the  standard  of  height  apparently  being  tem- 
porarily distorted  in  the  mind  of  the  cruiser. 

A  fifth  source  of  error,  the  volume  table  and  the  failure  to  coordinate  upper 
diameters  and  merchantable  lengths  with  the  standard  used  in  this  table,  serves 
to  exaggerate  the  per  cent  of  error  in  the  judgment  of  heights,  but  is  always  indi- 
cated when  the  average  heights  are  too  high  or  too  low  to  agree  with  the  measure- 
ments. When  the  volume  of  the  average  tree  is  high  or  low,  it  usually  means  an 
over-  or  under-estimate  of  diameters  or  heights.  The  exact  character  of  the  error 
in  diameter  and  height  is  ascertained  by  a  simple  check  as  follows :  the  cruiser  com- 
pares the  number  of  trees  in  each  diameter  class  with  that  of  the  standard  record  and 
sets  down  his  difference  plus  or  minus.  If  he  is  over-estimating,  but  has  the  right 
number  of  trees,  the  minus  sign  will  appear  opposite  the  smaller  diameters  and  the 
larger  diameters  will  show  excess  numbers.  If  under-estimating,  the  plus  signs 
will  appear  opposite  the  small  diameters.  The  same  rule  applies  to  heights.  An 
over-estimate  causes  minus  signs  to  appear  opposite  the  lower  height  classes  and 
corresponding  plus  numbers  in  those  of  greater  log  lengths.  The  size  of  these  dis- 
crepancies shows  the  degree  to  which  the  error  has  been  carried. 

It  is  the  tendency  in  cruising  as  in  scaling  logs,  in  an  effort  to  correct  a  known 
error,  to  incur  immediately  a  still  greater  error  in  the  opposite  direction;  but  when  it 
is  possible  to  check  against  a  measurement  which  the  cruiser  admits  is  infallible  and 
in  which  he  has  confidence,  this  tendency  to  fluctuation  is  soon  overcome  and  rapid 
improvement  is  noted,  not  only  in  the  total  per  cent  of  accuracy  which  is  sometimes 
merely  the  result  of  large  compensating  plus  or  minus  errors,  but  in  each  of  the  four 
elements  of  accuracy,  thus  insuring  a  consistent  degree  of  accuracy  from  day  to  day. 

The  cruiser  is  expected  to  master  but  one  detail  at  a  time,  and  the  schedule 
is  as  follows: 

1.  During  the  calipering  of  the  standard  plots,  the  eye  is  trained  in  estimating 
diameters  which  are  then  promptly  checked  by  the  measurements.  The  same  is 
true  of  heights. 

2.  The  second  period  is  devoted  to  a  total  or  100  per  cent  tree  by  tree  estimate 
with  a  tally  of  each  diameter  and  merchantable  length.  The  total  area  of  the 
plot  is  covered  by  eight  strips,  5  rods  wide,  the  crvuser  working  not  in  the  center,  but 
on  one  side  of  this  strip  with  compassman  marking  the  opposite  border.  Width  of 
strip  and  success  in  getting  100  per  cent  of  the  area  is  dependent  absolutely  upon 
use  of  eye,  checked  by  pacing  and  judging  distance,  and  the  men  are  not  permitted 
to  mark  the  boundaries  of  these  strips  to  prevent  overlapping.  Twenty  acres  per 
day  are  covered  by  this  method. 

3.  The  third  step  is  to  increase  the  area  covered  per  day  to  30  acres  by  doubling 
the  width  of  the  strip  to  10  rods,  the  cruiser  taking  the  middle  of  the  strip  and  judging 
5-rod  distance  on  each  side.  In  all  of  this  work,  the  cruiser  tallies  his  own  dimen- 
sions of  the  trees.  In  these  preliminary  100  per  cent  estimates,  constant  repeated 
checks  are  made  of  the  diameters  and  heights  to  contiiuic  the  imj^rovcment  of  the 
eye. 

4.  The  100  per  cent  estimate  is  continued,  but  the  tally  of  every  diameter  is 


TRAINING  REQUIRED  TO  PRODUCE  TIMBER  CRUISERS       307 


discontinued  and  a  total  count  substituted  with  a  tally  of  one  tree  in  three.  The 
area  is  increased  to  60  acres  per  day.  It  is  the  universal  testimony  of  cruisers 
that  this  simplification  of  the  tally  relieves  the  mind  of  a  strain  and  improves  the 
accuracy  of  the  dimensions  talUed  and  consequently  of  the  total  estimate.  It  has 
been  found  that  an  average  volume  is  obtained  through  a  tally  of  one-third  of  the 
stand  under  the  following  conditions : 

When  there  are  at  least  500  trees  per  40  acres  of  the  species  tallied  and  preferably 
1000. 

When  the  judgment  or  process  of  selection  is  entirely  eliminated  in  favor  of 
mechanical  selection  of  the  trees  to  be  tallied.  This  may  be  done  by  taking  every 
third  tree  in  succession  or  bj'  taking  the  nearest  tree  in  each  case.  Where  there  are 
insufficient  trees  to  insure  the  mechanical  average,  or  where  the  range  of  size  is  large, 
the  count  may  be  separated  into  two  groups,  segregating  the  large  from  the  small 
trees,  one  tree  in  three  tallied  separately  in  each  group.  This  adds  very  little  to 
the  detail  required  when  working  with  a  single  species. 

5.  Only  50  per  cent  of  the  area  is  estimated  by  the  above  method.  The  area  per 
day  is  nominally  120  acres.  The  remaining  area  is  inspected  by  eye  at  distance  of 
20,  40  and  60  rods  in  order  to  apply  a  weighted 

volume  correction  factor  as  described  in  §  229. 
In  this  method,  four  strips  are  run,  each  10  rods 
wide,  as  before,  starting  from  points,  5,  25,  45, 
and  65  rods  from  the  corner  and  alternating 
with  strips  not  estimated  as  per  Fig.  63. 

In  order  to  check  the  correction  factor,  the 
alternate  strips  not  previously  estimated  are  now 
in  turn  estimated,  keeping  the  record  separate 
from  the  original  four  strips.  The  correction 
factor  derived  from  observation  is  first  com- 
puted and  the  corrected  estimate  is  then  com 
pared  with  the  tally  of  the  strips  estimated. 

6.  Up  to  this  time  no  effort  has  been  made 
to  deduct  for  cull  which  would  introduce  an 
arbitrary  factor  interfering  with  the  comparison 
of  the  work  of  the  cruiser  with  the  measurement 
of  the  plot,  both  of  which  have  been  on  basis 
of   sound   contents,   disregarding   possible    cull. 

The  cull  factor  is  now  tested  by  close  examination  of  10  acres  in  which  every  tree 
is  individually  estimated  and  the  per  cent  of  probable  cull  recorded  and  subtracted 
from  the  estimate.  Per  cent  figures  also  are  obtained  from  the  scale  of  logs  of 
similar  timber  in  the  vicinity  and  these  per  cents  are  used  as  a  basis  of  cruising. 

7.  In  actual  cruising,  the  per  cent  of  area  covered  is  reduced  to  25.  The  area 
is  increased  to  320  acres  per  day,  and  4  miles  of  line  run.  A  cull  factor  is  used  and 
hardwoods  are  added  to  the  estimate  by  tallying  the  top  diameter  of  each  mer- 
chantable log,  inside  the  bark. 

8.  The  cruiser  is  then  brought  back  to  the  sample  plots  to  receive  training  in 
individual  estimating.     This  consists  of: 

The  use  of  circular  plots  covering  different  per  cents  of  the  area  by  a  systematic 
plot  method  and  finally  by  the  selection  of  a  sample  plot  by  eye.  On  these  plots, 
he  first  arrives  at  the  volume  of  the  average  tree  either  by  direct  approximation  or 
by  selection  of  a  tjT^ical  tree  whose  volume  is  ascertained  from  a  volume  table; 

A  tally  of  the  diameter  and  height  of  each  tree  on  the  plot  and  the  immediate' 
computation  of  the  volume  to  ascertain  the  true  average  tree  for  comparison  with 


Fig.  63. — Method  of  estimating  a 
forty  by  use  of  the  correction 
factor.  Points  at  which  obser- 
vations are  taken  shown  by 
dots. 


308        IMPROVING  THE  ACCURACY  OF  TIMBER  ESTIMATES 

the  ocular  guess.  Two  days  of  this  work  will  greatly  improve  the  ability  of  the  cruiser 
to  substitute  ocular  methods  for  measurements. 

An  opportunity  to  run  out  strip  estimates  in  which  he  does  his  own  compass  work, 
counting  the  trees  ahead  of  him  in  rectangular  blocks.  The  volume  of  these  trees 
is  obtained: 

By  the  log-run  method  of  estimating  the  number  of  logs  in  the  average  tree 
and  the  average  contents  of  the  log  or  log  run  per  thousand; 

By  selecting  an  average  tree  in  volume  for  each  of  eight  separate  strips,  the 
total  tally  of  which  is  kept  separate.  This  principle  could,  after  practice,  be  applied 
to  the  entire  forty,  or  to  separate  groups. 

The  exact  details  of  this  system  as'  to  size  of  sample  plots,  widths  of  strip  and 
methods  of  tallying  heights  were  worked  out  for  Southern  yellow  pine,  and  several 
of  these  points  would  need  modification  if  applied  to  timber  of  radically  different 
type  and  conditions.  But  the  general  method  of  careful,  original  measurement 
of  the  control  plots  and  of  proceeding  from  a  100  per  cent  intensive  estimate 
through  various  stages  of  less  intensive  work  in  which  the  six  classes  of  averages 
are  employed  as  substitutes  for  the  full  tally,  can  be  worked  out  for  any  forest 
type  and  form  the  basis  of  rapid  and  practical  training  in  the  art  of  timber 
cruising. 

239.  Check  Estimating.  Just  as  in  the  training  of  a  cruiser  his 
greatest  drawback  is  lack  of  any  check  on  his  estimates,  so  check  esti- 
mating does  not  benefit  the  cruiser  unless  he  can  be  told,  not  only  what 
the  extent  of  his  error  is,  but  just  how  he  made  it.  Check  estimating 
must  depend  either  upon  the  infallibility  of  the  check  estimator,  which 
may  be  questioned  in  the  mind  of  the  person  checked,  or  by  the  sub- 
stitution of  actual  measurements  on  a  basis  which  removes  all  source 
of  doubt,  leaving  only  cull  and  quality  to  be  judged.  Check  estimates 
should  therefore  be  made  on  definite  areas  or  strips,  prevously  or  sub- 
sequently estimated  by  the  cruiser  and  on  which  a  record  has  been  kept 
similar  to  that  indicated  in  the  description  of  the  methods  of  training 
timber  cruisers.  The  tree  count,  the  total  volume,  the  average  volume 
per  tree,  but  most  important,  the  tendency  to  over-estimate  heights 
and  diameters  should  all  be  checked  separately.  When  this  is  done, 
one  of  two  things  will  happen.  Either  the  cruiser  will  rapidly  acquire 
a  much  greater  accuracy  or  he  will  demonstrate  his  complete  unfitness 
for  the  job  of  timber  cruising  and  can  be  put  on  other  work. 

240.  Superficial  or  Extensive  Estimates.  The  preliminary  examina- 
tion of  a  tract  of  land  for  the  purpose  of  determining  roughly  whether 
it  has  timber  of  value  and  approximately  how  nmch,  calls  for  the  exercise 
of  the  maximum  of  skill  and  experience  in  order  to  attain  a  reasonable 
degree  of  accuracy  in  the  minimum  of  time  allowed. 

A  description  of  the  estimation  of  a  tract  of  2300  acres  for  the  Blov^ming  Grove 
Hunting  and  Fishing  Club,  located  in  Pike  County,  Pennsylvania,  will  serve  as  an 
illustration  of  methods  possible  in  such  an  examination.  The  field  work  on  Taylor's 
Creek  logging  unit  occupied  two  days  including  travel  to  and  from  the  unit.  Not 
much  over  one  day  was  put  on  the  estimate  itself.     The  fundamental  basis  of  the 


CHECK  ESTIMATING 


309 


methods  employed  was  the  location  of  corners  with  the  aid  of  a  guide,  the  use  of  a 
map  and  the  sketching  of  the  boundaries  of  areas  of  different  types  by  intersection, 
aided  by  rough  triangulation  from  known  points.  Cardinal  directions  for  strips  were 
not  attempted  in  any  instance.  This  tract  was  afterwards  estimated  by  the  strip 
method,  running  5  per  cent  of  the  area.     The  comparison  of  the  two  methods  and 


Estimate   of  Taylor' 


TABLE  XLVI 

Creek  Logging  Unit,  Blooming  Grove  Tract, 
County,  Pa.,  1911 

A.  By  extensive  methods,  in  two  days'  time,  one  man  with  guide.    . 

B.  By  4-rod  strip,  5  per  cent  of  area,  diameters  cahpered,  average  heights. 


Pike 


Type 


Area. 


Acres 


Method  of  cruising 

employed  under 

A 


Estimate. 


Error  by  First 
Method 


M 

feet 

B.M. 

A  2178 

B2214 

A 

248 

B 

445 

A 

750 

B 

397 

A 

750 

B 

527 

A 

250 

B 

89 

A 

100 

B 

125 

A 

250 

B 

282 

Amount 

M  feet 

B.M. 


Per  cent 


Pitch  pine, 
pure  stands 


scattered   on 
burns 


White  oak  and 
hardwoods 


Swamps  with 
hardwood 
and     conifers 


375 


1275 


200 


450 


Pitch  pine  j-acre    circular  plots 
for  sizes 
8-rodrectangularplots 
coimted,  when  con- 
venient 

Pitch  pine  16-rod  strip  counted, 
when  convenient 

White  oak  Total  count  of  large 
trees 
Average  trees  guessed 
at 

Spruce  [j-acre  circular  plots, 
selected  by  guess  for 
average  stand  per 
acre 

Hemlock 


36 


1.7 


-197 


+353 


-  47 


+  88 


Total . 


2300 


Yellow 

poplar 
Ash 

White 
pine 


Some  poplar  counted 


Treetops  counted 
from  hiU.  Average 
tree  guessed  at 

Uniform  old  growth 


+223  +  42 
+161  I  +181 
-  25        -  20 


32 


11.3 


A  4526      +526     i    +   10.9 
B  4079  i  i 


310         IMPROVING  THE  ACCURACY  OF  TIMBER  ESTIMATES 

their  results  is  made  on  the  basis  of  the  assumption  that  accurate  results  on  this 
area  were  obtained  by  the  strip  method.  The  cost  of  the  original  estimate  was  S60.00 
or  2.6fi  per  acre,  1.3^  per  thousand.  The  cost  of  the  subsequent  strip  estimate 
was  8p  per  acre  or  4?f  per  thousand.  The  results  clearly  show  that  the  average  stand 
per  acre  was  successfully  obtained  for  the  pitch  pine  types  in  which  the  timber  could 
be  seen,  and  where  the  area  was  carefully  mapped  in  two  degrees  of  density  of  stock- 
ing and  checked  by  strips  and  plots  carefully  selected  there  was  no  need  of  a  subse- 
quent estimate. 

The  method  of  counting  every  tree  was  successful  for  white  pine  since  all  of  the 
tree  tops  were  seen  and  the  average  tree  was  correctly  guessed  at,  but  for  white  oak, 
the  total  count  apparently  failed.  This  was  due  not  to  a  defect  in  the  method  or 
its  application,  but  to  the  fact  that  123,000  feet  of  white  oak  was  found  later  con- 
cealed in  the  swamps.  This  reduced  the  error  to  23  per  cent  for  the  portion  seen 
and  counted. 

The  estimate  of  spruce,  hemlock  and  poplar  broke  dowoi  because  of  the  funda- 
mental difficulty  of  applying  the  sample  plot  method  when  based  upon  selection 
and  not  on  systematic  arrangement.  The  swamp  should  have  been  crossed  and  all 
parts  examined.  As  it  was,  the  sample  plots  were  selected  near  the  boundary  where 
the  timber  was  one-half  to  two-thirds  again  as  heavy  a  stand  per  acre  as  in  the  wetter 
portions.  This  resulted  in  over-estimating  spruce,  hemlock  and  poplar.  An 
area  or  density  correction  here,  or  another  day  spent  on  that  portion  of  the  tract 
would  have  greatly  reduced  this  error. 

In  extensive  mapping  and  estimating  of  large  areas  for  purposes 
of  classification  as  in  the  preliminary  examinations  for  the  establish- 
ment of  national  forests,  rough  sketch  maps  of  the  areas  of  timber 
types  are  made  on  the  above  principles  by  location  of  the  cruiser  on 
a  map  and  by  triangulation.  The  estimate  must  depend  upon  the 
location  of  occasional  sample  plots  chosen  with  the  best  skill  possible 
to  get  average  stands. 

In  State  work  the  construction  of  maps  showing  the  tilnber  resources 
of  the  State  or  of  various  counties  is  usually  carried  on  by  similar 
methods  of  mapping,  using  roads  and  the  principle  of  the  wheel  or 
odometer  for  distances  and  sample  plots  for  average  stands.  In  Massa- 
chusetts a  different  principle  is  employed.  Strips  4  rods  wide  are  run 
at  |-mile  intervals  on  which  detailed  measurements  are  taken  of  the 
stand.  No  attempt  is  made  to  complete  the  map  of  timber  in  the  inter- 
vening areas,  but  the  data  are  assumed  to  show  the  average  for  an  entire 
town,  an  assumption  which  is  probably  correct  owing  to  the  large 
area  involved. 

241.  Estimating  by  Means  of  Felled  Sample  Trees.  In  the  absence 
of  volume  tables  in  earlier  Em'opean  practice,  it  was  found  that  volume 
of  stands  could  be  determined  by  calculating  the  diameter  of  the  aver- 
age tree,  felling  it  and  determining  the  cubic  volume.  This  volume 
multiplied  by  the  number  of  trees  in  the  stand  was  supposed  to  give 
the  number  of  cubic  feet  in  the  entire  stand.  Since  height  and  form 
factor  of  individual  trees  both  varied  over  a  wide  range,  it  was  quite 


METHOD  OF  DETERMINING  THE  DIMENSIONS  OF  A  TREE    311 

difficult  to  get  a  tree  which  was  actually  an  average  for  the  stand,  but 
when  the  stand  was  divided  into  diameter  groups,  any  required  degree 
of  accuracy  could  be  obtained,  according  to  the  number  of  groups  made. 

In  determining  the  diameter  of  the  average  tree,  the  arithmetical 
mean  of  diameters  gave  too  small  a  result  since  the  volumes  of  trees 
of  uniform  height  are  in  proportion  to  D'^.  With  a  table  of  the  areas  of 
circles,  the  total  basal  area  or  sum  of  the  areas  of  the  cross  sections  at 
D.B.H.  for  all  the  trees  on  the  plot  was  obtained  and  divided  by  the 
number  to  obtain  the  average  basal  area.  The  diameter  correspond- 
ing to  this  basal  area  was  that  of  the  tree  sought.  Where  a  tree  of  this 
exact  diameter  to  yV-inch  could  not  be  found,  a  larger  or  smaller  tree 
was  selected  and  the  difference  found  by  the  proportion  existing  between 
the  basal  areas  of  the  tree  measured  and  the  tree  desired.  This  method 
is  termed  the  Mean  Sample  Tree  Method. 

In  this  country  the  application  of  these  methods  has  been  confined 
to  a  few  early  investigations  into  the  cubic  volume  of  cordwood  in  second- 
growth  hardwoods.  The  difficulty  of  selecting  a  tree  of  average  height 
and  form  as  well  as  basal  area  and  the  expense  of  felling  and  measuring 
a  tree  makes  the  use  of  volume  tables  far  preferable  whenever  these 
are  dependable,  and  their  substitution  is  practically  universal.^ 

242.  Method  of  Determining  the  Dimensions  of  a  Tree  Contain- 
ing the  Average  Board-foot  Volume.  Another  use  of  sample  trees  is 
in  connection  with  the  determination  of  the  age  and  growth  of  stands 
rather  than  to  determine  their  volume.  For  this  purpose,  the  volume 
of  the  stand  is  first  found  from  volume  tables  and  the  average  tree  then 
determined.  The  volume  sought  is  that  of  a  tree  which  when  multi- 
plied by  the  namber  of  trees  on  the  plot,  will  give  the  total  volume  of 
the  plot  in  the  unit  of  volume  which  was  used  in  estimating. 

1  A  recent  test,  1920,  by  J.  Nelson  Spaeth,  Harvard  Forest  School,  in  second- 
growth  hardwoods,  in  which  mean  sample  trees  for  each  3-ihch  diameter  group 
were  measured,  gave  the  following  comparison  of  accuracy  with  the  use  of  a  standard 
volume  table,  although  the  latter  was  for  but  one  species,  red  maple,  comprising  but 
15  per  cent  of  the  stand : 


Method 

Yields  per  |  acre. 
Cords 

Error. 
Per  cent 

Actual  volume  cut 

5.725 

5.772 
5.935 

Standard  volume  table       

+  1  70 

+3.84 

The  refinements  of  these  methods,  known  as  Draught's,  Urich's  and  Hartig's 
Methods,  are  set  forth  in  Graves'  Mensuration,  pp.  224-242.  For  application  to 
American  problems  that  of  the  Mean  Sample  Tree  is  probably  sufficient. 


312         IMPROVING  THE  ACCURACY  OF  TIMBER  ESTIMATES 

Wlien  cubic  volume  is  used  the  average  tree  will  not  be  the  same 
in  diameter  as  when  the  board-foot  unit  is  employed.  The  explanation 
for  this  difference  is  that  the  volume  sought  is  a  weighted  average  of 
the  merchantable  contents  of  all  of  the  trees  on  the  plot.  Trees  of 
different  diameters  do  not  have  the  same  weight  in  this  average  when 
measured  for  board  feet  as  when  measured  for  cubic  contents.  The 
tree  containing  the  average  board-foot  volume  will  be  larger  than  the 
other.  The  smaller  trees  in  the  stand  when  measm-ed  in  board  feet 
are  more  immature  than  they  are  for  cubic  feet  and  the  merchantable 
portion  of  the  stand  actually  includes  a  lesser  proportion  of  the  whole. 
In  stands  which  are  not  of  even  age,  this  merchantable  portion  would 
exclude  many  of  the  younger  trees  as  being  unmerchantable  although 
they  would  be  included  in  the  cubic  volume,  and  the  average  age  as 
well  as  size  of  the  portion  merchantable  for  board  feet  is  greater  than 
that  included  in  the  cubic  volume.  (The  increase  in  average  age  of 
stands  due  solely  to  the  exclusion  of  a  portion  of  the  stand  is  a  recog- 
nized fact  in  European  practice.) 

To  determine  the  size  as  well  as  volume  of  the  average  tree  of  a 
stand,  we  have  two  variables,  height  and  diameter,  one  of  which  must 
be  fixed  or  eliminated  before  the  other  can  be  determined.  The  first 
step  is,  therefore,  to  determine  the  average  height  of  trees  of  each  diam- 
eter by  a  height  curve  (§  209).  The  average  tree  can  then  have  but  a 
single  height  and  diameter  and  these  dimensions  may  be  found  from 
a  curve  of  volume  based  on  diameter  for  the  plot. 

This  curve  may  be  taken  from  a  standard  volume  based  on  diam- 
eter and  height  (§  143)  by  selecting  the  volumes  corresponding  to  the 
average  heights  for  each  diameter  interpolated  if  necessary  to  the 
nearest  foot.  At  only  one  point  on  this  curve  will  the  average  volume 
coincide  with  the  diameter. 

243.  The  Measurement  of  Permanent  Sample  Plots.  The  purpose 
of  locating  and  measuring  permanent  sample  plots  is  to  determine  the 
growth  of  stands.  Their  original  measurement  therefore  must  be  made 
by  methods  which  will  permit  of  an  exact  scientific  comparison  of  these 
wuth  subsequent  measurements.  In  this  way,  not  only  can  the  growth 
of  individual  trees  be  determined,  but  all  changes  which  take  place  in 
the  forest  by  decadence  and  by  the  operation  of  natural  forces,  insects, 
fungi  and  cutting  and  thinning,  or  other  silvicultural  measures  may  be 
noted. 

Permanent  sample  plots  should  be  located  on  land  under  perma- 
nent and  stable  ownership  and  should  be  accessible  and  easily  found  for 
subsequent  inspection  and  for  a  maximum  of  protection.  The  plot 
should  be  square  or  rectangular  and  marked  by  permanent  corners, 
plainly  labeled.     Sample  plots  should  be  located  in  stands  having 


THE  MEASUREMENT  OF  PERMANENT  SAMPLE  PLOTS        313 

uniform  conditions  and  their  size  should  be  governed,  first,  by  the 
possibility  of  securing  this  uniformity  and  second,  by  the  expense  of 
measurement  which  limits  the  size  of  the  plot.  Third,  wherever 
possible,  there  should  be  a  control  strip  of  exactly  similar  timber  sur- 
rounding the  plot  on  all  four  sides  in  order  to  eliminate  the  influence 
of  different  conditions  of  density  or  site  around  the  borders  of  the  plot. 

The  merchantable  timber  on  these  plots  is  measured  as  follows: 

Tree  Number.  Each  tree  should  be  permanently  numbered  either 
by  white  paint  or  by  attaching  a  metal  tag  to  the  tree  with  a  copper 
nail. 

D.B.H.  The  point  at  D.B.H.  is  measured  and  spotted  with  white 
paint  or  by  the  position  of  the  tag.  The  D.B.H.  is  measured  with  a 
diameter  tape. 

Crown  Class.     The  crown  class  is  one  of  the  following  : 

re  =  trees  standing  alone; 

d  =  dominant; 

c  =  co-dominant; 

z  =  intermediate; 

s  =  over-topped,  suppressed. 

Height.  The  height  is  measured  to  the  nearest  even  foot  with  a 
standard  hypsometer.  The  Klaussner  principle,  which  gives  one 
measurement,  is  preferred. ^ 

Forms  are  used  which  provide,  for  each  tree,  five  vertical  columns 
in  which  to  record  the  original  and  four  subsequent  measurements 
which  are  taken  at  either  5-  or  10-year  intervals. 

The  trees  on  such  plots  are  usually  numbered  and  measured  indi- 
vidually down  to  4  inches,  although  in  some  instances  2  inches  is 
adopted  as  the  basis  for  individual  tree  records. 

Immature  timber  below  these  sizes  usually  calls  for  smaller  plots 
which  are  sometimes  laid  out  as  subdivisions  of  a  larger  permanent 
plot.  The  sizes  of  these  plots  are  in  proportion  to  the  intensiveness  of 
the  problem  and  the  age  of  the  timber.  For  determining  the  conditions 
which  affect  germination,  plots  from  10  to  20  feet  square  are  large 
enough.  On  these  plots  every  seedling  is  counted  and  sometimes  each 
is  marked  by  inserting  a  pin  on  which  a  tag  can  be  attached.  In  this 
way  the  mortality  and  survival  of  the  seedlings  can  be  later  ascertained. 
For  the  study  of  the  development  of  reproduction,  larger  plots,  up  to 
1  acre  in  size,  are  required.     On  such  plots  there  is  no  effort  to  keep 

1  Some  New  Aspects  Respecting  the  Use  of  the  Forest  Service  Hypsometer, 
Herman  Krauch.     Journal  of  Forestry,  Vol.  XVI,  No.  7,  p.  772. 

Comparative  Tests  of  the  Klaussner  and  Forest  Service  Hypsometer,  D.  K. 
Noyes,  Proc.  Soc.  Am.  Foresters,  Vol.  XI,  1916,  p.  417. 


314        IMPROVING  THE  ACCURACY  OF  TIMBER  ESTIMATES 

a  history  of  each  individual  tree,  but  the  total  number  of  trees  in  each 
class  is  recorded  in  height  classes  as  follows: 

Overtopped  0  =|'  in  height; 
I' =  2'  in  height; 
2' =  4' in  height; 
4'=1"  in  diameter. 
Free,  same  classes. 

By  inch  classes,  1,  2  and  3  inches.  In  these  inch  classes 
the  trees  are  recorded  in  five  crown  classes:  x,  d,  c,  i, 
and  s  previously  indicated. 

References 

"  Average  Log  "  Cruise,  W.  J.  Ward,  Forestry  Quarterly,  Vol.  V,  1907,  p.  268. 
Errors  in  Estimating  Timber,  Louis  Margolin,  Forestry  Quarterly,  Vol.  XII,  1914, 

p.  167. 
A  Method  of  Timber  Estimating,  Clyde  Leavitt,  Forestry  Quarterly,  Vol.  II,  1904, 

p.  161. 
Forest  Mapping  and  Timber  Estimating  as  Developed  in  Maryland,  F.  W.  Besley, 

Proc.  Soc.  Am.  Foresters,  Vol.  IV,  1909,  p.  196. 
An  Efficient  System  for  Computing  Timber  Estimates,  C.  E.  Dunstan,  C.  R.  Gaffey, 

Forestry  Quarterly,  Vol.  XIV,  1916,  p.  1. 
Timber  Estimating  in  the  Southern  Appalachians,  R.  C.  Hall,  Journal  of  Forestry, 

Vol.  XV,  1917,  p.  311. 
Some  Problems  in  Appalachian  Timber  Appraisal,  W.  W.  Ashe,  Journal  of  Forestry, 

Vol.  XV,  1917,  p.  322. 
Determining  the  Quality  of  Standing  Timber,  Swift  Berry,  Journal  of  Forestry, 

Vol.  XV,  1917,  p.  438. 

Reviews 

Error  of  Strip  Survej  (Sweden),  Journal  of  Forestry,  Vol.  XVI,  1918,  p.  938. 

Estimating  for  Yield  Regulation,  Schubert,  Forestry  Quarterly,  Vol.  XIII,  1915, 
p.  399. 

European  Methods  of  Estimating  Compared  for  Accuracy,  Forestry  Quarterly, 
Vol.  XIV,  1916,  p.  521. 

Volume  Tables  and  Felling  Results,  Forestry  Quarterly,  Vol.  IX,  1911,  p.  632. 

Results  of  Errors  in  Measuring,  Schiffel,  Forestry  Quarterly,  Vol.  IX,  1911,  p.  628. 

Methods  of  Estimating  Compared,  Prof.  Zoltan  Fekete  (Hungary),  Forestry  Quar- 
terly, Vol.  XIV,  1916,  p.  521. 

A  New  Method  of  Cubing  Standing  Timber  (Hungary),  Forestry  Quarterly,  Vol. 
XII,  1914,  p.  474. 


PART  III 
THE  GROWTH  OF  TIMBER 


CHAPTER  XXn 
PRINCIPLES    UNDERLYING    THE    STUDY    OF    GROWTH 

244.  Purpose  and  Character  of  Growth  Studies.  The  growth  of 
timber  is  studied  in  order  to  determine  the  rate  of  annual  production 
of  wood  as  a  crop  on  forest  land.  The  yield  of  farm  products  is  annual 
and  is  measured  at  harvest.  The  essential  difference  between  farm 
and  wood  crops  is  that  the  period  required  to  produce  the  latter  is  many- 
years  in  extent,  and  due  to  this  fact  forest  land  is  not  the  only  capital 
involved  in  crop  production.  The  growth  which  the  trees  lay  on 
annually  becomes  in  turn  part  of  the  capital  to  which  future  growth 
is  added  in  the  same  manner  as  interest  which  is  added  to  a  savings 
account. 

This  increase  in  total  volume  of  a  stand  of  timber  does  not  continue 
indefinitely,  but  only  up  to  a  certain  age,  which  marks  the  culmination 
of  growth  of  the  stand,  from  which  time  the  losses  occurring  in  the  stand 
more  than  counterbalance  growth,  and  its  volume  and  value  diminish. 
Forest  crops  therefore  mature  as  do  annual  crops  and  one  of  the  pur- 
poses of  growth  study  is  to  determine  the  period  required  for  maturity. 

The  basic  facts  to  be  determined  in  the  study  of  growth  are,  first, 
the  total  yield  of  stands  in  terms  of  quantity  of  products,  quality,  and 
money  value,  for  the  period  requued  to  grow  a  crop  of  timber  from 
origin  to  maturity;  second,  the  average  annual  rate  of  growth  to  which 
this  final  yield  is  equivalent,  which  is  termed  the  mean  annual  growth 
and  is  comparable  to  sunple  interest  on  land  as  capital  or  to  annual 
crops;  thud,  the  actual  growth  or  increase  in  volume,  quality,  or  value, 
laid  on  during  definite  periods  in  the  growth  of  the  stand.  The  growth 
for  these  short  periods  is  expressed  either  as  current  annual  growth  which 
is  the  growth  for  a  single  year,  periodic  annual  growth  which  is  the  aver- 
age annual  growth  for  a  short  period,  or  periodic  growth  which  is  the 

315 


316         PRIN'CIPLES  UNDERLYING  THE  STUDY  OF  GROWTH 

total  growth  for  the  short  period.  The  length  of  these  periods  is  com- 
monly a  decade,  but  may  be  from  5  to  40  years.  The  term  current 
annual  growth  is  commonly  used  in  place  of  the  term  periodic  annual 
growth,  as  indicating  the  average  annual  growth  for  a  short  period 
instead  of  the  separate  growth  for  a  single  year,  though  this  use  of  the 
term  is  technically  incorrect . 

Finally,  the  relation  which  the  increase  in  volume  or  growth  bears 
to  the  volume  of  the  tree  or  stand  on  which  it  is  produced  may  be 
expressed  as  growth  per  cent,  and  indicates  the  rate  of  increase  with 
relation  to  the  wood  capital  required  for  its  production.  This  growth 
per  cent  may  be  computed  for  volume  alone,  for  growth  in  quality  of 
wood,  or  for  growth  in  the  unit  price  of  the  product  (§  334).  A  growth 
per  cent  figure  is  not  an  index  of  absolute  increase  in  either  volume, 
quality  or  price,  since  it  is  merely  the  expression  of  a  relation  between 
capital  and  increment  existing  at  a  given  time.  Growth  per  cent  is 
usually  based  upon  a  single  year's  growth,  either  current  or  average 
for  a  period.  One  year's  growth  is  seldom  measured,  since  a  decade, 
or  at  a  minimum,  a  five-year  period  is  required  to  eliminate  variable 
factors  affecting  a  single  season's  growth  caused  by  climatic  conditions. 
Hence  periodic  annual  growth  is  commonly  substituted  for  current 
annual  growth  as  a  basis  for  computing  growth  per  c?nt. 

245.  Relation  between  Current  and  Mean  Annual  Growth.  Growth 
may  be  studied  either  for  an  individual  tree  or  for  a  stand,  expressed  in 
terms  of  growth  per  acre.  In  either  case,  the  current  annual  growth 
in  volume  increases  at  first  slowly  and  then  more  rapidly  to  a  maximum, 
after  which  it  begins  to  decline  and  finally  ceases  with  the  death  of  the 
tree  or  the  beginning  of  actual  decadence  of  the  stand.  The  sum  of  the 
current  annual  growths  laid  on  for  the  entire  period  gives  the  total 
growth.  The  total  growth  or  volume  divided  by  the  age  in  years 
gives  the  mean  annual  growth  (Fig.  64). 

The  mean  annual  growth  is  an  average  rate  of  growth  representing 
the  total  growth  or  yield  at  a  given  age,  distributed  or  spread  over  this 
period.  The  actual  productiveness  of  the  forest  is  in  this  way  compared 
with  annual  crops,  which  basis  is  otherwise  obscured  by  the  varying 
rate  or  curve  of  growth  in  volume  of  the  trees  from  decade  to 
decade. 

The  mean  annual  growth  at  any  given  year  is  this  average  of  past 
production.  Current  growth  for  the  year  or  decade  tends  to  increase 
constantly  up  to  a  given  maximum.  During  this  period  the  volume 
added  each  year  to  the  total  volume  of  the  stand  is  greater  than  the 
average  or  mean  annual  growth  up  to  that  year.  Hence  this  average 
is  raised  and  the  curve  of  mean  annual  growth  increases.  But  it  can- 
not increase  at  as  rapid  a  rate  as  the  current  growth  curve,  since  the 


CURRENT  AND  MEAN  ANNUAL  GROWTH 


317 


effect  of  this  increase  for  the  year  upon  the  average  increase  is  spread 
over  all  previous  years. 

When  the  current  annual  growth  curve  reaches  its  culmination  and 
begins  to  decline,  the  successive  average  or  mean  annual  growth  figures 
for  each  year  still  continue  to  increase  in  spite  of  this  fact,  since  the 
amount  of  growth  added  to  the  stand  during  the  year  although  less 
than  formerly  is  still  greater  than  the  average  or  mean. 

When  the  current  growth  for  the  year  finally  falls  to  an  amount 
equal  to  the  average  or  mean  for  the  entire  crop  period,  the  curve  of 
mean  annual  growth  has  reached  its  highest  point.     During  the  follow- 


160 

140 

gl20 
fa 

sioo 


^ 

\ 

/ 

\ 

y 

\ 

c 

r 

\ 

Ij 

\ 

Year 
ilea 

ofCul 
1  Ann 

minat 
alGr 

on  of 
wth 

: 

,^-^ 

^ 

> , 

, , 

c 

§/ 

■M 

f" 

r 

\. 

^ 

^ 

/ 

»v 

f 

H 

/r 

0       5      ID      15      20     25     30      35     40     45      50     55      60     65     70 
Age  in  Yearg 

Fig.  64. — Current  and  mean  annual  growth  of  a  normal  stand. 
Jack  Pine   Minnesota. 


ing  and  subsequent  years  the  current  growth  laid  on  is  less  than  this 
mean,  hence  this  average  or  mean  begins  to  drop,  but  only  to  the  extent 
that  it  is  pulled  down  by  the  effect  of  this  lesser  current  annual  growth 

for  single  years    upon   the   fraction, ^ ■.     Hence    as  before, 

age  m  years 

this  mean  growth    curve   falls  more  slowly  than   the  current  growth 

curve.     Unless  these  stands  are  cut,  losses  in  the  stand  will  finally 

exceed  the  growth,  and  the  current  growth  curve  would  then  become 

negative.     But  until  the  entire  stand  is  destroyed,  the  curve  of  mean 

annual  growth  will  still  be  positive.     When  properly  computed  on  the 

basis  not  merely  of  volume,  but  of  quality  and  price  increment  as  well, 

the  year  of  culmination  of  mean  annual  growth,  rather  than  the  current 

growth  data,  indicates  the  maturity  of  a  stand  and  the  age  at  which, 

if  cut,  it  wUl  produce  the  greatest  average  yields,  when  the  period  of 

production  is  taken  into  account. 


318 


PRINCIPLES  UNDERLYING  THE  STUDY  OF  GROWTH 


246.  The  Character  of  Growth  Per  Cent.  The  growth  per  cent  of 
a  tree  or  stand  cannot  be  compared  with  the  per  cent  of  interest  earned 
annually  on  a  fixed  capital,  since  this  growth  is  not  separable  from 
the  wood  capital  on  which  it  is  laid,  and  thus  causes  this  capital  or  base 
volume  to  increase  annually.  To  maintain  the  same  rate  of  growth 
per  cent  on  this  increasing  volume,  the  amount  of  the  annual  growth 
must  continue  to  increase  at  a  geometric  rate.  Although  the  increase 
in  volume  of  a  stand  during  the  period  of  most  rapid  current  growth 
for  a  time  does  approach  a  geometric  rate  when  compared  to  a  given 
or  fixed  initial  volume,  yet  even  here  the  effect  of  the  constantly  and  rapidly 
increasing  volume  of  accumulated  wood  capital  upon  the  current  annual 
rate  of  increase  will  cause  this  rate  of  growth  per  cent  to  drop  consistently 
throughout  the  entire  life  of  a  tree  or  stand.  The  actual  behavior  of 
the  growth  per  cent  of  a  stand  is  shown  by  the  following  table: 

TABLE  XLVII 

Growth  of  Jack  Pine,  Minnesota  * 


Age. 

Yield  per  acre. 

Periodic 

Mean 

Periodic 

annual  growth. 

annual  growth. 

annual  growth. 

Years 

Cubic  feet 

Cubic  feet 

Cubic  feet 

Per  cent 

20 

160 

8 

25 

650 

98 

26 

24.20 
14.12 
9.52 
4.68 
2.40 
1.56 
1.24 
1.08 
0.88 
0.80 

30 

1360 

142 

45 

35 

2210 

170 

63 

40 

2800 

118 

70 

45 

3160 

72 

70 

50 

3420 

52 

68 

55 

3640 

44 

66 

60 

3840 

40 

64 

65 

4010 

34 

62 

70 

4180 

34 

60 

♦From  Bui.  820,  U.  S.  Dep.  Agr.,  1920,  Table  10,  p.  14. 

247.  The  Law  of  Diminishing  Numbers  as  Affecting  the  Growth 
of  Trees  and  Stands.  The  growth  in  volume  of  individual  trees  tends 
at  first  to  follow  a  rate  of  geometric  increase.  Were  the  diameter  growth 
of  trees  to  remain  uniform  for  a  long  period,  a  condition  characteristic 
of  many  species,  notably  white  and  sugar  pine,  the  resultant  area  and 
volume  growth  would  increase  at  a  ratio  similar  to  that  of  D^,  rather 
than  D  (§  270).  This  rate  of  volume  growth  is  strengthened  by  height 
growth.  With  maturity,  the  height  growth  of  trees  falls  to  insignificant 
proportions  and  the  diameter  growth  of  many  species  falls  off  to  a  marked 
extent.     The  result  is  a  flattening  out  of  the  curve  of  volume  growth, 


LAW  OF  DIMINISHING  NUMBERS 


319 


which  would  otherwise  continue  to  ascend  sharply.  This  influence 
of  age  and  maturity  upon  individual  trees  which  survive  is  due  to  loss 
of  vitality,  but  the  same  effect  is  observed  in  all  the  remaining  trees 
which  are  suppressed  during  the  growth  of  the  stand  and  ultimately 
die  because  the  space  needed  for  their  normal  expansion  is  appropriated 
by  more  vigorous  trees. 

A  forest  or  stand  represents  an  area  of  land  stocked  with  trees. 
The  number  of  trees  which  can  grow  and  thrive  upon  the  acre  is  in 
inverse  ratio  to  the  size  of  crown  spread  and  space  required  by  the 
individual  tree.  As  trees  increase  in  size  their  numbers  will  be  reduced. 
Ths  enormous  number  of  seedlings  which  may  spring  up  on  an  acre 
is  merely  a  guarantee  that  a  few  will  survive  to  maturity.  The  curve 
of  diminishing  numbers  which 
is  characteristic  of  all  species 
and  classes  of  timber,  drops 
very  rapidly  in  the  first  few 
years,  and  more  gradually  later  o 
on.  Numbers  diminish  most  <^''''^ 
rapidly  during  the  period  of  1^^*^ 
rapid  height  growth  and  crown  t^°^ 
expansion.  When  trees  have  ^i°°° 
reached  their  mature  heights,  |  ^so 
their  numbers  have  been  re-  =  eoo 
duced  to  a  point  where  the  250 
further  diminution  is  a  much 
slower  process. 

The   cause    of    reduction   is    Yig.   65.— Number   of  trees  per  acre  at  dif. 
at   first   failure    to    survive   the        ferent    ages    in    fully    stocked    stands    of 
juvenile  period  because  of   un-      white  pine.    From  Table  XLVIII. 
favorable  climatic  or  soil  factors 

and  competition  with  other  vegetation,  followed  by  suppression  due 
to  the  competition  of  older  trees  or  of  trees  of  the  same  age  which  have 
attained  dominance  by  some  advantage  at  the  start.  The  crown  is 
restricted  in  size  and  spread,  is  finally  overtopped,  and  the  tree  dies. 

This  process  is  accompanied  by  a  change  in  the  rate  of  diameter 
growth  for  the  trees  whose  crowns  and  growing  space  are  restricted 
in  the  struggle.  Consequently  the  dominant  trees  maintain  at  all 
times  the  most  rapid  rate  of  diameter  and  volume  growth,  while  others 
which  at  a  given  period  have  not  yet  lost  their  dominance  and  still 
show  a  rapid  rate  of  growth,  will  later  on,  with  the  closing  of  the  crowns 
and  crowding  of  the  tree,  show  a  falling  off  in  growth,  sometimes  quite 
sudden  in  character.  The  prediction  of  the  future  growth  of  an}^  single 
tree  is  therefore  impossible  without  knowing  whether  the  tree  will  main- 


40     50     60     70     80     90    100 
Age,  years 


320  PRIN'CIPLES  UNDERLYING  THE  STUDY  OF  GROWTH 

tain  its  position  in  the  stand  and  subdue  its  competitors.     The  net 
growth  on  an  acre  is  the  sum  of  the  growth  of  the  surviving  trees. 

At  am-  given  period  or  year  in  the  life  of  a  stand,  the  number  of 
trees  is  considerably  less  than  were  present  and  living  at  any  previous 
period  or  decade,  and  is  considerably  greater  than  the  number  which 
will  be  alive  at  any  given  period  or  decade  in  the  future.  This  loss  in 
numbers,  accompanied  by  rapidly  lessening  rates  of  growth  of  a  portion 
of  the  surviving  trees,  plus  the  normal  growth  of  the  remainder,  produces 
the  net  result  or  increase  in  the  stand  for  the  period,  and  any  method 
of  study  of  growth  which  does  not  take  this  natural  loss  and  change 
into  account  will  be  ineffectual  in  predicting  or  measuring  the  growth 
of  forests  or  stands. 

248.  Yields,  Definition  and  Purpose  of  Study.  The  past  growth 
of  the  surviving  portion  of  stands  is  represented  by  their  present  volume, 
the  measurement  of  which  is  dealt  with  in  Part  11.  This  present 
volume  represents  the  yield  of  the  area,  provided  nothing  has  pre- 
viously been  removed  as  thinnings  or  otherwise.  But  without  a  knowl- 
edge of  the  period  required  to  produce  this  volume,  the  word  yield  is 
meaningless  as  it  cannot  be  expressed  in  terms  of  the  rate  of  produc- 
tion per  3^ear  or  mean  annual  growth.  An  estimate  of  standing  timber 
is  merely  a  statement  of  the  volume  at  present  found  on  the  area.  A 
yield,  on  the  other  hand,  is  a  statement  of  the  volumes  produced  on 
the  area  within  a  definite  period  of  time.  If  the  total  volume  is  to  be 
expressed  as  a  yield,  then  the  total  age  of  the  stand  must  also  be  known. 
If  the  yield  for  a  shorter  period,  such  as  a  decade,  is  to  be  stated,  then 
only  that  portion  of  the  volume  of  the  standing  timber  must  be  shown 
as  was  laid  on  during  this  period.  Otherwise,  the  rate  of  growth  per 
year  is  not  indicated. 

The  growth  of  forests  is  studied  primarily  for  the  purpose  of  pre- 
dicting future  growth  on  forest  land.  On  the  basis  of  past  records  of 
growth  of  trees  and  stands  as  shown  by  measurements  of  present 
attained  volumes  and  of  age,  predictions  can  be  made  as  to  the  future 
growth  of  these  and  of  similar  stands. 

This  application  or  prediction  may  be  made  in  one  of  two  ways: 

1.  By  projecting  the  rate  of  growth  of  an  existing  stand  into  the 
future.  This  is  done  either  by  assuming  that  the  rate  shown  in  the 
immediate  past  will  continue  unchanged  in  the  immediate  future,  or 
else  that  this  rate  will  change  and  that  this  tendency  of  future  growth 
may  be  predicted  by  the  shape  of  the  past  growth  curve.  Of  these 
two  assumptions  the  second  is  apparently  the  more  accurate,  but  in 
neither  case  is  it  possible  to  predict  the  growth  for  more  than  a  short 
period. 

2.  Some  better  method  of  prediction  is  required  to  cover  longer 


YIELD  TABLES 


321 


periods  and  to  determine  the  probable  yield  of  crops  of  timber,  the 
production  of  which  is  the  purpose  of  forestry.  This  is  accomplished 
b}^  the  second  general  method  of  prediction  which  rests  on  the  principle 
of  comparison.  The  past  growth  of  existing  stands  is  taken  as  an  indi- 
cation of  the  expected  future  growth  of  other  younger  stands  whose 
prediction  is  desired  for  a  similar  period.  It  is  assumed  that  similar 
stands  will  grow  in  a  similar  manner.  The  task  consists  of  demon- 
strating the  relation  between  the  stands  whose  past  growth  is  measured 
and  those  whose  future  growth  is  sought. 

249.  Yield  Tables.  The  most  practical  and  useful  expression  of 
growth  is  a  yield  table  which  shows  the  yields  per  acre  for  even-aged 
stands  at  different  ages  by  five-  or  ten-year  periods  separated  into 
different  qualities  of  site.  An  example  of  such  a  yield  table  is  shown 
below : 

TABLE  XLVIII 

Yield  Table  for  White  Pine  * 
Quality  II  f 


Average 

Diameter 

Number 

Basal 

Total  Yield 

height 
of 

breast- 
high  of 

of 
trees 

area 
per 

Age. 

dominant 

average 

per 

acre 

trees. 

tree. 

acre 

Cubic  feet 

Board  feet 

Years 

Feet 

Inches 

Square  feet 

10 

6.0 

1.4 

2015 

20 

650 

15 

12.0 

2.2 

1834 

50 

1,150 

20 

19.5 

3.2 

1626 

90 

1,750 

25 

28.0 

4.1 

1420 

131 

2,420 

5,400 

30 

36.5 

5.1 

1192 

169 

3,250 

9,600 

35 

44.5 

6.1 

950 

193 

4,180 

15,900 

40 

51.5 

7.1 

760 

209 

5,130 

23,500 

45 

58.0 

.8.0 

633 

221 

6,100 

30,600 

50 

64.0 

S.9 

537 

232 

7,000 

36,600 

55 

69.5 

9.8 

460 

241 

7,800 

42,000 

60 

74.5 

10.7 

397 

248 

8,500 

46,900 

65 

79.0 

11  6 

348 

255 

9,200 

51,600 

70 

83.0 

12.4 

311 

261 

9,840 

56,100 

75 

86.5 

13.3 

277 

267 

10,400 

60,200 

80 

90.0 

14.1 

251 

272 

10,930 

64,000 

85 

93.0 

14  9 

229 

277 

11,400 

67,500 

90 

95.5 

15.7 

210 

282 

11,850 

70,900 

95 

98.0 

16.4 

195 

286 

12,250 

74,000 

100 

100.0 

17.1 

182 

290 

12,630 

77,000 

*  Taken  from  Tables  4  and  6  in  "  White   Pine  under  Forest  Management,"  U.  S.  Dept.  Agr. 
Bui.  13,  Washington,  1914,  pp.  22  and  23. 

t  Similar  tables  are  prepared  for  Qualities  I  and  III. 


322 


PRINCIPLES  UNDERLYING  THE  STUDY  OF  GROWTH 


From  the  above  table,  the  periodic  growth  for  separate  five-year 
periods  may  easily  be  obtained  by  subtracting  the  volume  at  one  age 
from  that  of  the  succeeding  period. 

250.  The  Application  of  Yield  Tables  in  Predicting  Yields.  An 
example  of  the  prediction  of  volume  growth  in  existing  stands  of  timber, 
on  the  basis  of  periodic  growth  by  decades  is  given  in  the  following 
table  which  shows  the  present  yield  of  timber  over  10  inches  and  the 
future  yield  which  may  be  realized  upon  the  timber  left  standing  below 
this  diameter  limit,  and  not  shown  in  the  table. 


TABLE  XLIX 

Yield  per  Acre  of  Spruce  Cutting  to  Various  Diameter  Limits  * 

Based  on  stands  containing  approximately  5000  feet  B.M.  of  timber   10   inches 
and  over  in  D.B.H.  per  acre 


Am't 

Second  Cut 

Second  Cut 

Second  Cut 

• 

of  first 

after  Ten 

after  Twen- 

after Thir- 

cut. 

Years 

ty  Years 

ty  Years 

Interval 
required 

between 

Num- 

Num- 

Num- 

equal 

ber  of 

ber  of 

ber  of 

cuts 

Board 

mer- 

Board 

mer- 

Board 

mer- 

Board 

in 

feet 

chant- 
able 
trees 

feet 

chant- 
able 
trees 

feet 

chant- 
able 
trees 

feet 

years 

Cutting  to  a  10-inch  limit 

5213 

7.3 

365 

16.2 

1087 

26.8 

2483 

43 

Cutting  to  a  12-inch  limit 

4341 

14.3 

1208 

21.6 

2325 

30.5 

4109 

32 

Cutting  to  a  14-inch  limit 

3382 

10.3 

1470 

16.8 

3044 

40.8 

6351 

21 

♦Compiled  from  Yield  Tables  in  "  Practical  Forestry  in   the  Adirondacks,"  Bui.  26,  Division 
of  Forestry,  U.  S.  Dept.  Agr.,  1899,  pp.  83  and  84. 

To  understand  the  use  or  application  of  a  yield  table  in  predicting 
growth,  it  must  be  realized  that  the  stand  or  rate  of  growth  upon  a 
given  acre  or  tract  will  seldom  if  ever  exactly  agree  with  that  shown  in 
a  yield  table  even  when  these  yields  are  separated  by  qualities  into 
3,  4  or  5  classes  of  site.  In  the  case  of  bare  land  or  very  young  timber, 
this  probable  difference  may  be  ignored,  the  site  regarded  as  equivalent 
to  one  of  the  site  classes  given  and  the  yield  predicted  as  if  it  would 
coincide  with  that  of  the  table.  But  for  most  stands  which  have  already 
reached  a  considerable  age  and  the  prediction  of  whose  further  growth 
is  desired,  a  comparison  with  the  yield  table  should  give  a  more  exact 
prediction  of  the  growth  of  the  stand  in  question.     The  yield  table  in 


PREDICTION  OF  GROWTH 


323 


this  case,  instead  of  predicting  exact  future  growth,  is  used  as  a  standard 
to  express  the  relative  increase  or  decrease  in  the  yield  or  stand  per  acre. 
The  yields  may  be  plotted  and  will  form  curves  of  growth  in  volume, 
per  acre.  The  yield  of  any  stand  whose  present  volume  and  age  are 
known  represents  a  definite  per  cent  of  some  existing  yield  from  this 
table.  The  growth  of  this  stand  may  be  predicted  by  using  the  same 
per  cent  of  the  values  in  the  table  for  the  future. 

In  Fig.  66  the  present  yield  of  a  plot  of  white  pine  of  fifty  years  is 
indicated  and  the  basis  of  prediction  for  its  future  yield  is  shown. 
This  percentage  relation  based  upon  standard  yield  tables  is  exten- 
sively applied   in  forestry  to  obtain  the  actual  yields  of  large  forest 


10,000 

9,000 

«  8,000 

^7,000 

•g0,OOO 

55,000 
■g 

fl  4,000 

13,000 

>  2,000 

1,000 

0 


^ 

Quali 

yi 

^ 

^' 

''" 

< 

Quali 

y  n 

/ 

y 

f''" 

/ 

/ 

y 

y 

^ 

Quali 

ym 

/ 

/ 

-'y 

■^ 

/, 

/] 

\y 

/ 

/ 

/ 

riot  X 

They 

at  50  'years  yields 
f  Quality  I  standar 
eld  at!65  years  is 

J. 

M 

'/ 

predicted  as 
standard  at 
For  P;lot  o 

92  5t  of  the 
that  a'ge. 
he  relation 

^ 

// 

108  5f 
to  ye 

^s^" 

lity  I  I  at 

7" 

25      30     35     40 


45      50      55 
Age  in  Years 


Fig.  66. — Method  of  predicting  yields  of  specific  stands  by  comparison  with  standard 
curves  of  yield  for  different  qualities  of  site.     White  Pine,  Mass. 

areas.     It  is  the  basic   idea   underlying   the   prediction   of  growth  by 
the  method  of  comparison. 

251.  Prediction  of  Growth  by  Projecting  the  Past  Growth  of  Trees 
into  the  Futiire.  By  either  of  these  methods,  comparison  or  projec- 
tion, it  is  assumed  that  no  records  exist  of  the  past  condition  of  the 
stands  whose  growth  is  to  be  found.  Their  present  volume,  and  the 
age  and  past  growth  in  diameter,  height  and  volume  oj  the  trees  now 
standing  can  be  studied,  but  there  is  no  reliable  indication  of  the 
number  of  trees  lost  during  the  past  period,  though  evidences  remain 
for  a  time  in  the  form  of  dead  and  down  trees. ^ 


^  The  writer  once  noticed  in  a  densely  stocked  stand,  the  stems  of  hundreds  of 
small  lodgepole  pine  which  had  fallen  across  a  tamarack  log  and  been  preserved  from 
decay,  when  all  trace  of  similar  dead  trees  on  the  forest  floor  had  disappeared. 


324  PRINCIPLES  UNDERLYING  THE  STUDY  OF  GROWTH 

In  using  the  past  growth  of  a  stand  on  which  to  base  the  prediction 
of  its  future  growth,  these  records  of  past  growth  of  the  Hving  trees 
in  diameter,  height  and  volume  are  the  only  data  available.  This 
prediction  is  based  on  one  of  two  assumptions,  either  that  the  growth 
for  a  future  period  will  continue  at  the  same  rate  as  shown  for  a  past 
period,  or  that  this  future  growth  will  be  at  a  different  rate,  either  increas- 
ing or  decreasing,  and  that  the  amount  of  this  change  may  be  deter- 
mined by  a  study  of  past  growth. 

In  the  use  of  either  of  these  methods  to  predict  the  growth  of  trees, 
the  method  may  be  applied  either  to  the  volume  of  the  tree  or  to  its 
diameter  and  height  instead.  If  a  volume  analysis  is  made  for  two 
or  more  past  decades,  it  may  be  assumed  either  that  this  rate  of  volume 
growth  will  continue  unchanged,  an  assumption  which  is  practically 
never  correct,  or  that  the  curve  of  volume  growth  which  may  be  plotted 
from  past  volumes  can  be  prolonged  to  indicate  the  growth  of  the  next 
decade. 

But  the  method  more  commonly  employed  is  to  substitute  a  study 
of  diameter  and  height  growth  for  volume  analysis.  If  future  diameter 
growth  is  assumed  to  be  at  the  rate  shown  in  the  past  decade,  future 
volume  growth  will  increase  (§  270).  If  the  past  growth  in  diameter 
is  plotted,  and  a  curve  projected,  the  future  diameter  so  obtained  is 
the  basis  of  the  predicted  growth  in  volume. 

252.  The  Effect  of  Losses  versus  Thinnings  upon  Yields.  The 
first  conception  in  the  study  of  growth  is  apt  to  be  that  it  consists  chiefly 
of  measuring  the  growth  in  diameter,  height  and  volume  of  individual 
trees.  Although  it  is  true  that  growth  per  acre  is  based  primarily  upon 
the  rate  of  growth  of  the  individual  trees  which  make  up  the  stand 
and  that  according  as  this  rate  of  tree  growth  is  rapid  or  slow,  the  yield 
per  acre  will  be  large  or  small,  yet  the  total  giowth  per  acre,  which  is 
the  result  desired  in  all  growth  studies,  is  the  product  of  the  growth 
of  individual  trees  and  the  number  of  trees  surviving  to  the  end  of  a 
future  period  plus  such  growth  as  may  take  place  on  trees  which  die 
and  are  removed  during  the  period.  The  death  of  a  certain  number  of 
trees  in  the  stand  during  the  period  will  have  this  effect,  that  if  these 
trees  can  be  removed  as  thinnings,  their  volume  at  the  beginning  of  the 
period,  augmented  slightly  by  growth  which  takes  place  in  them  before 
they  die,  is  part  of  the  yield  for  the  period,  but  does  not  appear  in  the 
volume  of  the  standing  timber  alive  at  its  end.  If  these  trees  cannot 
be  harvested,  their  total  volume  as  originally  measured  will  disappear 
from  the  live  stand,  and  constitute  a  negative  growth  or  loss  which 
must  be  deducted  from  the  growth  on  the  surviving  trees  before  the  actual 
volume  of  the  stand  at  the  end  of  the  period  can  be  correctly  ascertained 
from  its  volume  at  the  beginning. 


AGE  IN  EVEN-AGED  VERSUS  MANY-AGED  STANDS  325 

This  problem  may  be  illustrated  as  follows : 

A  stand  of  pine  has  now  10,000  board  feet  per  acre.  The  growth  for  ten  years 
upon  the  trees  which  will  survive  will  be  4000  board  feet.  The  trees  which  will  die 
in  ten  years  have  now  a  volume  of  1500  board  feet.  This  means,  first,  that  the 
growth  of  4000  board  feet  is  actually  put  upon  a  present  volume  of  8500  board  feet; 
second,  that  the  remaining  1500  board  feet  must  either  be  included  in  or  deducted 
from  the  final  yield,  on  the  basis  of  whether  it  is  actually  salvaged  or  not.  There 
may  have  been  some  growth  on  these  trees,  but  this  can  be  neglected.  On  the  assump- 
tion that  no  cutting  of  thinnings  is  possible,  the  net  yield  on  this  acre  at  the  end  of 
the  decade  is  12,500  board  feet.  If  thinnings  are  harvested,  the  yield  is  14,000  board 
feet.  Had  the  growth  prediction  been  attempted  by  measuring  the  growth  of  indi- 
vidual trees,  those  representing  the  1500  board  feet  would  have  to  be  excluded  from 
the  calculation  of  total  growth  in  either  case.  Unless  salvaged,  they  represent  an 
actual  negative  growth  reducing  the  net  gain  by  1500  board  feet. 

Unless  it  is  possible  to  guess  just  how  many  and  which  trees  are 
going  to  die,  not  only  the  volume,  but  the  growth  for  ten  years  on  some 
of  these  trees  wiU  probably  be  erroneously  included,  instead  of  being 
subtracted  from  the  predicted  total  yield  in  ten  years.  The  possible 
error  in  subtracting  either  too  few  or  too  many  trees  is  very  large 
since  the  size  of  the  eiTor  is  doubled  for  stands  when  thinnings  are 
impractical.  It  is  obvious  that  a  method  depending  instead  on  direct 
measurement  of  the  result  at  the  end  of  the  period  on  older  stands 
and  the  comparison  of  such  measurements  with  similar  younger  stands 
furnishes  a  safer  basis  of  growth  predictions  on  these  younger  stands 
for  any  considerable  period  than  efforts  to  project  into  the  next  period 
the  rate  of  growth  of  the  trees  now  standing. 

Where  stands  are  under  intensive  management,  the  trees  which 
will  die  are  thinned  out,  probably  at  the  beginning  of  the  period,  and 
utilized.  The  loss  for  the  succeeding  ten-year  period  is  then  exceedingly 
small  unless  accidental  im-oads  occm-  from  wind,  insects  or  other  destruc- 
tive agencies  not  anticipated.  It  is  therefore  safer  to  predict  growth 
for  short  periods  on  stands  which  have  been  under  management  and 
have  been  thinned  than  it  is  on  stands  where  thinnings  and  utilization 
of  the  dying  material  is  impossible. 

253.  The  Factor  of  Age  in  Even-aged  versus  Many-aged  Stands. 
Where  stands  are  measured  as  a  unit  to  determine  the  production  per 
acre,  three  factors  are  needed:  first,  the  present  volume  of  the  stand; 
second,  its  average  age  or  the  time  which  it  took  to  produce  this  volume; 
third,  the  area  which  it  occupies.  The  age  of  the  stand  as  a  whole 
is  desired.  If  the  stand  is  even-aged  it  is  sufficient  to  determine  merely 
the  age  of  one  of  the  trees  adequately  to  measure  the  period  of  pro- 
duction and  the  rate  per  year.  This  can  be  done  by  counting  the  annual 
rings  of  growth  without  any  measurement  whatever,  on  the  assumption 
that  the  species  has  formed  but  one  annual  ring  per  j'ear.  This  premise 
does  not  always  hold  good,  since  with  certain  species  in  certain  localities, 


326         PRINCIPLES  UNDERLYING  THE  STUDY  OF  GROWTH 

false  rings  may  be  formed,  giving  two  rings  per  season  (§  256).  Pro- 
vided age  can  be  determined,  the  study  of  diameter,  height  and  volume 
growth  of  individual  trees  is  entirely  uimecessary  for  even-aged  stands, 
as  a  means  of  determining  the  yields  per  acre. 

But  where  stands  are  composed  of  trees  of  different  ages  on  the 
same  area,  it  becomes  practically  impossible  to  determine  the  average 
age  of  the  stand  by  any  such  direct  method.  Within  certain  limits, 
that  is,  if  the  ages  of  the  trees  composing  the  stand  do  not  vary  too 
greatly,  it  is  possible  to  determine  an  age  which  may  be  accepted  as 
the  average  period  required  to  produce  the  present  volume.  Where 
the  diversit}^  of  age  is  so  great  that  this  is  impossible,  it  is  necessary 
to  shift  the  basis  of  age  determination  from  the  mere  counting  of  the 
rings  to  a  determination  of  the  age  of  trees  of  a  given  size  or  diameter. 
To  determine  ages,  trees  must  be  cut  down  or  the  center  reached  by 
borings  or  choppings.  While  possible  on  one  or  two  trees,  it  becomes 
out  of  the  question  to  test  every  tree  in  this  manner  without  cutting 
down  the  stand.  Diameter,  on  the  other  hand,  can  be  readily  measured. 
For  stands  of  mixed  ages,  therefore,  two  methods  are  possible.  By 
the  first,  the  average  diameter  of  the  trees  in  the  stand  is  found,  and  the 
age  of  a  tree  of  this  size  is  determined  and  is  assumed  to  indicate  the 
average  age  of  the  stand.  By  the  second,  no  attempt  is  made  to 
determine  the  age  of  the  stand,  but  instead  the  growth  may  be  studied 
for  trees  of  given  diameters,  and  for  a  short  current  period,  past  and 
future.  Either  method  requires  the  measurement  of  the  diameter 
growth  of  trees  to  determine  the  number  of  years  or  period  which  is 
required  to  produce  trees  of  given  sizes  or  to  grow  1  inch  in  diameter. 

254.  The  Tree  or  Stem  Analysis  and  the  Limitations  of  its  Use. 
The  volume  growth  of  an  individual  tree  may  be  analyzed  with  almost 
absolute  accuracy  by  cross-sectioning  the  bole  and  measuring  the  width 
of  the  annual  rings  at  different  sections  by  decades.  This  is  termed 
stem  analysis,  or  tree  analysis.  The  accuracy  of  these  results  for  a  single 
tree  is  apt  to  create  a  false  impression  in  the  minds  of  investigators 
as  to  the  value  of  the  figures  thus  obtained.  To  what  use  will  volume 
or  total  tree  analyses  of  growth  of  trees  be  put?  What  question  will 
they  answer?  Will  they  predict  the  growth  per  acre  of  stands  or  the 
rate  of  growth  per  year  on  an  acre  of  land?  The  cost  of  a  tree  analysis 
is  excessive  compared  with  the  direct  measurements  of  yields  and 
total  age  or  even  the  measurement  of  diameter  growth  on  the  stump. 
The  number  of  trees  which  may  be  analyzed  is  therefore  limited.  How 
shall  these  trees  be  selected?  It  has  been  seen  in  the  study  of  volume 
tables  that  trees  vary  quite  extensively  in  form.  To  get  average 
growth  we  must  be  sure  of  obtaining  average  form.  Average  form  is 
best  obtained  by  averaging  hundreds  of  trees  as  is  done  in  the  prepa- 


CLASSES  OF  GROWTH  DATA,  CHART  GROWTH  STUDIES       327 

ration  of  volume  tables,  but  the  few  trees  analyzed  for  growth  may 
be  either  cylindrical  or  neiloidal  in  form.  We  therefore  may  have  a 
perfect  record  of  the  past  growth  of  certain  selected  trees  which  vary 
in  form  and  volume  at  least  10  per  cent  from  the  average  desii'ed. 

Even  if  this  difficulty  can  be  overcome  by  careful  selection  of  trees 
of  average  form  quotient,  and  a  few  of  these  average  trees  analyzed 
for  past  growth,  how  are  these  past  results  to  be  applied  in  predicting 
future  growth?  It  is  evident  that  the  growth  of  individual  trees  is 
only  a  part  of  the  problem,  for  the  average  tree  in  a  well-stocked  stand 
at  a  given  age  does  not  remain  the  average  tree  for  future  periods  and 
was  not  the  average  tree  at  any  period  in  the  past.  The  trees  which 
die  in  a  stand  are  naturally  the  smaller,  more  suppressed  specimens 
with  the  smallest  diameters.  In  the  lapse  of  a  ten-year  period,  the 
loss  of  a  number  of  trees  from  the  lower  diameter  classes  will  raise  the 
average  diameter  and  volume  of  the  remaining  trees  so  that  the  tree 
which  is  now  the  average  is  in  ten  years  dropped  into  a  class  below  the 
average. 

There  is  but  one  way  of  even  approximating  the  growth  of  a  stand 
in  the  future  by  means  of  the  analysis  of  volume  growth  of  individual 
trees.  If  the  number  of  trees  which  will  probably  survive  to  a  given 
age  can  be  predicted  (which  can  best  be  ascertained  by  the  method 
of  comparison  and  yield  tables),  the  selection  of  this  number  from  a 
younger  stand,  taking  trees  wholly  in  the  dominant  class,  will  indicate 
the  character  of  tree  which  must  be  cut  and  measured  to  determine 
the  growth  for  the  future.  Yet  even  here  it  is  better  to  take  a  tree 
which  is  fully  mature  and  shows  the  growth  for  the  entire  period,  in 
which  case  the  stand,  rather  than  the  tree,  is  the  better  unit. 

255.  Relative  Utility  of  Different  Classes  of  Growth  Data,  and 
Chart  of  Growth  Studies.  To  sum  up  these  principles:  past  growth 
is  measured  in  order  to  predict  future  growth.  Growth  on  an  area 
and  not  the  growth  of  single  trees  is  wanted.  The  three  essentials 
of  growth  are  volume,  time  and  area.  For  even-aged  stands  the  time 
element  is  the  total  age  and  may  be  determined  by  counting  rings  on 
one  or  two  sample  trees.  This  requires  a  minimum  of  investigation 
in  addition  to  volume  measurements. 

Diameter  growth  of  trees  comes  next  in  importance  and  is  used 
when  size  must  be  depended  upon  to  determine  age  either  for  the  total 
period  or  for  shorter  current  periods  of  growth  when  diameter  is  sub- 
stituted for  age. 

Height  growth  of  trees  comes  third  in  importance  since  it  is  used 
to  indicate  site  quality  (§  296).  It  may  also  be  used  together  with 
diameter  growth,  to  predict  the  volume  growth  of  trees  by  a  method 
much  shorter  than  volume  analysis  (§  288). 


328 


PRINCIPLES  UNDERLYING  THE  STUDY  OF  GROWTH 


Volume-growth  analysis  of  individual  trees,  although  apparently 
the  most  accurate  and  scientific  basis  of  growth,  is  in  reality  the  least 
important  and  most  inefficient  when  expense  is  compared  with  results. 
It  is  invaluable  to  determine  the  laws  of  tree  growth  and  the  changes 
which  may  take  place  in  the  form  of  individual  trees  as  the  result 
of  changed  conditions,  as  for  instance,  on  cutover  lands,  and  as  a  pre- 
caution against  accepting  general  figures  based  on  volume  tables  and 
other  short  methods  of  growth  study.  But  ordinarily,  even  where 
volume  of  trees  is  desired,  it  will  be  obtained  from  diameter  and  height 
growth  supplemented  by  use  of  the  form  quotient  rather  than  from 
the  stem  analyses  of  trees.  Many  thousands  of  stem  analyses  have 
been  made  in  the  past  whose  results  were  either  not  worked  up  at  all 
or  since  compilation  have  reposed  in  the  archives  of  Government  and 
States  while  investigators  vainly  sought  an  answer  to  the  pressing 
problems  as  to  what  was  the  actual  rate  of  growth  per  year  on  national, 
state  and  private  forests. 

The  best  possible  basis  for  growth  predictions  is  the  actual  records 
of  the  growth  in  successive  periods  of  specific  forest  stands  whose 
history  is  known  and  whose  conditions  of  management  are  fixed.  The 
establishment  of  sample  areas  which  are  measured  successively  by 
ten-year  periods  will  give  a  firm  basis  for  growth  predictions  superior 
either  to  the  method  of  comparison,  based  on  past  growth  of  older 


Chart  of 


Purpose  of  growth  study  §  244 


I  [Normal   or   index   yields 

Productive  capacity  of  different  qualities  of  forest      per  acre  for  even-aged 

stands 
,  Pure  stands — §  304 


Field  measurements 


1,   Diameters  B.H. 
§  309 
2.  Mixed  stands— §  314   2.  Heights,  total 


3.   Count  of  annual  rings 
on  average  trees — 
§262 


Prediction  -of 
future 
growth  and 
yiel  d  s  on 

natural'  For  total  age 
forest  areas      or  long  per- 
—§§247-         iods— 
248  §§249-250 


For  even-aged  stands 
— §§  256-262 


Comparison  of  stands  1.  Timber  estimate  sepa- 
with  normal  yields  at  rated  by  age  classes — 
same  age — §  301  §  344 

2.  Counts  of  annual  rings 
on  average  trees — 
§262 


CLASSES  OF  GROWTH  DATA,  CHART  GROWTH  STUDIES     329 

stands,  or  to  the  effort  to  predict  the  growth  of  stands  from  that  of 
the  trees  which  they  contain.  As  a  result  of  similar  actual  records 
of  production  the  working  plans  for  some  European  forests  dispose  of 
the  subject  of  growth  quickly,  stating  substantially  that  the  growth 
in  this  class  of  forest  is  known,  from  past  records  covering  (perhaps) 
200  years,  to  be  about  so  much. 

In  the  chart,  on  pages  328-333,  eleven  main  lines  of  investigation 
of  growth  are  listed,  as  a  guide  to  the  discussions  in  the  following  chap- 
ters. The  object  of  a  study  should  first  be  understood,  and  the  con- 
dition of  the  stands  to  which  it  is  to  be  applied,  as  indicated  in  the 
three  columns  under  "  Purpose  of  Growth  Study."  In  the  column 
under  "  Basis  "  the  principles  on  which  the  solution  of  the  problem 
depends  are  outlined. 

The  remaining  columns  are  self-explanatory.  Column  6  shows  the  steps 
by  which  the  study  can  be  applied  to  large  areas  of  forest  land,  thus  secur- 
ing the  data  for  which  the  preceding  steps  are  merely  preliminar>\ 

By  using  this  chart  as  a  guide,  and  consulting  the  references  to 
discussions  of  principles  and  methods,  under  each  step,  one  may  hold 
the  purpose  of  growth  studies  clearly  in  mind  and  choose  the  best 
method  of  accomplishing  the  desired  object. 

The  relative  importance  and  reliability  of  the  methods  given  are 
indicated  by  the  quality  of  type  used  in  the  table. 

Growth  Studies 


Office  rcfords 


Final  data  obtained 


Application  to  forest 
areas 


Data  derived  from  the 
investigation 


1.  Area  of  sample  plots —  1.  Volume  per  acre — • 


«!  308 

Volumes  of  trees  (vol 

ume  tables) — §  131 

Age  of  sample  trees- 

§  255,  §  257 

Height     of     dominant 

trees— §    310,    §    311 

§312 


V)  306 

Age  of  stands- 


3.  Height  of  stands 


Classification  of  site  qual- 
ities—§  294,  §  345         I 

1.  On    basis     of    heightil.  Mean    annual    growth 
growth— §§  296-310     |  — §  245 

2.  On    basis    of    volume  2.  Number   of   trees   per 
growth— §  295,  §  312  acre 

3.  Basal  area  per  acre 


4.  Maturity   of   stands- 
§  244  (rotation) 

5.  Maximum  yields 


Area  of  stand  or  age 
class 


Volumes  of  trees  (vol 
ume  tables) §  131 


3.  Age  of  sample  trees — 
$  256,  §  257 

4.  Average    volume    per 
acre  for  age  class 


Reduction  per  cent  or  1. 
relative    volume     de- 
rived  from   this   com- 
parison— §  317 
Empirical    yield    table  2. 
based   on   this   reduc- 
tion—§§  304  316  I 


Empirical  yield  table  to 
predict  future  growth 
on  each  age  class 

Correction    for    i  n  -  2. 
fiuence  of  number  of 
trees  per  acre  at  differ- 
ent ages— §§  301-317 


Future  yields  based  on 
actual  stocking — 
§  301,  §  343 

Losses  due  to  natural 
agencies — §  293 


Gains  possible  from 
protection  and  silvi- 
culture 


330         PRINCIPLES  UNDERLYING  THE  STUDY  OF  GROWTH 

Chaet  of  Growth 


Purpose  of  growth  study 

Basis 

Field  measurements 

III 

1.   Segregation    of    large 

1.  Diameters  B.H. 

For  large  age  groups — 

age  groups — §  320 

§  318,  §  321 

2.  Comparison   of   group 
with  normal  yields  at 
average  age — §  301 

2.  Heights,  average 

based  on  diameter 

3.  Growth  in  diameter  at 
stump,  based  on  age  of 
trees— §§  265-269, 
§320 

Prediction 

of       future 

growth  and 
yields       on 

For  total  age 
or  long  per- 

IV 

1.  Diameter      groups      substi- 

1. Diameters  B.H. 

natural  for- 

iods— 

§§  249-250 

For      many-aged     stands — 

tuted  for  age  classes — §  276 

§  298,  by  diameter  groups 

2.  Comparison     of      diameter 

est  areas — 

—§323 

group  with  normal  yields  at 

2.  Heights 

§§  247-248 

Indicated  age— §  301 

3.  c:ounts  oJ  annual  rings  on 
trees  of  each  diameter  class — 
§  276 

Va 

1.  Space  required  for  develop- 

1. Diameters  of  crowns  based 

For  many-aged  stands  based 

ment  of  Individual   trees— 

on  D.B.H.— §  324 

on  crown  space— §  298 

§  300 
2.  Normal  number  of  trees  per 
acre  at  different  ages— §  247 

2.  Growth  In  diameter  at  stump 
based    on    age    of    trees— 
51  275-279 

3.  Growth  in  height  based  on 
age— §  284 

Vb 

On  thinned  areas — §  326 

Same  as  Va 

Same  as  Va 

Measure  only  dominant  trees — 
§  263 

VI 

Same  as  II 

Same  as  II 

For   even-aged   stands 

— §  335 

VII 

Past   growth    of   existing 

For  many-aged  stands 

trees— §  336 

§253,  §299 

1.   Diameters     B.H.     by 

Predic  tion 

crown  classes 

o  f      future 

For    short 

growth  and 

periods   or 

yields       on 

current 

natural  for- 

growth— 

est  areas — 

§§  251-252 

2.  Heights,  average 

§§  247-248 

based  on  diameter 

3.  Growth  in  diameter  at 

B.H.  or  stump 

— for  given .  period  of 
years— §  278 

— separated  into  2  or  3 
periods  of  five  to 
ten  years — §  279 

CLASSES  OF  GROWTH  DATA,  CHART  GROWTH  STUDIES     331 


Studies — Continued 


Office  records 

Final  data  obtained 

Application  to  forest 

Data  derived  from  the 

areas 

investigation 

1.  Total  number  of  mer- 

1. Areas      occupied      by 

1.  Empirical   yield    table 

S.ame  as  for  II— §  301 

chantable  trees 

each  of  two  age  groups 

applied    to    area    and 

—§319 

age    of    each    group— 
§  322  and  §  346 

2.  Volumes  of  trees  (vol- 

2. Volumes  in  each  age 

2.  Correction  by  segrega- 

ume tables)    (average, 

group — §  321 

tion    of     areas     occu- 

on diameter) 

pied  by  immature  age 

3.  Age   as   basis   of  each 

3.  Reduction  per  cent — 

classes— §§     341  -348, 

group,     from     normal 

§317 

§349 

yield  table 

4.   Diameter  of  tree  of  in- 

4. Empirical   yield   taljle 

dicated  age — §  275 

—§316 

5.  Volume  of  tree  of  indi- 

cated diameter — §  278 

6.   Number    of    trees    in 

each  age  group — §  321 

1.  stand    table    by    diameter 

1.  Areas     occupied     by     each 

1.  Empirical    yield    table    ap- 

Results only  approximate  due 

classes— §  188 

diameter  group — §  319 

plied  to  area  of  each  diam- 

to substitution    of   diameter 

eter  group 

for  age 

2.  Volumes  of  trees 

2.  Volumes  In  each  group 

2.  Correction  by  segregation  ol 

3.  Average  age  of  trees  of  given 

3.  Reduction  per  cent— §  317 

areas  occupied  by  Immature 

diameters— §  276,  §  323 

4.  Empirical  yield  table — §  316 

age  classes—!   341.    §   348. 
§  350 

1.  Space  occupied  by  circular 

Artificial    normal    yield    table 

Reduction  per  cent  for  applica- 

Substitute for  yields  based  on 

crowns  and  resulting  num- 

based on  number  and  size  of 

tion    of    yield    table    deter- 

even-aged stands  when  latter 

ber  per  acre— §  324 

trees  at  each  age — §  324 

mined     by     comparLson     of 

cannot  be  obtained 

2.   Relation      between      crown 

numbers    of    trees    of    each 

spread      and       diameter — 

diameter  on  area  with  num- 

§ 324 

ber  per  acre  In  table — §  325 

3.   Height  and  volume  of  trees 

of  each  diameter— §  288 

4.   Average  diameter  of  trees  at 

each  age— §  275 

Same  as  Va 

Same  as  Va 

Same  as  Va 

Means  of  predicting  yields  of 
thinned  stands 

Same  is  II 

Same  as  II 

Same  as  II 

Most  accurate  basis  for 
current  growth  f  o  r 
short  periods,  on  even- 
aged  stands — §  327 

Growth  per  cent 

As  applied   to   trees  and 

stands 

1.  Stand  table  by  diam- 

1. Growth  in  volume  of 

I.  Future  growth  of  trees 

General  method  for  cur- 

eter classes — §  188 

trees  for  future  period 

by    comparison    with 

rent  growth  of  stands 

growth     attained     by 

of    any     character    of 

other  larger  trees  for- 

stocking, form  or  ages, 

merly  of  same  diame- 

and mixture  of  species 

ter — §  278 

— §§  245-342 

2.  Growth    in    diameter 

2.   Number  and  character 

2.  By  extending  into  fu- 

Growth per  cent  (§  246) 

and  height  of  trees  by 

of  trees  which  will  die 

ture  the  past  growth  in 

for    trees    or    stand.s — 

diameter     classes     for 

during  period — §  257 

diameter    on    trees 

This    cannot    in    turn 

past  i^criod — §  277 

whose  future  growth  is 

be      substituted      for 

3.  Volumes  of  trees  now 

3.  Net  volume  growth  for 

sought 

growth    measurements 

and  at  end  of  period. 

stand— §  252 

— by    assuming   it   to 

except     on     similar 

From  volume  tables — 

equal    past    growth 

stands— §§  331-333 

§  288.     (Stem  analyses 

— by  prolonging  curve 

For    stands    whose     age 

only    as    a    check    on 

based  on  past  peri- 

classes  cannot  be  deter- 

accuracy  of  2  and  3) — 

odic     diameter      mined 

§  2.^4 

growth— §  279           i 

332         PRINCIPLES  UNDERLYING  THE  STUDY  OF  GROWTH 

Chart  of  Growth 


Purpose  of  growth  study 


Field  measurements 


— for  last  inch  or  half- 

For  many-aged  stands 

Past    growth  of  existing 

inch    of    radius — 

Prediction 

§  253,  §  299 

trees— §  33G 

§278 

of       future 

For     short 

4.  Growth  in  height 

growth  and 

periods    o  r 

— by  cutting  hack  tip 

yields       on      current 

for    required    pe- 

natural for- 

growth— 

riod— §  294 

est  areas — 

§§  251-252 

— by    substitution    of 

§§  247-248 

relation  of  height 
to  diameter — 
§  285 

VIII 

Past  growth  of  trees  for 

I,  2  and  4  same  as  VII 

For    short 

For  many-aged  stands 

period  since  cutting,  on 

3.  Growth     in     diameter 

periods — 

-§254 

fr)rmerly  cut-over  areas 

preferably  at  B.H.:  for 

§336 

— §  286,  §  336 

period    since    previous 
cutting.    May  be  sepa- 
rated into  five-  or  ten- 
year  periods — §§  278- 

Prediction    oi 

280 

future 

growth  and 

yields      o  n 

c  u  t  0  V  e  r 

areas    on 

For  long  periods 

IX 

1.  Proportion  of  total  area  re- 

Same as  III  or  IV— §  320 

residual 

—5  338 

For  even-aged,  or 

maining  stocked  after  cut- 

stands — 
§280 

large  age  groups  or 

ling,  based  on  density  equal 

diameter  groups 

to  empirical  yield  tables  for 

—5  339 

forest  previous  to  cutting 

2.  Residual  area  assumed  to  be 

clear  cut 

3.  Growth  predicted  for  stocked 

area  by  empirical  yield  table 

—see  II— §  316 

X 

Permanent  sample  plots 

1. 

Diameters  B.H.   with 

Historical  record  of  growth  per  acre — §  326 

remeasured    at   stated 
intervals — §  243 

diameter   tape — §  190 

2. 

Total  heights,  from 
fixed  stations — §  199 

3. 

Crown  classes  and 
condition 

4. 

Plot  description 

5. 

Tree  tags  and  perma- 
nent boundary  monu- 
ments 

XI 

Relation    between   diam- 

1. 

Diameters  B.H. 

Effect  of  numerical  density  of  stocking,  and  of  thin- 

eter     growth,      crown 

2. 

Heights 

nings  on  growth  of  individual  trees  and  on  stand — 

classes  and  numljer  of 

3. 

Growth    in    diameter 

§  270,  §  273,  §  274 

trees    per    acre,    from 

based  on  age,  but  rings 

sample  plots— §  300 

counted  inward,  per- 
mitting study  of  cur- 
rent growth  on  same 
trees— §§  265-269 

CLASSES  OF  GROWTH  DATA,  CHART  GROWTH  STUDIES     333 


Studies — Continued 


Office  records 


Final  data  obtained 


Application  to  forest 
areas 


Data  derived  from  the 
investigation 


4.  Tally  of  trees  with 
suppressed  crowns  or 
those  apt  to  die 


As  applied  to  forest  areas 

1.  Stand  table  by  diam- 
eter classes 

2.  Growth  from  diam- 
eter and  height 
growth  and  volume 
tables 

3.  Correction  for  loss  in 
numbers  of  trees 


Source  of  inaccuracy  is  in 
determining  mortality 
per  cent,  hence  cannot 
be  applied  to  long 
periods 


1,  2,  3  and  4  same  as  VII|] 
5.  Partial  stem  analyses] 
for  current  growth  in 
volume  on  sample 
trees  as  check  on  effect 
of  increased  growth  at 
stump— §  290 


Probable  growth  in 
volume  of  trees  left  on 
cut-over  areas 

2.  Proportion  of  stand 
showing  increased 
growth— §  337 

3.  Loss  in  numbers  and 
net  growth  in  volume 


Future   growth    of    trees 
by     comparison     with 
growth     attained      by 
trees  on  areas  after  cut- 
ting 
Growth  on  forest  areas 
1,  2  and  3  same  as  VII 
4.  Per     cent     of     stand 
showing    increased 
growth— §  337 


Effects  of 

— expansion  of  areas 
of  crowns  and  in- 
creased growing 
space 

— c  ompetition  of 
species  left  after  cut- 
ting 

— degree  of  severity  of 
cutting  on  remaining 
stand 


III  or  IV— §  321 


Areas  In  each  age  class  lorSame  as  III  or  IV — 5  322 
timber  left  on  cut-over  a 


Volumes  In  each  age 
§  339 


Minimum      or       conservative 

yields  on  cut-over  areas 
Xo  Increased  growth  assumed 

Conditions    would     coincide 

with    cutting   of    even-aged 

stands 
Results   contrasted   with   VIII 

as  check  on  that   method   of 

prediction 
Safe    for    application    to    long 

periods 


I 
1.  Individual    record     of  1.  Permanent    record    of  1.   Location  of  plots  with 


each  tree  on  plot  by 
number,  compared  for 
successive  measure-' 
ments  at  five-  or  ten- 
year  intervals  ' 

Record    of    conditions  2.   Causes  and  extent  of 
and    of    external 
fluences 


changes  in  volume, 
number  of  trees,  and 
dimensions  for  plot 


damage 


in  control  strips  on 
areas  showing  typical 
conditions  to  be 
studied 


Current  growth,  measure- 
ment of  all  factors  of 
change  in  stands  under 
conditions  selected — 
§  340 

Yield  tables  for  stands 
grown  under  manage- 
ment. Ultimate  solu- 
tion of  all  growth  prob- 
lems— §  313 


Diameter  growth  for  trees 
of  separate  classes,  by 
diameters,  and  crowns 
— §  275,  §  276,  §  277 


Effect  of  spacing  or  thin 
ning  upon  volume 
growth  and  upon  aver 
age  sizes  and  quality  of 
individual  trees — §  301 


Stand  tables  by  diam 
cter  classes 

Ages  of  stands.  The 
data  are  applied  inten- 
sively to  individual 
stands  in  silviculture 


Proper  spacing  for  plan- 
tations 

Character,  and  frequency 
of  thinnings 

Class  of  material  to  grow 

Character  of  initial  natu- 
ral stocking  desired 

Growth  per  cent  on  stand- 
ing trees — §  330 


334         PRINCIPLES  UNDERLYING  THE  STUDY  OF  GROWTH 


References 

Climatic  Cycles  and  Tree  Growth,  A.  E.  Douglass,  Carnegie  Institute  Pub.  No.  289. 
Tree  Growth  and  Chmate  in  the  United  States.   K.   W.   Woodward.   Journal  of 

Forestry,  Vol.  XV,  1917,  p.  520. 
The  Climatic  Factor  as  Illustrated  in  Arid  America,  Ellsworth  Huntington,  Carnegie 

Institution  of  Washington,  D.  C,  1914,  Chapter  XII. 
Density  of  Stand  and  Rate  of  Growth  of  Arizona  Yellow  Pine  as  Influenced  by 

Climatic  Conditions,  Forrest  Shreve,  Journal  of  Forestry,  Vol.  XV.,  1917    p 

695. 


CHAPTER  XXIII 
DETERMINING  THE  AGE  OF  STANDS 

256.  Determining  the  Age  of  Trees  from  Annual  Rings  on  the  Stimip. 

The  age  of  standing  timber  can  only  be  determined  from  the  ages  of 
the  trees  which  compose  the  stands.  The  age  of  a  tree  is  the  period 
elapsing  from  the  germination  of  the  seed  or  origin  of  the  sprout  to  the 
present  year.  A  record  of  the  number  of  years  of  growth  in  a  tree  is 
made  by  the  formation  of  the  annual  rings  in  which  the  light  spring 
wood  is  sharply  differentiated  in  color  and  texture  from  the  heavier 
and  darker  band  of  summer  wood  of  the  year  preceding.  The  count- 
ing of  these  annual  rings  determines  the  age  of  the  tree. 

It  is  not  always  possible  or  easy  to  make  this  determination.  Unless 
the  growth  of  a  tree  is  marked  by  annual  seasonal  changes,  there  are 
no  annual  rings  to  distinguish.  This  is  true  of  most  species  of  tropical 
woods,  except  those  growing  in  regions  marked  by  an  annual  cessation 
of  growth  due  to  annual  recurrence  of  dry  seasons.  In  some  species 
of  hardwoods  there  is  such  a  slight  difference  between  the  texture  of 
the  spring  and  summer  wood  that  the  annual  rings  can  be  detected 
only  with  difficulty  and  by  the  aid  of  coloring  matter  and  magnifying 
glass.  This  is  true  of  such  trees  as  basswood,  hard  maple  and  sweet 
gum.  Many  trees  on  dry  sites  grow  so  slowly  that  the  annual  rings 
are  almost  impossible  to  distinguish  except  by  a  glass.  In  counting 
rings  it  is  usually  necessary  to  smooth  off  the  surface  with  a  sharp  knife 
or  chisel  in  order  to  bring  out  the  contrast. 

Where  growth  is  affected  by  severe  droughts,  and  sometimes  where 
the  trees  are  defoliated  by  insect  attacks  and  later  acquire  new  foliage, 
a  false  ring  may  be  formed,  giving  two  rings  in  a  single  year  which 
would  lead  to  an  exaggeration  in  the  age  of  the  tree.  This  was  found 
to  be  the  case  with  Rocky  Mountain  juniper  on  dry  sites.  False 
rings  may  be  detected  if  sufficient  care  is  used,  since  they  seldom  form 
a  complete  circle,  but  are  present  on  only  a  portion  of  the  circum- 
ference and  are  therefore  imperfect. 

The  last  annual  ring  of  wood  is  not  completed  until  after  the  growth 
for  the  year  is  finished.     It  must  be  distinguished  from  the  ring  of 
new  bark  laid  down  in  the  same  season.     The  first  two  or  three  rings ' 
on  some  seedlings  are  difficult  to  distinguish. 

335 


336 


DETERMINING  THE  AGE  OF  STANDS 


The  increment  borer  (§  277)  may  be  used  to  determine  the  age 
of  standing  trees  at  breast  height  or  at  any  section  accessible,  provided 
the  diameter  is  not  too  great  and  the  position  of  the  core  of  the  tree 
can  be  found  by  the  instrument.  This  method  is  used  with  such 
species  as  spruce. 

257.  Correction  for  Age  of  Seedling  below  Stump  Height.  The 
number  of  rings  in  any  cross  section  of  a  tree  will  indicate  only  the  age 
of  the  tree  at  that  cross  section  and  not  the  total  age.  No  rings  can 
be  formed  at  a  given  height  above  the  ground  until  the  tree  reaches 
that  height.  The  age  of  each  cross  section  made  in  sectioning  a  tree 
will  be  less  than  that  of  the  section  below  by  just  the  number  of  years 
occupied  in  height  growth  between  the  two  points.  Although  the 
total  age  of  a  tree  can  be  determined  theoretically  by  taking  a  section 
even  with  the  surface  of  the  ground,  this  is  seldom  if  ever  done.  The 
rings  are  counted  at  the  stump,  which  gives  the  age  of  the  tree  minus 
the  time  which  it  took  the  seedling  to  reach  this  height.  To  get  the 
true  age  of  any  tree,  seedling  ages  based  on  height  must  be  added  to 
ring  counts  taken  at  stump  heights.  By  cutting  at  the  ground  and 
counting  the  rings  on  a  sufficient  number  of  dominant  seedlings  which 
are  sure  to  survive  and  therefore  represent  the  average  height  growth 
of  mature  timber  when  at  this  age,  a  table  is  constructed  showing  the 
relation  between  the  age  of  seedlings  and  different  stump  heights.  In 
rapidly  growing  trees  this  makes  from  one  to  five  years'  difference 
in  the  total  age,  but  with  some  species  which  have  a  long  juvenile  period, 
as  much  as  twenty  years  may  be  required  for  a  seedling  to  grow  2  feet 
in  height.  This  is  true  of  certain  Western  conifers.  Hardwood  sprouts 
on  the  other  hand  attain  stump  height  in  the  first  year. 

TABLE  L 

Height  of  Seedlings  at  Different  Ages,  Western  Yellow  Pine,  Colfax  Co., 
New  Mexico 


Age. 

Height. 

Age. 

Height. 

Years 

Feet 

Years 

Feet 

1 

7 

1.7 

2 

0.5 

8 

1.9 

3 

0.7 

9 

2.2 

4 

0.9 

10 

2.4 

5 

1.1 

11 

2.7 

6 

1.4 

12 

3.0 

*  Forest  Tables— Western  YeUow  Pine.     Circular  127,  U.  S.  Forest  Service,  1908. 


ANNUAL  WHORLS  OF  BRANCHES  AS  AN  INDICATION  OF  AGE   337 

The  juvenile  period  for  conifer  seedlings  is,  as  a  rule,  longer  than 
that  for  hardwoods,  though  there  are  exceptions.  Stump  height  may 
be  separated  into  6-inch  height  classes  for  determining  the  number  of 
years  to  add  for  seedling  heights  to  get  total  age  of  tree. 

258.  Annual  Whorls  of  Branches  as  an  Indication  of  Age.  There 
is  another  method,  of  very  limited  application,  for  determining  the  age 
of  standing  trees.  This  is  applied  to  conifers  and  is  confined  to  those 
species  which  form  but  one  whorl  of  branches  per  year.  Species  like 
jack  pine  or  loblolly  pine,  which  form  two  or  more  whorls  per  year, 
cannot  be  judged  in  this  manner.  The  approximate  age  of  the  tree 
and  stand  is  obtained  by  counting  the  number  of  whorls.  This  record 
holds  good  only  when  the  branches  or  dead  stubs  remain  visible  and 
when  the  height  growth  continues  normal.  The  record  is  lost  if  all 
traces  of  the  lower  whorls  are  obliterated.  If  this  is  only  for  a  height 
of  from  5  to  10  feet,  the  average  age  of  trees  of  this  height  may  be 
obtained  from  a  study  of  seedling  heights  and  used  to  supplement 
the  remaining  count.  When  the  height  growth  of  the  tree  has  reached 
its  maximum,  a  new  whorl  of  branches  is  no  longer  formed  annually, 
but  the  leader,  as  well  as  the  branches,  extends  its  growth  by  prolonging 
a  single  shoot. 

The  ages  of  seedlings  of  many  species  may  be  determined  by  count- 
ing whorls  of  branches,  or  terminal  bud  scars  if  the  whorls  are  not  all 
there.  In  such  cases  it  is  not  necessary  to  cut  the  seedlings  and  count 
rings.  The  bud  scars  are  distinct  for  many  years  on  species  such  as 
Douglas  fir,  Alpine  fir,  and  others. 

259.  Definition  of  Even-aged  versus  Many-aged  Stands.  The  age 
of  trees  determines  the  age  of  stands.  But  unless  it  is  known  that 
the  entire  stand  originated  in  a  single  year,  as  is  the  case  with  sprouts 
or  with  some  species  of  conifers,  such  as  jack  pine  or  loblolly  pine 
on  burns,  there  will  be  a  variation  in  age  due  to  natural  seeding  for 
a  period  of  reproduction  which  may  extend  to  fifteen  or  twenty  years. 
Stands  are  termed  even-aged  if  their  crowns  form  practically  a  single 
canopy  or  one-storied  forest,  which  is  true  when  the  period  of  repro- 
duction does  not  exceed  approximately  one-fifth  of  the  rotation  or 
period  required  to  reach  full  maturity.  Where  the  crown  cover  of 
stands  of  mixed  ages  varies  so  greatly  that  it  is  composed  of  different 
stories,  and  must  be  separated  into  component  age  classes  whose  aver- 
age age  is  separately  distinguished,  the  stand  is  termed  many-aged 
or  in  some  cases  all-aged.  The  separation  of  such  stand  may  be  either 
directly  into  age  groups,  or  into  groups  based  on  size  or  diameter  with 
a  limited  range  of  age,  whose  average  age  is  sought. 

260.  Average  Age.  Definition  and  Determination.  The  average 
age  of  a  group  of  trees  showing  a  range  of  ages  nuist  be  that  age  which 


338  DETERMINING  THE  AGE  OF  STANDS 

indicates  or  determines  the  rate  of  volume  production  per  year  at 
which  the  stand  has  grown;  therefore,  the  average  age  must  be  a 
weighted  age  based  on  volume.  The  determination  of  average  age 
applies  only  to  those  stands  which  fall  under  the  definition  of  even-aged 
stands,  yet  have  within  the  limits  of  the  group  a  sufficient  range  of  ages 
so  as  to  require  a  further  investigation  in  order  to  fix  the  weighted  or 
average  age  of  the  group.  For  many-aged  stands,  the  average  age  of 
each  age  class  must  be  determined  separately. 

For  a  given  age  class  or  even-aged  stand  as  thus  defined,  the  average 
age  is  the  age  which  would  be  required  to  produce  an  even-aged  stand 
containing  the  same  volume  as  that  of  the  uneven-aged  stand  in  ques- 
tion. 

The  methods  possible  for  determining  the  weighted  average  age 
of  the  trees  comprising  the  age  class  usually  involve  the  choice  of 

1.  Treating  the  entire  age  class  as  a  single  group,  or  subdividing 

it  into  from  two  to  three,  usually  not  over  two,   sub- 
groups. 

2.  Determining  the  average  tree,  for  the  entire   class,  or   sepa- 

rately for  each  sub-group. 

3.  Ascertaining  the  age  of  these  average  trees. 

4.  Weighting  the  resultant  ages  of  average  trees  of  sub-groups, 

to  determine  the  weighted  average  age  of  the  age  class. 

261.  Determining  the  Volume  and  Diameter  of  Average   Trees. 

Subdivision  of  a  group  into  two  or  more  sub-groups  will  be  made,  if  at 
all,  on  the  basis  of  diameters,  by  the  diameter  group  method  (§  251). 

In  determining  the  average  tree  for  the  age  class,  or  for  a  sub- 
group, there  are  two  reasons  for  basing  this  selection  on  average  volume. 
In  the  first  place,  if  these  selected  trees  are  to  be  felled,  and  their  ages 
taken  as  indicating  that  of  the  stand,  the  larger  trees  must  be  avoided, 
for  in  aU  probability  they  are  advance  growth,  several  years  older 
than  the  rest  or  possibly  belonging  to  an  entirely  different  age  class. 
The  smaller  trees  would  also  be  rejected  since  they  may  be  late  seedlings 
some  years  younger  than  the  average,  or  in  extreme  cases,  so  badly 
suppressed  that  a  certain  number  of  rings  may  be  lacking  and  the 
growth  difficult  to  determine.  Trees  of  about  average  size  for  the  group 
or  stand  must  then  be  chosen.  Where  two  or  more  groups  are  made, 
an  average  tree  for  each  group  is  separately  selected. 

Volume  is  the  determining  factor  upon  which  the  weighted  average 
age  is  to  be  based,  hence  the  tree  whose  age  is  taken  to  indicate  that  of 
the  stand  must  be  a  tree  whose  volume  is  an  average  of  the  stand. 
This  principle  applies  not  merely  to  cubic  volume,  but  to  the  merchant- 
able volumes  expressed  in  units  of  product,  such  as  board  feet.     Since 


DETERMINING  AGE  OF  AVERAGE  TREES  AND  STAND        339 

the  purpose  of  the  investigation  is  to  determine  the  period  which  will 
produce  an  equal  volume  of  material  in  an  even-aged  stand,  the  product 
in  terms  of  which  this  volume  is  measured  actually  affects  the  average 
age  (§260).  For  board-foot  contents  which  increases  more  slowly  at 
first  and  more  rapidly  later  in  the  life  of  an  individual  tree,  the  average 
tree  wiU  be  larger  and  older  than  for  cubic  contents,  since  a  portion  of 
the  stand  will  be  rejected  altogether  and  fall  in  a  younger  age  group 
or  else  will  logically  receive  a  smaller  weight  in  the  average  for  determin- 
ing the  equivalent  age  of  an  even-aged  stand. 

The  first  step  is  therefore  to  determine  the  volume  of  the  average 
tree  of  the  stand  or  sub-group.  It  is  evident  that  the  inclusion  of  a 
large  number  of  trees  of  the  smaller  diameters  in  a  large  group  will 
pull  down  the  volume  of  the  average  tree  and  tend  to  unduly  lower  its 
age.  The  plan  of  subdividing  age  classes  into  smaller  diameter  groups 
is  chiefly  useful  in  avoiding  this  tendency  to  error,  and  is  accomplished 
by  throwing  together  trees  varying  but  little  in  size,  to  obtain  the 
average.  It  is  of  advantage  therefore  to  make  two  or  more  of  these 
sub-groups  where  possible. 

When  volume  is  measured  in  cubic  feet,  basal  area  may  be  sub- 
stituted for  volume  and  the  diameter  of  a  tree  of  average  basal  area 
determined.  To  obtain  this,  the  sum  of  the  basal  areas  of  the  trees 
in  the  group  is  divided  by  the  number  of  trees  to  obtain  average  basal 
area.  The  diameter  of  a  tree  of  this  area  is  found  in  Table  LXXVIII, 
Appendix  C,  p.  490. 

When  measured  in  board  feet,  the  volume  of  the  average  tree  is 
found  directly  by  dividing  the  total  volume  of  the  stand  or  of  the  sub- 
group in  board  feet  by  the  number  of  trees.  As  in  case  of  basal  area, 
the  diameter  of  a  tree  of  this  volume  is  now  required  if  sample  trees 
are  to  be  felled  to  determine  age.  For  this  purpose  a  local  volume 
table  based  on  diameter  is  used  (§  142)  from  which  the  D.B.H.  of 
a  tree  of  the  given  volume  can  be  determined  to  within  iV-inch. 

262.  Determining  the  Age  of  Average  Trees  and  of  the  Stand.  The 
age  of  these  selected  trees  can  then  be  obtained  by  felling  trees  of  this 
diameter.  In  stands  of  variable  age  from  two  to  three  trees  are  pref- 
erable to  one.  As  a  substitute  for  this  method,  where  it  is  extremely 
uncertain  that  the  tree  selected  will  have  the  average  age,  a  table  of 
diameter  growth  showing  the  ages  of  trees  of  different  diameters  may 
be  prepared  from  similar  stands  in  the  vicinity.  If  the  average  rate 
ot  growth  thus  obtained  applies  to  the  stand  in  question,  the  age  of  a 
tree  of  the  given  diameter  may  be  taken  from  this  curve  instead  of 
from  felled  timber.  On  account  of  the  uncertainty  of  the  correlation 
between  the  growth  figures  obtained  in  this  way  and  of  the  age  of  the 
stand  in  question,  the  method  has  not  been  widely  used  and  the  felling 


340 


DETERMINING  THE  AGE  OF  STANDS 


of  the  test  trees  or  their  age  determination  by  borings  or  chopping^ 
is  the  standard  practice  in  determining  the  age  of  stands.  When  the 
stand  is  treated  as  a  single  group,  the  average  of  the  ages  of  the  test 
trees,  all  of  which  will  be  of  the  same  average  diameter,  is  taken  as  the 
age  of  the  stand.  When  two  or  more  sub-groups  have  been  separated, 
the  age  of  the  entire  stand  must  be  calculated  by  weighting  the  pre- 
determined ages  of  the  sub-groups,  in  the  proper  proportions. 

The  following  illustration  will  bring  out  the  different  methods  possible  in  doing 
this.  An  "  even-aged  "  stand  composed  of  30  trees  is  divided  into  two  groups  as 
follows : 


Trees 

Average  volume. 
Board  feet 

Total  volume  of  group. 
Board  feet 

Average  age  of  trees  in 
group. 
Years 

10 
20 

500 
125 

5000 
2500 

100 
70 

1.  If  each  of  these  groups  occupies  an  equal  area  and  is  given  equal  weight,  the 
average  age  may  be  found  by  adding  the  ages  of  the  sample  trees  and  dividing  by  2. 
This  gives  eighty-five  years,  and  is  known  as  the  arithmetical  mean  sample  tree 
method.  This  method  does  not  conform  to  the  basic  principle  of  weighted  ages 
sought. 

2.  When  the  trees  are  weighted  by  number  the  result  is  : 

10X100  =  1000 
20  X  70  =  1400 
Total,  2400^30  =  80  years 
This  overemphasizes  the  number  of  trees  rather  than  their  volume,  hence  is  unsat- 
isfactory. 

3.  Trees  are  Aveighted  by  volume  on  the  principle  by  which  weighted  volume 
averages  are  always  obtained: 

100  years  X  5000  =  500,000 

70  years  X  2500  =  175,000 

Total,  675,000-^7500  =  90  years.     This  method  is  acceptable. 

4.  The  sum  of  the  mean  annual  growth  for  the  groups  is  obtained.  The  total 
volume  divided  by  this  sum  gives  the  average  age.  This  method  is  considered 
by  European  investigators  to  be  more  accurate  than  the  others.     As  applied: 

5000-^100  =  50 

2.500 -^  70  =  35.7 

Total  mean  annual  growth  for  stand,  85 . 7 

7500 -=-85.7  =  87  years. 

By  either  method  3  or  4,  it  is  seen  that  the  average  age  is  influenced  by  volume 
rather  than  by  area  or  number  of  trees. 


AGE  AS  AFFECTED  BY  SUPPRESSION.     ECONOMIC  AGE       341 

263.  Age  as  Affected  by  Suppression.  Economic  Age.  When  stands 
are  comparatively  even-aged  and  the  trees  composing  tliem  have  grown 
up  as  dominant  individuals,  free  from  suppression,  the  actual  age  of 
such  trees  is  a  fair  indication  of  the  age  which  an  even-aged  stand  would 
require  to  produce  an  equal  volume.  But  under  this  same  definition, 
the  age  of  a  tree  which  has  been  suppressed  in  the  early  period  of  its 
life  does  not  indicate  the  required  age  but  one  considerably  greater. 
The  correction  of  the  actual  ages  of  suppressed  trees  to  determine  the 
age  desired  is  known  as  the  determination  of  economic  age.  What  is 
wanted  is  the  rate  of  growth  of  an  average  dominant  tree  on  the  same 
site  as  that  occupied  by  the  suppressed  trees.  Where  reproduction 
takes  place  under  a  stand  either  of  the  same  or  of  a  different  species, 
the  problem  of  growth  is  one  of  having  two  crops  of  timber  on  the  same 
land  at  the  same  time,  and  the  rate  of  production  per  acre  is  the  sum 
of  these  two  successive  crops  divided  by  the  total  period  required  to 
produce  them  both.  To  isolate  the  period  required  for  a  single  crop, 
we  must  determine  the  rate  of  growth  of  the  crop  as  if  it  were  in  sole 
possession  of  the  area. 

A  composite  growth  curve  may  be  built  up  for  average  trees  by 
measuring  the  growth  on  these  trees  only  down  to  the  point  at  which 
they  were  evidently  freed  from  suppression  and  substituting  from  this 
point  on  the  average  growth  of  seedlings  and  saplings  measured  on 
dominant  specimens.  For  instance,  if  the  first  2  inches  of  an  average 
tree  shows  suppression,  the  average  rate  up  to  2  inches  must  be  taken 
from  other  dominant,  younger  trees,  and  added  to  the  remaining  years 
to  get  the  total  economic  age  of  the  tree  in  question.  This  factor  has 
been  neglected  in  American  growth  studies,  for  the  reason  that  with 
such  species  but  few  attempts  have  been  made  to  determine  total 
age,  investigators  being  content  with  ascertaining  growth  for  short 
period  based  upon  the  diameter  of  the  trees. 


CHAPTER  XXIV 
GROWTH  OF  TREES  IN  DIAMETER 

264.  Purposes  of  Studying  Diameter  Growth.  One  purpose  of 
studying  the  growth  of  trees  in  diameter  is  to  determine  the  total  volume 
of  trees  of  given  ages,  or  the  growth  in  volume  of  trees  for  a  short  period. 
The  volume  of  trees  is  based  on  D.B.H.  and  height.  The  diameter 
growth  must  always  be  correlated  with  D.B.H.  for  the  trees  measured, 
and  height  growth  is  usually  required.  A  second  purpose  is  to  determine 
the  dimensions  or  sizes  reached  by  trees  in  a  given  period. 

265.  The  Basis  for  Determining  Diameter  Growth  for  Trees.  It 
is  impractical  to  cut  sections  at  B.H.  for  growth  measurements.  Not 
only  is  there  a  needless  waste  of  timber,  but  the  labor  of  felling  and  sec- 
tioning the  tree  may  also  be  avoided  if  the  measurements  are  taken 
at  the  stump  following  logging  operations.  Where  current  growth  for 
short  periods  is  tested  with  an  increment  borer  (§  277)  the  measure- 
ment is  taken  at  D.B.H.  The  growth  measurements  on  stumps  require 
three  steps  to  determine  the  ages  of  trees  of  given  D.B.H.  outside  the 
bark;  namely, 

1.  Diameter  growth  on  the  stump. 

2.  Correction  for  age  of  the  seedling. 

.3.  Correlation  between  stump  diameter  inside  bark  and  D.B.H. 
outside  bark. 
As  diameter  increases  rapidly  at  the  stump,  the  lower  a  stump  is 
cut  the  greater  will  be  the  apparent  rate  of  growth  for  the  tree.  Stump 
height  classes  differing  by  6  inches  may  be  made  in  growth  studies, 
but  this  is  not  often  done.  Stump  heights  usually  vary  with  stump 
diameters  in  a  ratio  of  from  one-third  to  two-thirds  of  the  diameter, 
depending  on  the  closeness  of  utilization.  For  a  given  region  and 
standard,  the  stump  heights  for  given  diameters  are  fairly  constant 
and  the  average  rate  of  growth  is  found  for  stumps  of  each  diameter 
with  all  stump  heights  averaged  together. 

266.  The  Measurement  of  Diameter  Growth  on  Sections.  The 
section  measured  nuist  l)e  at  right  angles  with  the  axis  of  the  bole. 
In  stumps  this  means  a  horizontal  cross  cut.  Slanting  cross  cuts  exag- 
gerate the  length  of  the  radius  and  result  in  a  slight  plus  error  in  growth 
measurements.     The  procedure  is  as  follows: 

312 


MEASUREMENT  OF  DIAMETER  GROWTH  OX   SECTIONS      343 


tion  fifty  years  old 
showing  eccentric 
growth,  position  of 
the  two  average 
radii  AB  and  AC 
and  rot  on  radius 
AB.  Decades  of 
growth  are  shown. 
The  growth  must  be 
measured  on  radius 
AC. 


An  average  radius  is  located.  Its  length  must  equal  just  one-half 
of  the  average  diameter  inside  bark  (§  25).  To  determine  the  average 
diameter,  cahpers  graduated  to  ro-inch  may  be  used  (§  189).  In  all 
cross  sections  which  are  not  perfect  circles,  the 
lengths  of  the  radii  from  the  pith  or  center  of 
growth  vary  more  widely  than  the  diameters  owing 
to  the  fact  that  the  pith  is  alwaj's  located  at  one 
side  of  the  geometric  center  of  the  cross  section. 
Leaning  trees  grow  largely  on  the  under  side  and 
this  general  law  accounts  for  the  position  of  the 
pith.  On  an  eccentric  cross  section  there  are  but  ^^S;  67.— Stump  sec 
two  radii  which  are  average  in  length  and  can  be 
measured  for  growth.  It  often  happens  that  one 
or  both  of  these  radii  (Fig.  67)  are  interfered  with 
either  by  the  undercut  or  by  the  presence  of  rot 
or  defects  which  prevent  growth  measurement. 
If  either  one  is  clear,  the  section  may  be  meas- 
ured. Otherwise,  if  measurement  is  absolutely 
necessary,  a  longer  or  shorter  radius  can  be  taken 
and  the  measurements  reduced  by  proportion  to 
the  required  length.^ 

Method  of  Counting  Decades.  The  next  step  is  to  count  the  number 
of  annual  rings  and  indicate  with  a  pencil  the  points  at  w^hich  the  decades 
fall.  Except  in  scientific  investigations  where  each  year's  growth  may 
be  separately  measured  to  determine  the  influence  of  climate  on  annual 
growth,  the  decade  is  ordinarily  the  smallest  interval  used  in  measure- 
ment of  diameter  growth.  For  current  periodic  growth  a  five-year 
period  is  sometimes  used  in  order  to  get  points  for  a  curve  in  predicting 
the  growth  (§  279). 

Unless  the  total  age  of  the  stump  falls  on  a  decade,  as  thirty,  or 
forty  years,  there  will  be  one  fractional  decade  laid  off,  representing 
from  one  to  nine  j^ears,  depending  on  this  total  age.  The  diameter 
growth  is  alwoys  measured  outward  beginning  with  the  pith  or  center 
of  growth.  But  in  counting  the  annual  rings  to  lay  off  these  decades 
of  growth,  two  distinct  methods  of  procedure  are  followed.  In  one, 
the  count  begins  at  the  center,  laying  off  ten  j^ears  from  the  pith,  and 
throwing  the  fractional  decade  to  the  outside  as  on  the  right  side  of 
Fig.  68.  By  the  other,  the  count  begins  at  the  cambium  laj^er  or 
outer  ring,  and  this  throws  the  fractional  decade  to  the  center  as  on 
the  left  side  of  the  figure. 

Purpose  of  Counting  Inward  from  Outer  Ring  to  Center.     The  choice 

1  E.g.,  if  the  average  radius  is  9  inches,  and  a  radius  of  10  inches  is  measured, 
each  measurement  must  be  reduced  by  the  factor  ^  or  .9 


344 


GROWTH  OF  TREES  IN  DIAMETER 


of  these  methods  is  based  on  the  purpose  of  the  study.  In  all  measure- 
ments of  diameter  growth,  an  average  rate  is  to  be  found  by  combining 
the  growth  of  a  large  number  of  trees.  This  means  averaging  together 
the  growth  by  decades.  The  trees  so  averaged  usually  differ  in  age, 
sometimes  over  a  v/ide  range.  The  growth  of  the  last  decade,  or  current 
periodic  growth  on  all  trees,  regardless  of  their  total  age,  is  represented 
by  the  outside  or  last  ten  rings.  Any  influence,  such  as  cutting,  fire  or 
climate,  which  affects  diameter  growth,  must  be  studied  on  the  basis 
of  current  growth.     In  making  a  tree  analysis,  which  requires  the  growth 


Countinii 
from 
Center, 
Years 


Fig.  68. — Alternate  methods  of  counting  and  measuring  annual  rings  on  a  cross 
section  36  years  old.  On  left,  rings  are  counted  in  decades  beginning  with 
outer  ring.     On  right,  count  begins  with  center  and  odd  rings  fall  on  outside. 

in  diameter  of  upper  sections  (§  289)  the  separation  of  the  growth  in 
volume  for  each  past  decade  requires  the  measurement  of  the  same 
ten  rings  on  each  of  the  sections  analyzed.  This  is  secured  by  counting 
back  from  the  outer  ring.  When  growth  is  studied  for  these  purposes, 
rings  must  always  be  counted  from  the  outside  inward.  In  this  case 
the  first  measurement  from  the  pith  outward  will  be  the  fractional 
decade.  The  average  growth  for  this  period  represents  the  average 
number  of  years  less  than  10  which  were  measured.  This  may  vary 
from  1  to  9  years  but  tends  to  average  5  years.  The  second  decade 
will  include,  on  different  trees,  the  years  2  to  19,  the  third,  12  to  29; 


MEASUREMENT  OF  DIAMETER  GROWTH  ON  SECTIONS 


345 


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346  GROWTH  OF  TREES  IN  DIAMETER 

e.g.,  on  a  tree  21  j^ears  old,  the  decades  are  1,  2-11,  12-21  years.     On 
a  tree  29  years  old  the  decades  are  9,  10-19,  20-29  years. 

Purpose  of  Counting  Outward  from  Center  to  Outer  Ring.  In  tracing  the  growth 
of  trees  in  diameter,  based  on  their  age,  to  determine  the  average  sizes  reached  at 
each  decade,  the  above  averages  might  tend  to  conceal  or  flatten  out  any  changes 
characteristic  of  the  juvenile  period.  In  this  case  a  more  clear-cut  definition  of 
growth  may  be  obtained  if  age  is  actually  made  the  basis,  and  the  same  decades 
averaged  for  each  stump,  e.g.,  1-10,  11-20  years. 

For  this  purpose  the  count  would  be  made  outward  from  the  pith,  coinciding  in 
direction  with  the  measurement  of  growth,  throwing  the  fraction  to  the  outside. 
But  this  causes  the  fractional  decades  to  fall  in  as  many  different  columns  as  there 
are  trees  of  different  ages  by  decades.  In  tree  analyses  it  would  result  in  measur- 
ing different  fractions  at  each  upper  section  instead  of  the  same  rings.  It  does 
not  give  current  diameter  growth  for  a  stand.  The  age  of  the  seedling,  which  is 
usually  a  fractional  decade,  must  still  be  added.  For  these  reasons  the  first  method 
is  considered  standard.  But  for  the  purpose  indicated,  diameter  growth  based  on 
age,  the  last  fractional  decade  on  the  outside  although  recorded  could  be  dropped 
in  obtaining  average  growth  of  several  trees;  e.g.,  a  43-year  stump  can  be  computed 
for  its  first  four  decades  only.     By  this  plan,  the  averaging  is  simplified. 

Method  of  Measurement.  The  measurement  of  diameter  growth  is 
usually  made  with  a  steel  rule  graduated  to  inches  and  twentieths,  or 
.05  inch,  which  is  the  smallest  graduation  commonly  emploj'ed. 
When  the  radius  has  been  laid  off  and  each  decade  marked,  the  zero 
of  the  rule  is  placed  at  the  center  and  the  distance  read  to  each  decade 
point.  The  measurements  are  cumulative,  that  is,  the  rule  remains 
in  the  same  position  until  the  complete  radius  is  read.  This  avoids 
errors  which  are  sure  to  occur  in  moving  the  zero  from  on«  decade 
to  another  to  separate  the  decade  measurements.  The  form  of  record 
is  shown  on  p.  345.  The  accuracy  of  the  reading  should  be  checked 
by  noting  that  twice  the  total  radius  should  equal  the  average  diameter. 

267.  The  Determination  of  Average  Diameter  Growth  from  the 
Original  Data.  The  average  diameter  growth  for  the  trees  measured 
may  be  obtained  by  arithmetical  means,  and  by  the  aid  of  graphic 
methods. 

Table  LI  shows  the  method  of  computing  the  average  growth. 
When  the  decades  have  been  counted  from  the  pith  with  the  final 
fraction  rejected,  each  decade  is  full  and  the  averages  fall  at  10,  20, 
30  years,  etc.  This  completes  the  table  in  the  form  desired.  But 
when  the  rings  are  counted  from  the  outside,  the  first  decade  being 
fractional,  the  growth  is  not  shown  for  full  decades,  but  for  odd  years 
as   7,  17,  27  years,  etc. 

To  obtain  the  growth  at  the  required  decades,  a  curve  of  radius 
growth  based  on  age  is  plotted  as  shown  in  Fig.  69,  each  point  being 
plotted  above  its  proper  age.     The  radius  scale  is  then  doubled  to 


AVERAGE  DIAMETER  GROWTH  FROM  ORIGINAL  DATA    347 

read  directly  in  diameter  growth.     From  this  curve,  the  growth  at 
10,  20,  30  years,  etc.,  is  then  read  for  the  table. 


y\ 

A. 

? 

A 

\ 

§ 

— ^ 

^x 

\ 

l\ 

^, 

X|. 

^ 

^^° 

^ 

^^ 

^ 

^ 

^ 

L^ 

X 

^ 

^ 

^ 

^ 

4^ 

] 

\^ 

^ 

\\ 

^ 

\ 

\ 

^s 

\\ 

. 

"^ 

M 

^ 

"X 

o      - 

o 


Radius,  Inches 

(Double  to  read  Diameter) 

Fig.  69. — Growth  in  radius  of  5  spruce  trees  plotted  separately,  and  curve  of  average 
growth.  The  average  number  of  years  in  first  fractional  decade  is  7.  The 
successive  decade  averages  are  plotted  on  17,  27,  etc.  The  last  three  points 
represent  averages  based  on  less  than  five  trees  and  should  not  be  plotted  on 
the  same  curve. 

The  growth  of  each  tree  is  shown  by  curves.  In  plotting  data  for  a 
growth  curve  the  points  plotted  for  single  trees  would  not  ordinarily  be  con- 
nected. The  average  would  either  be  sketched  by  eye,  or  plotted  from  the 
position  of  the  average  points  as  indicated. 


Substitution    of    Graphic    for    Arithmetical    Method.     For    this    computation 
graphic  plotting  of  the  original  data  is  sometimes  substituted.     This  method  is  also 


348  GROWTH  OF  TREES  IN  DIAMETER 

illustrated  in  Fig.  69,  in  which  the  growth  of  five  spruce  trees  is  plotted,  their  rings 
being  counted  from  the  outside  inward.  Each  tree  is  plotted  on  the  exact  years  on 
which  its  measurements  fall  as  determined  by  its  total  age.  Where  a  large  number 
of  trees  are  plotted,  the  points  are  not  connected  but  form  a  band,  on  which  the 
curve  of  average  growth  is  sketched  by  eye.  This  method  is  intended  to  save  the 
labor  of  calculating  the  averages  arithmetically. 

Where  trees  of  different  ages  are  included  in  the  average,  the  upper  extremity  of 
the  growth  curve  will  represent  a  smaller  number  of  trees,  whose  growth,  if  dominant, 
will  exceed  the  average  rate,  but  if  suppressed,  will  fall  below  it,  causing  the  curve 
to  depart  from  a  true  growth  curve,  as  illustrated  in  this  Figure. 

268.  Correction  of  Basis  of  Diameter  Growth  on  Stump  to  Conform 
to  Total  Age  of  Tree.  Tlie  next  step  is  to  correlate  this  curve  of  growth 
with  the  total  age  of  the  tree.  The  average  age  of  seedlings  must  be 
determined  for  the  given  average  stump  height  (§257).  The  number 
of  years  thus  indicated  is  added  to  the  scale  by  moving  the  zero  the 
required  number  of  points  to  the  left.  This  new  zero  causes  a  shift 
in  the  age  of  each  section  to  correspond.  The  curve  now  shows,  not 
the  diameter  of  stump  sections  of  various  ages,  but  the  diameter  of 
trees  of  various  ages  when  measured  at  the  height  of  the  stump. 

269.  Correlation  of  Stump  Growth  with  D.B.H.  of  Tree.  The  third 
step  is  to  determine  the  D.B.H.  for  these  same  trees  in  order  to  correlate 
this  with  age.  What  is  desired  is  not  the  age  of  the  section  at  B.H. 
but  the  D.B.  H.  of  the  tree,  whose  total  age  and  growth  at  stump  are  now 
known. 

A  tree  of  a  given  stump  diameter,  whose  total  age  has  been  found, 
has  a  set  of  upper  diameters  or  tapers  representing  its  form,  as  expressed 
in  a  taper  table  (§  167).  Of  these  the  most  important  is  D.B.H.  This 
third  step  then  consists  simply  of  determining  the  average  taper  of  the 
butt,  from  stump  height  to  B.H.  so  as  to  find  the  D.B.H.  corresponding 
to  each  inch  stump-diameter  class. 

Standard  stump  tapers  show  the  D.I.B.  (§135)  of  stumps  at  heights 
of  1,  2,  3,  4,  and  4|  feet,  corresponding  to  each  D.B.H.  class.  But 
to  determine  growth  of  trees  at  B.H.  corresponding  to  growth  on  the 
stump  inside  the  bark,  heights  of  stumps  are  usually  averaged,  and  a 
direct  comparison  is  made  of  average  D.B.H.  outside  bark  with  average 
D.I.B.  on  the  stump  for  all  trees  falling  in  the  given  stump-diameter 


Stump  tapers  may  be  taken  on  the  butt  logs  of  felled  trees  in  the 
measurement  of  volumes  (§  168).  The  number  of  measurements  so 
obtained  is  often  insufficient  and  may  be  supplemented  by  measuring 
the  diameter  at  stump  height  and  width  of  bark  to  get  D.I.B.,  on  stand- 
ing trees,  together  with  D.B.H.  Owing  to  the  great  variation  in  diam- 
eters at  the  stump  compared  with  D.B.H.,  a  large  number  of  stump 
tapers  are  required  to  produce  a  curve  free  from  irregularities,  as  illus- 


CORRELATION  OF  STUMP  GROWTH  WITH  D.B.H.  OF  TREE     349 

trated  in  Fig.  70  for  loblolly  pine.     These  data  can  be  obtained  very 
rapidly  and  without  much  extra  cost. 

These  stump  tapers  are  then  classified  on  the  basis  of  stun.D  diam- 
eter inside  bark  and  not  on  D.B.H.  since  they  are  to  be  plotted  on  the 
curve  of  stump  diameter.  An  arithmetical  average  of  these  relations 
is  obtained,  and  expressed  in  the  form  of  Table  LII  (p.  3cO). 


20  30  40 

Age  of  Tree  including  Seedling 

Fig.  70. — Diameters,  inside  bark  at  stump,  outside  bark  at  B.H.,  and  inside  bark 
at  16  feet  above  stump,  for  trees  at  different  ages.  Loblolly  pine,  old  fields, 
Urania,  La. 


The  D.B.H.  outside  bark  for  each  stump-diameter  class  is  now 
plotted  on  the  curve  of  D.I.B.  on  the  stump  as  shown  in  Fig.  70.  Since 
this  curve  is  based  on  age  of  tree,  the  diameter  at  any  point  on  the 
bole  of  a  tree  of  a  given  age  will  fall  on  the  indicated  vertical  line  cor- 
responding to  this  age.  Thus,  a  tree  measuring  14  inches  on  the  stump 
in  Table  LH  is  30  years  old  at  the  stump,  and  33  years  old  when 
corrected  for  age  of  seedling  which  is  8  years.  The  D.B.H.  for  a  14- 
inch  stump  is  13.2  inches,  which  is  plotted  above  33  j^ears.  In  the 
same  way,  D.I.B.  at  the  top  of  the  first  16-foot  log,  which  is  10.8  inches, 
would  fall  above  the  same  33-year  point  on  the  scale.  In  this  manner 
the  stump  tapers  are  each  plotted  by  first  finding  the  corresponding 


350 


GROWTH  OF  TREES  IN  DIAMETER 


D.I.B.  at  stump,  on  the  curve  of  growth,  which  indicates  the  required 
age  of  the  tree  above  which  the  remaining  dimensions  are  to  be  plotted. 

TABLE  LII 

Stump  Tapers— Based  on  Stump  DIB.  for  Stumps  1  Foot  High 
Loblolly  Pine,  Urania,  La. 


Stump  diameter 
class. 

.Average  D.I.B. 
stump. 

Average  D.B.H. 

Inches 

Inches 

Inches 

5 

5  1 

4.5 

6 

6.0 

6.1 

7 

6.8 

6.8 

8 

8.2 

7.0 

9 

9.1 

8.3 

10 

10.0 

9.6 

11 

11.1 

10.4 

12 

11.9 

11.0 

13 

13.2 

12.3 

14 

14  1 

12.7 

15 

15.1 

12.9 

16 

16,0 

15.6 

17 

17.2 

15.8 

18 

17.8 

16.7 

19 

18.7 

18.2 

The  D.B.H. 's  for  different  stump  diameters  are  now  connected  by 
a  curve,  which  shows  D.B.H.  for  trees  of  intervening  ages,  and  for 
all  stump  diameters.  From  this  curve  the  D.B.H.  corresponding  to 
each  decade  in  the  h  e  of  the  tree  can  be  read,  in  the  form  of  Table 
LHI. 

TABLE  LIII 

Growth  op  Loblolly  Pine,  Old  Field,  in  D.B.H.,  Based  on  Age  op  Tree, 

Urania,  La. 


Diameter  at  top 

Age. 

D.B.H. 

of  first  16-foot 
log  inside  bark. 

Years 

Inches 

Inches 

10 

3.6 

10 

20 

9.8 

7.0 

30 

12.5 

9.9 

40 

14.7 

12.0 

50 

17.0 

13.8 

DIAMETER  GROWTH  OF  TREES  GROWING  IN  STANDS       351 

Since  there  can  be  no  D.I.B.  at  16  feet  until  the  tree  has  reached 
this  point  in  height,  the  curve  of  these  points  would  terminate  at  zero 
diameter  at  an  age  equal  to  that  required  for  the  tree  to  grow  16  feet 
in  height,  above  the  stump,  which  is  8  years  in  Fig.  70.  In  the  same 
manner  the  D.B.H.  curve  would  terminate  at  a  point  representing  the 
year  in  which  the  tree  reached  4^  feet  in  height,  which  is  4  years.  The 
stump  curve  has  already  been  shown  to  terminate  at  an  age  repre- 
senting the  growth  of  the  seedling  to  stump  height  at  3  years.  This 
principle  is  later  explained  more  fully  in  connection  with  a  method 
of  plotting  the  volume  growth  of  different  trees  (§  291). 

270.  Factors  Influencing  the  Diameter  Growth  of  Trees  Growing 
in  Stands.  Diameter  is  the  most  variable  factor  of  tree  growth,  dif- 
fering with  a  wider  range  of  conditions  and  showing  greater  diversity 
between  trees  in  the  same  stand  than  height  growth.  Growth  in  diam- 
eter influences  growth  in  volume  of  the  tree  to  a  much  greater  extent 
than  does  height  growth,  the  relation  being  that  of  dr  or  area.     Since 

the  growth  in  area  bears  this  fixed  relation  — -,  the  area  growth  of  indi- 
vidual trees  is  never  studied,  as  all  problems  for  which  it  is  desired 
are  solved  by  the  study  of  diameter  growth.  The  rate  of  diameter 
growth  is  determined  by  four  factors:  species,  quality  of  site,  density 
of  stand,  and  crown  class. 

Secondary  factors  modifying  diameter  growth  are  the  amount  of 
shade  endured  by  the  specific  trees  studied,  and  the  treatment  of 
the  stand. 

271.  Effect  of  Species  on  Diameter  Growth.  Different  species 
have  developed  specific  differences  in  average  rate  of  diameter  growth. 
Those  accustomed  to  growing  on  soil  of  good  quality  as  dominant 
species  have  acquired  the  fastest  growth  rate.  Intolerant  trees  usually 
grow  faster  than  tolerant  since  they  must  maintain  their  dominance. 
Of  this,  the  cottonwood  is  an  example.  Trees  which  have  the  power 
of  enduring  shade  usually  grow,  even  in  the  open,  at  a  somewhat  slower 
rate  than  intolerant  trees. 

Trees  do  not  indefinitely  maintain  a  given  rate  of  diameter  grov/th. 
Until  a  tree  actually  dies,  it  continues  to  increase  in  diameter,  but  there 
comes  a  period  when,  in  spite  of  the  dominant  position  of  the  tree, 
its  rate  of  diameter  growth  diminishes.  The  period  at  which  this 
diminution  sets  in  marks  the  maturity  and  the  beginning  of  decadence 
of  the  tree.  The  life  cycle  of  different  species  of  trees  is  as  distinct 
as  that  of  different  animals.  Short-lived  trees,  like  jack  pine  and 
tamarack,  show  this  falling  off  at  70  or  80  years  or  sooner,  and  disappear 
within  30  or  40  years  thereafter.  The  same  is  true  of  aspen.  The  life 
cycle  of  conifers  is  apparently  affected  by  general  climatic  conditions. 


352  GROWTH  OF  TREES  IN  DIAMETER 

That  of  western  conifers  is  double  the  cycle  characteristic  of  those 
in  the  East,  while  that  for  redwoods  and  Sequoia  is  fully  five  times 
as  great  as  for  most  of  the  remaining  western  conifers. 

The  life  cycle  of  any  individual  tree  is  governed  by  the  average  for 
the  species  but  appears  to  depend  on  size  and  not  age.  A  tree  is  mature 
when  it  has  reached  the  maximum  size  permitted  by  its  site  and  vigor 
of  crown,  whether  this  is  secured  by  continuous  rapid  growth  as  a 
dominant  tree  or  is  delayed  by  a  period  of  suppression.  Trees  character- 
istically intolerant  and  dominant,  and  accidentally  suppressed  in  youth, 
if  they  recover  from  this  suppression,  will  add  the  period  of  suppression 
to  the  average  age  which  they  attain  and  continue  to  grow  until  they 
reach  the  usual  size.  Trees  naturally  undergoing  and  recovering  from 
a  period  of  suppression,  such  as  spruce  and  balsam,  may  attain  maturity 
under  these  conditions  100  years  later  than  trees  of  the  same  species 
growing  in  the  open,  and  their  life  cycle  will  be  that  much  longer.  This 
law  was  also  found  to  hold  true  for  the  Sequoia  gigantea.^ 

272.  Effect  of  Quality  of  Site.  The  greater  productive  capacity 
of  better  sites  is  reflected  in  the  increased  rate  of  growth  in  diameter 
of  the  species  on  these  sites.  Either  deficiency  or  continuous  excess 
of  moisture  greatly  reduces  the  site  quality  and  slows  down  diameter 
growth.  The  final  expression  of  site  quality  is  found  in  terms  of  total 
volume  or  rate  of  growth  per  year,  of  which  this  average  diameter 
growth  is  one  of  the  l^est  indications. 

273.  Effect  of  Density  of  Stand.  The  rate  of  growth  of  the  individ- 
ual or  average  tree  is  profoundly  influenced  by  the  number  of  trees 
in  the  stand.  The  original  number  of  trees  germinating  and  becoming 
established  on  a  site  bears  no  relation  to  the  number  which  may  grow 
to  maturity.  The  reduction  of  numbers  with  increased  size  and  crown 
spread  is  accomplished  by  competition  between  individuals,  resulting 
in  the  death  of  the  weaker  trees.  With  species  which  become  estab- 
lished in  dense  stands  in  a  single  year  and  maintain  an  even  height 
growth,  the  inability  of  the  stand  to  differentiate  itself  and  destroy 
the  necessary  proportion  of  the  weaker  trees  is  reflected  in  a  great 
reduction  in  diameter  growth  on  all  of  the  trees.  Of  this  tendency, 
lodgepole  pine  gives  the  best  examples.  In  almost  all  species  of  conifers 
and  many  hardwoods,  dense,  even  stocking,  unless  artificially  corrected 
by  thinning,  gives  a  much  lower  rate  of  diameter  growth  than  the  aver- 
age which  may  and  should  be  secured  by  the  species.  Diameter  growth 
is  therefore  apt  to  be  greatly  reduced  by  increased  number  of  trees 
per  acre  in  the  stand,  or  overstocking. 


"  Ellsworth  Huntingdon,  The  Climatic  Factor,  as  Illustrated  in  Arid   America, 
Carnegie  Institution  of  Wash.,  D.  C,  1914,  Chap.  XII. 


EFFECT  OF  CROWN  CLASS  353 

274.  Effect  of  Crown  Class.  The  Individual  rate  of  diameter 
growth  varies  over  a  wide  range  with  the  same  species,  site  and  stand. 
The  rate  of  growth  is  coordinated  directly  with  the  crown  spread  of 
the  tree.  There  exists  a  relation  between  width  of  crown  and  diameter 
which  is  found  to  hold  good  under  almost  everj^  condition  and  for  every 
species,  although  vaiying  with  the  species  and  its  habit  of  growth. 
This  law,  which  might  be  of  great  use  in  determining  the  number  of 
trees  which  should  exist  per  acre  for  a  given  species  in  mixed  stands, 
is  somewhat  interfered  with  by  the  fact  that  the  volume  of  the  crown, 
rather  than  its  mere  diameter,  is  the  factor  affecting  diameter  growth, 
and  with  western  conifers,  with  very  tall  and  slender  crowns,  width 
alone  does  not  properly  express  this  value.  As  crowns  receive  more 
growing  space  and  expand,  diameter  growth  correspondingly  increases. 
This  elasticity  of  diameter  growth  correlated  with  crown  spread  is  the 
principal  means  of  adjustment  which  a  stand  of  trees  possesses,  by 
which  it  constantly  tends  to  fill  in  blanks  and  form  a  complete  crown 
canopy  provided  only  that  the  distribution  of  the  trees  is  such  as  to  bring 
these  blanks  within  the  possible  maximum  spread  of  individual  crowns. 

Effect  of  Shade.  Diameter  growth  during  the  life  of  a  tree  de- 
pends upon  its  history  with  respect  to  the  remaining  trees  in  the  stand. 
A  tree  which  has  remained  dominant  since  germination  maintains  a 
maximum  rate  of  diameter  growth.  The  crown  spread  at  successive 
decades  is  a  maximum.  Trees  which  are  at  first  dominant  and  later 
suppressed,  cease  to  grow  in  diameter  because  their  crowns  cease  to 
expand.  The  relation  between  diameter  and  crown  is  maintained, 
but  neither  continues  to  increase.  Trees  which  were  originally  sup- 
pressed and  later  freed  may  show  a  marked  increase  in  diameter  growth 
coinciding  with  an  increased  spread  of  crown,  thus  maintaining  the 
proportion  under  the  changed  conditions.  But  if  their  crowns  have 
lost  the  power  to  recuperate,  which  depends  upon  both  the  specific 
character  and  the  age  of  the  tree,  no  increase  is  made  in  diameter 
growth  by  reason  of  this  liberation. 

Effect  of  Treatment.  The  growth  in  diameter  of  trees  can  be  pro- 
foundly influenced  by  the  artificial  treatment  of  a  stand.  Since  for 
the  individual  tree  it  is  a  function  of  crown  spread  and  its  rate  is  governed 
by  the  ability  of  the  cro%vn  to  expand,  diameter  growth  is  the  most 
easily  governed  and  most  adaptable  function  of  tree  growth.  The 
stand  per  acre  or  rate  of  growth  for  a  period  measured  in  cubic  contents 
may  not  be  subject  to  great  modification,  but  the  sizes  of  the  stock 
produced  and  consequently  the  value  per  acre  can  be  greatly  influ- 
enced by  management.  The  behavior  of  trees  in  thinned  stands  and 
on  cutover  lands  must  be  studied  separately  from  those  subjected  to 
the  natural  laws  of  survival  in  original  unthinned  forests. 


354  GROWTH  OF  TREES  IN  DIAMETER 

275.  Laws  of  Diameter  Growth  in  Even-aged  Stands,  Based  on 
Age.  The  struggle  of  the  individual  trees  for  space  produces  different 
results  in  even-aged  and  in  many-aged  stands,  although  the  general 
effect  is  a  final  reduction  in  numbers  in  either  case.  In  the  even-aged 
stand  the  area  occupied  by  an  age  class  is  definitely  fixed.  Expansion 
of  the  crowns  of  individual  trees  can  occur  only  by  the  prevention  of 
corresponding  expansion  of  other  crowns  and  by  securing  of  additional 
space  through  the  actual  death  of  the  weaker  trees.  This  process 
results  in  a  continuous  differentiation  of  diameter  classes  in  an  even- 
aged  stand  with  advancing  age.  As  the  trees  become  fewer  in  number, 
the  difference  in  size  of  the  survivors  increases.  These  relations  are 
shown  in  Fig.  71,  in  which  the  numl^er  of  diameter  classes  existing  at 
different  ages  in  an  even-aged  stand  is  indicated. 

The  growth  in  diameter  of  the  trees  which  compose  this  even-aged 
stand  is  shown  in  Fig.  72,  The  diminution  in  diameter  growth  due 
to  suppression  of  crowns  affects  successive  trees  of  larger  and  larger 
diameter.  The  average  tree  at  a  given  decade  is  seen  to  fall  into  the 
lower  half  of  the  stand  in  the  succeeding  decade  and  at  some  future 
period  will  become  suppressed  and  finally  die. 

In  Fig.  71  is  shown  the  difference  in  basis  and  composition  of  the  curves  based 
respectively  on  age  and  on  diameter.  The  curve  based  on  age  in  this  figure  is 
composed  of  averages  of  all  the  diameter  classes  in  successive  even-aged  stands,  as 
shown  in  the  vertical  colvmins.  The  curve  based  on  diameter  takes  all  trees  of  a 
given  diameter  for  each  successive  average,  thus  including  trees  from  a  number 
of  different  age  classes  or  stands  as  read  horizontally  in  the  diagram.  This  curve  as 
plotted  in  Fig.  71  is  reversed,  with  the  basis,  diameter,  plotted  on  the  vertical  scale. 
The  proper  form  of  such  a  curve  is  shown  in  Fig.  73.  The  wide  divergence  possible 
in  the  two  bases,  for  dominant  larger  trees,  is  indicated  in  Fig.  71. 

It  is  evident  that  growth  measurements  of  diameter  based  on  age,  which  include 
trees  whose  total  age  varies  from  20  to  50  years,  corresponding  with  the  diameter 
classes  A  to  L  in  Fig.  72,  will  not  be  correct  for  any  single  tree  in  the  stand  D.  The 
portion  of  this  curve  representing  the  earlier  decades  is  depressed  or  lowered  by  the 
inclusion  of  the  slower  growing  trees  F  to  L  which  afterwards  die.  With  the  suc- 
cessive dropping  out  of  these  trees  from  the  average,  the  latter  portion  of  the 
curve  shows  a  more  rapid  growth  than  that  of  the  trees  which  compose  it. 

To  get  the  actual  past  growth  of  an  average  tree  for  a  stand  of  a  given  age,  C,  it 
is  evident  that  only  trees  which  have  reached  this  age  must  be  measured,  A  to  E. 
To  secure  average  diameter  growth  for  mature  timber  which  in  the  future  will  be 
gi'own  to  the  given  sizes  and  numbers  per  acre  characteristic  of  this  class  of  timber,  it 
is  incorrect  to  include  measurements  of  average  trees  for  stands  which  have  not  yet 
reached  this  age,  F  to  L.  By  confining  the  selection  of  trees  to  timber  of  the  desired 
age  and  by  taking  the  growth  of  all  of  the  trees  found  on  an  area  of  sufficient  size, 
we  obtain  an  average  rate,  showing  the  past  growth  of  these  trees,  which  is  a  true 
growth  curve,  C.  If  it  is  desired  to  predict  the  rate  of  growth  for  the  average  tree  of 
a  given  age  and  character  of  mature  stand,  dominant  trees  must  be  selected  from 
younger  stands  rather  than  the  average  tree.  The  fewer  of  these  trees,  and  the 
greater  their  relative  crown  spread  or  dominance  compared  to  the  remaining  stand, 


LAWS  OF  DIAMETER  GROWTH  IN  EVEN-AGED  STANDS       355 

the  greater  the  age  with  which  the  resulting  growth  curve  will  coincide  as  an  expres- 
sion of  yield  per  acre  and  average  tree;  e.g.,  for  predicting  the  growth  to  35  years  of 
stands  now  20  years  old,  the  group  of  trees,  A  to  H,  whose  average  tree  is  D,  must  be 
included,  omitting  classes  J  to  L  which  would  lower  the  average  tree  at  20  years 
to  F. 


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Fig.  71. — Number  of  trees  in  each  diameter  class  in  normal  stands  at  four  successive 
ages,  and  resulting  curves,  when  averaged  respectively  on  basis  of  age  and  of 
diameter. 


The  composite  curve  of  average  growth  in  which  each  successive  decade  is  based 
on  a  lesser  number  of  trees  than  the  preceding  period,  is  a  useful  tabulation  to  show 
the  average  diameter  of  surviving  trees  at  given  ages,  but  as  shown  does  not  correctly 
indicate  the  progress  of  growth  for  any  of  the  trees  on  which  it  is  based,  unless  it  is 
confined  to  a  given  number  of  trees  throughout. 


356 


GROWTH  OF  TREES  IN  DIAMP:TER 


Diameter  growth  based  upon  age  is  used,  in  practical  studies,  princi- 
pally as  an  aid  in  indicating  the  difference  in  rate  of  growth  of  species, 
sites,  and  different  methods  of  treatment  and  as  an  aid  in  determining 
the  average  age  of  stands  in  the  forest  under  different  conditions. 
This  application  is  much  more  hmited  than  is  commonly  supposed 


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Fig.  72. — Differentiation  of  diameter  growth  a.s  result  of  different  rate.s  of  develop- 
ment of  crowns,  in  normal  stands,  even-aged. 


since  for  many  problems  the  substitution  of  yields  per  acre  based  directly 
on  total  age  answers  the  questions  more  directly  and  accurately,  while 
for  forests  in  which  the  average  age  for  stands  cannot  be  ascertained, 
diameter  growth  is  not  based  on  total  age,  but  on  diameter  classes 
(§  336). 


LAWS  OF  DIAMETER  GROWTH  IN  MANY-AGED  STANDS      357 


276.  Laws  of  Diameter  Growth  in  Many-aged  Stands,  Based  on 
Diameter.  When  diameter  growth  is  studied  in  order  to  determine 
the  age  of  trees  of  given  diameters,  the  basis  of  the  average  is  entirely 
different  from  that  required  when  the  diameter  or  size  of  trees  of  given 
ages  is  required.  By  the  inspection  of  Fig.  71,  it  will  be  seen  that 
when  based  on  age  for  each  decade,  several  different  diameter  classes 
are  averaged  together.  The  average  diameter  even  for  the  oldest 
age  class  is  several  inches  less  than  the  maximum  diameters  reached 
by  the  dominant  trees.  To  prolong  a  curve  of  growth  based  on  age 
until  the  diameter  of  the  maximum  tree  is  reached,  would  add  several 
decades  to  the  apparent  age  of  a  tree  of  this  diameter. 

On  the  other  hand,  if  diameter  is  actually  the  basis  and  the  average 
age  is  sought,  the  classes  included  to  obtain  these  averages  are  read 
horizontally  in  Fig.  71  and  include  under  the  same  diameter  several 
different  age  classes.  The  principal  effect  of  this  difference  in  the  basis 
of  averaging  is  found  when  the  larger  diameters  are  reached.  In 
stands  composed  wholly  of  intolerant  trees,  where  suppression  and 
prolonging  of  the  life  cycle  is  not  a  factor,  the  difference  between  the 
age  of  the  larger,  dominant  diameter  classes  which  exceed  the  average 
and  the  average  age  of  smaller  diameter  classes,  which  include  many 
trees  fully  as  old  as  the  dominant  classes,  is  much  less  than  would  be 
indicated  by  a  curve  based  on  age.  A  curve  showing  the  average  age 
of  trees  of  given  diameter  is  not  expected  to  show  the  progress  of  trees 
in  diameter  from  dec- 
ade to  decade,  but 
expresses  directly  the 
result  of  the  total 
growth  or  period  for  the 
specific  class  of  trees 
concerned. 

There    is    but    one 
way   to   determine   ac- 
curately   the     average 
age  of  trees  of  separate 
diameter     classes    and 
that  is  by  a  total  count 
of  rings  for  several  trees    Fig.  73.— Ages  of  trees  of  different  diameters,  shown 
in    each  diameter   class        for    two    groups    of    longleaf    pine,    the   first   com- 
to   obtain    the    average       posed     of    second-growth    stands,    the    second     of 
age     directly     on      this        veteran  or  old-growth  timber, 
diameter  basis.     When 

these  points  or  averages  are  plotted,    they  will  show  a  relation  about 
as  indicated  in  Fig.  73. 


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358  GROWTH  OF  TREES  IN  DIAMETER 

The  application  of  such  a  growth  study  is  to  determine  correctly 
the  average  age  of  trees  of  given  diameter  classes  and  diameter  groups 
in  a  forest  or  stand  when  the  basis  of  age  for  the  stand  cannot  be  directly 
determined  (§320).  This  presupposes  that  the  stands  are  not  even- 
aged,  but  many-aged  in  character.  In  mixed  many-aged  stands  or 
groups,  suppression  usually  plaj^s  a  large  role  and  again  interferes  with 
this  determination  by  requiring  the  substitution  of  the  economic  age 
for  the  actual  age  (§  263).  But  for  the  species  such  as  the  Southern 
pines,  which  are  fireproof  to  a  certain  extent,  and  the  Western  yellow 
pine,  for  the  same  reason,  the  age  groups  may  be  intermingled  and  yet 
the  dominant  character  of  growth  maintained.  Under  these  circum- 
stances, the  direct  determination  of  age  based  on  diameter  may  be 
used  for  determining  the  avei'age  age  of  diameter  groups,  especially 
for  the  upper  or  dominant  classes. 

277.  Current  Periodic  Growth  Based  on  Diameter  Classes.  The 
Increment  Borer.  A  more  common  application  of  growth  based  on 
diameter  classes  is  for  the  prediction  of  current  periodic  growth  in  specific 
stands,  for  short  periods,  by  predicting  the  growth  of  each  tree  in  the 
stand  in  diameter  and  correlating  this  data  with  volume  growth.  The 
drawbacks  to  this  method  have  been  discussed  in  §  251.  Dealing, 
as  it  does,  with  the  specific  stand  and  actual  number  of  trees,  it 
is  directly  applicable  to  stands  of  all  degrees  of  density  and  to 
the  actual  stocking  found  on  the  ground,  and  to  this  extent  is 
applicable  directly  to  the  existing  forest  without  the  necessity 
for  a  yield  table.  Tables  showing  the  growth  in  diameter  which 
maybe  expected  of  trees  of  given  diameters  may  be  applied  directly 
to  stand  tables  showing  the  number  of  trees  of  these  diameters  on 
the  average  acre. 

The  current  growth  of  trees  of  given  diameter  is  measured  either 
on  the  stump  or  directly  at  B.H.  Growth  measurements  taken  on  the 
stump  must  be  laid  out  on  an  average  radius  (§25).  As  the  growth 
in  D.B.H.  outside  bark  is  frequently  less  than  that  on  the  stump  inside 
bark  (§  269)  correct  results  would  require  the  reduction  of  the  radial 
growth  on  the  stump  to  its  equivalent  at  D.B.H.  This  is  not  usually 
done,  first  because  for  trees  of  the  smaller  diameters  D.O.B.  at  B.H. 
tends  to  coincide  with  D.I.B.  on  the  stump;  second,  because  the  total 
error  thus  incurred  in  measuring  the  growth  based  on  age  is  proportion- 
ately reduced  in  measuring  current  growth,  although  the  percentage 
of  error  remains  the  same.  This  may  be  considered  too  small  to  require 
correction.  When  measured  directly  at  B.H.,  it  is  important  to  secure 
an  average  radius  if  possible.  The  only  method  by  which  this  can  be 
done  is  to  take  two  readings  on  opposite  sides  of  the  tree,  and  determine 
the  mean. 


CURRENT  PERIODIC  GROWTH  BASED  ON  DIAMETER  CLASSES  359 

The  increment  borer  (Fig.  74)  can  be  used  for  measuring  radial 
growth  at  B.H.     This  instrument  consists  of  three  parts: 

(a)  A  hollow  auger,  A,  from  4  to  10  inches  long,  tapering  and 
threaded  at  one  end,  and  square  in  cross  section  at  the  other  end. 

(6)  A  hollow  metal  handle,  B,  with  a  square  opening  in  the  center 
into  which  the  auger  fits  when  in  use.  At  the  ends  of  this  handle  are 
detachable  caps. 

(c)  A  narrow  wedge,  C,  furnished  at  one  end  with  a  flat  head,  and 
incised  on  one  side  at  the  other  end. 


iWvW/iAl 


TAWvWN 


Fig.  74. — Increment  borer,  showing  construction. 


The  wedge  and  the  auger  are  carried  inside  the  hollow  handle  when 
the  instrument  is  not  in  use. 

To  use  the  instrument  one  bores  into  a  tree  to  the  desired  depth, 
then  inserts  the  wedge  through  the  auger  with  the  incised  de  turned 
inward.  The  wedge  is  jammed  down,  thus  holding  tightly  in  place 
the  core  of  wood  within  the  auger.  The  handle  is  then  turned  sharply 
to  the  left,  severing  the  core  from  the  wood.  The  cylinder  of  wood  is 
then  drawn  out,  and  the  rings  counted  or  measured. 

The  best  type  of  instrument  is  made  in  Sweden,  and  cores  of  from 
6  to  8  inches  may  be  secured  by  the  larger  sizes.  The  instrument  is 
easily  taken  apart  and  is  convenient  to  carry.     When  taken  at  B.H. 


360 


GROWTH  OF  TREE8  Ix\  DIAMETER 


these  measurements  require  no  correction.  Care  must  be  taken  if 
but  a  single  measurement  is  made  on  standing  trees,  to  select  the  point 
for  testing  on  neither  the  lower  nor  the  upper  side  of  a  leaning  tree, 
the  growth  of  which  is  veiy  eccentric,  coinciding  with  its  position. 

278.  Method  Based  on  Comparison  of  Growth  for  Diameter  Classes. 
In  Chapter  XXII  it  was  shown  that  growth  is  measured  in  order  that 
future  growth  may  be  predicted.  This  may  be  done  either  by  pro- 
jecting the  growth  of  a  past  period  into  the  future  on  the  specific  trees 
or  stands  measured,  or  by  the  method  of  comparing  the  growth  on 
trees  or  stands  which  have  reached  a  certain  size  or  age,  with  younger 
or  smaller  trees  which  are  assumed  to  grow  at  a  like  rate.  These 
principles  must  be  applied  in  utilizing  the  growth  of  trees  for  determin- 
ing that  of  stands. 

Since  diameter,  not  age,  is  now  the  basis  of  the  growth  study,  trees 
are  classified  for  growth  on  the  basis  of  their  present  diameters  at 
B.H.  and  an  average  rate  is  determined  for  each  class.  The  result  of 
such  a  study  is  applied  to  trees  of  given  diameter  classes  in  the  stand 
or  forest.  By  the  method  of  comparison,  a  tree  now  15  inches  in 
diameter  which  has  grown  1  inch  in  the  last  8  years,  was  14  inches 
D.B.H.  8  years  ago,  and  trees  now  14  inches  D.B.H.  if  compared  with 
this  growth,  will  presumably  grow  at  like  rate  for  8  years. 

This  requires  current  growth  to  be  measured  by  inches  of  diameter, 
or  half-inches  of  radius,  and  not  by  decades  or  periods,  in  order  that 
the  basis  of  comparison,  D.B.H.  classes  in  the  past,  may  be  obtained. 
The  rings  in  successive  half-inches  of  radius  are  counted  and  avera 
by  diameter  classes,  in  the  following  form : 


TABLE  LIV 

Current  Growth  of  Spruce,  Adirondacks  Region,  New  York 


Present 

Number  of  rings 

Diameter  to 

diameter. 

in  last  inch  cf 

which  appHed. 

Inches 

diameter 

Inches 

5 

6  5 

4 

6 

5.0 

5 

7 

5.3 

6 

8 

6.6 

7 

9 

5.4 

8 

10 

5.1 

9 

PROJECTION  OF  GROWTH  BY  DIAMETER  CLASSES  361 

By  plotting  the  values  In  column  2  on  the  basis  of  diameter,  a  curve 
may  be  drawn  to  even  out  the  irregularities  shown.  To  apply  such 
a  table  in  pretlicting  growth  for  a  period  of  20  years,  for  4-inch  trees, 
the  grow^th  of  successive  inch  classes  is  used;  e.g.,  the  4-inch  tree  takes 
6.5  years  to  reach  5  inches,  5  years  to  reach  6  inches,  and  5.3  jears  to 
reach  7  inches,  or  a  total  of  16.8  years.  The  next  inch  requires  6.6 
years,  3.2  of  which  lie  in  the  20-year  period,  equivalent  to  about  |-inch. 
The  tree  will  grow  to  be  7|  inches  in  diameter  in  20  years.  In  this 
way  the  growth  for  each  D.B.H.  class  can  be  predicted  for  am-  given 
period  on  the  assumption  that  the  basis  of  comparison  is  trustworthy. 
This  is  the  simplest  method  of  growth  prediction  for  trees  in  many- 
aged  forests.  In  obtaining  the  average  number  of  years  in  the  last 
inch,  all  trees  included  in  the  table  must  be  measured  for  the  same 
period,  i.e.,  the  basis  must  be  |-inch  of  radius.  If  instead  the  last 
20  years  is  measured,  divided  into  half-inches  of  radius,  and  a  fast- 
growing  tree  used  in  the  table  as  the  equivalent  of  several  smaller  inch 
classes,  its  influence  on  the  average  will  be  increased  in  like  proportion 
and  too  rapid  an  average  rate  obtained. 

Where  trees  are  measured  for  a  past  decade  or  fixed  period  of  years, 
the  results  are  expressed  as  growth  in  inches  for  the  period.  This  rate 
of  growth  may  then  be  reduced  to  mean  periodic  growth  (average 
growth  per  year  for  the  period).  Dividing  1  inch  by  this  annual 
growth  gives  the  number  of  years  required  to  grow  an  inch 
in  diameter  for  each  inch  class.  This  method  is  equally  reliable,  and 
most  tables  of  current  diameter  growth  have  been  derived  in  this 
manner. 

The  assumption  underlying  the  basis  of  comparison,  namely,  that 
the  rate  of  diameter  growth  is  a  function  of  diameter,  is  most  nearly 
approximated  in  many-aged  forests  of  tolerant  species  such  as  spruce 
and  for  averages  which  include  a  wide  range  of  ages  and  condi- 
tions. 

279.  Method  Based  on  Projection  of  Growth  by  Diameter  Classes. 
For  single  stands  or  specific  conditions,  growth  for  trees  of  the  same 
diameter  varies  tremendously  (§  274  and  §  275)  and  shows  its  greatest 
diversity,  first  in  even-aged  stands,  second,  between  open-grown  and 
shaded  trees.  For  such  problems,  prediction  based  on  past  grow^th 
of  the  present  trees,  rather  than  comparison,  is  a  more  reliable 
method. 

For  this  purpose,  past  current  growth  is  measured  for  the  last  5-  or 
10-year  period,  or  for  two  to  four  such  periods,  as  required.  If  it  is 
assumed  that  future  diameter  growth  will  equal  past  growth,  the  growth 
is  tabulated  as  follows: 


362 


GROWTH  OF  TREES  IN  DIAMETER 


TABLE  LV 
Short-leaf  Pine,  Louisiana 
Growth  by  Diameter  Classes 


DBH 

Growth  in 

DBH 

Growth  in 

10  Years. 

10  Years. 

Inches 

Inches 

Inches 

Inches 

10 

1.03 

16 

1.76 

11 

1.60 

17 

1.82 

12 

1.36 

18 

1.84 

13 

1.44 

19 

1.78 

14 

1.67 

20 

2.05 

15 

1.52 

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Fig.  75.  —  Method  of  predicting 
future  growth  of  trees  of  differ- 
ent diameter  classes  based  on  past 
growth  in  diameter  and  harmon- 
ized curves.     Loblolly  pine,  La. 


These  values  can  be  evened  off 
as  described  for  Table  LIV  (p.  360). 

This  assumption  of  unchanging 
future  diameter  growth  is  a  make- 
shift, inaccurate  under  most  con- 
ditions and  not  as  reliable  as  the 
method  of  comparison.  But  by 
measuring  the  growth  for  two  or 
three  periods,  which  for  the  pur- 
pose are  preferably  shortened  to 
5  years  so  as  to  bring  out  any 
recent  tendencies  of  current  growth, 
the  past  growth  of  trees  of  each 
diameter  class  may  be  used  to  pre- 
dict future  growth  by  means  of  a 
curve  drawn  through  these  past 
points  (Fig.  75). 

The  original  data,  and  the  re- 
sultant prediction  of  growth  are 
shown  in  Table  LVI. 

The  advantages  of  this  method 
show  most  distinctly  with  even- 
aged  stands,  in  which  case  the 
flattening  out  or  termination  of 
the  curve  of  the  lowest  diameter 
classes  occurs  successively,  and  in- 
dicates the  death  of  these  smaller 
trees  by  suppression. 


INCREASED  GROWTH.     METHOD  OF  DETERMINATION       363 


TABLE  LVI 

Current  Growth,  Loblolly  Pine,  by  Diameters 


Growth 

IN  Past 

Growth  in  FuTtJRE 

D.B.H. 

10  Years. 

20  Years. 

10  Years. 

20  Years. 

Inches 

Inches 

Inches 

Inches 

Inches 

10 

0.76 

2.26 

0.3 

11 

.76 

2.24 

.3 

12 

.77 

2.19 

.4 

0.6 

13 

1.00 

2.50 

.5 

.8 

14 

.82 

2.40 

.6 

1.0 

15 

.80 

2.90 

.7 

1.0 

16 

.76 

1.77 

.7 

1.1 

17 

1.22 

3.32 

.7 

1.2 

18 

.75 

2.23 

.7 

1.2 

19 

1.33 

2.77 

.6 

1.1 

20 

.77 

1.83 

.6 

1.0 

280.  Increased  Growth.  Method  of  Determination.  The  effect  on 
diameter  growth  of  trees  of  releasing  their  crowns  by  removal  of  a  portion 
of  the  stand  in  logging  cannot  be  predicted  accurately  on  stands  pre- 
vious to  cutting.  The  release  of  additional  supplies  of  soil  moisture 
and  fertility,  increased  light  and  other  favorable  influences,  is  not  deter- 
minative. The  ability  of  the  tree  to  take  advantage  of  these  favorable 
circumstances  varies  with  the  age  and  vigor  of  the  individual  crown. 
When  trees  have  passed  a  certain  relative  age  and  have  become  over- 
mature, they  no  longer  respond  as  vigorously,  and  some  species  make 
no  response  at  all,  while  others,  such  as  lodgepole  pine,  seem  to  retain 
the  power  of  increasing  their  growth  throughout  their  life.  Some  trees 
are  not  released  in  partial  cuttings;  hence  increased  growth  cannot 
be  expected  except  on  those  trees  which  are  benefited  and  have  the 
power  of  respon.se. 

The  factor  of  increased  growth  after  cutting  must  therefore  be  meas- 
ured by  studying  trees  growing  on  tracts  which  have  been  cut  over  at 
some  previous  period  coinciding  in  length  with  the  period  for  which 
the  prediction  of  growth  is  desired.  This  may  be  10,  20  or  30  years. 
Increase  in  growth  due  to  cutting  tends  to  disappear  as  the  stand 
adjusts  itself  to  the  new  conditions  and  closes  its  crown  canopy.  The 
competition  of  different  species  in  a  mixed  stand  and  their  ability  to 
occupy  space  released  by  cutting,  determines  which  of  these  species 
will  benefit  in  form  of  increased  growth. 


364  GROWTH  OF  TREES  IX  DIAMETER 

In  order  to  predict  growth  of  trees  for  anj-  given  set  of  conditions 
from  a  stud}'  of  diameter  growth  of  existing  trees,  it  is  necessary  to  select 
trees  whose  conditions  of  growth,  for  the  past  period  measured,  coincide 
as  closely  as  possible  with  the  conditions  of  site,  density  of  stand  and 
crown  spread  of  the  trees  whose  growth  is  to  be  predicted.  Only  in 
this  way  can  the  excessive  variability  of  diameter  growth  be  averaged 
on  a  useful  and  accm'ate  basis. 

Probably  the  greatest  utility  of  the  study  of  diameter  growth  is  as 
an  indication  of  the  possibilities  of  management.  Its  direct  relation 
to  the  crown,  and  its  dependence  on  growing  space  make  it  an  index 
of  the  results  of  thinning,  spacing  in  plantations,  and  selection  of  trees 
for  removal  in  mature  stands.  Maintenance  of  diameter  growth 
thi'oughout  the  life  of  a  stand  is  the  proof  of  successful  intensive  manage- 
ment. Since  the  rotation,  or  period  required  to  grow  timber,  is  indi- 
cated in  part  by  the  sizes  or  diameters  of  the  trees  which  permits  of 
their  use  for  given  products,  the  rate  of  diameter  growth  in  unthirmed 
versus  thinned  stands  gives  a  direct  indication  of  this  rotation  period, 
and  is  so  used. 

References 

Some  Suggestions  for  Predicting  Growth  for  Short  Periods,  J.  C.  Stetson,  Forestry 

Quarterly,  Vol.  VIII,  1910,  p.  326. 
Accelerated  Growth  of  Balsam  Fir  in  the  Adirondacks,  E.  E.  McCarthy,  Journal  of 

Forestry,  Vol.  XVI,  1918,  p.  304. 
Method  of  Taking  Impressions  of  Year  Rings  in  Conifers,  L.  S.  Higgs,  Forestry 

Quarterly,  Vol.  X,  1912,  p.  1. 
Notes  on  Balsam  Fir,  Barrington  Moore  and  R.  L.  Rogers,  Forestry  Quarterly,  Vol. 

V,  1907,  p.  41. 
Accelerated  Growth  of  Spruce  after  Cutting,  in  the  Adirondacks,  John  Bentley  Jr., 

A.  B  Recknagel,  Journal  of  Fore.stry,  Vol.  XV,  1917,  p.  896. 
Notes  on  a  ]Method  of  Studying  Current  Growth  Percent,  B.  A.  Chandler,  Forestry 

Quarterly,  Vol.  XIV,  1916,  p.  453. 


CHAPTER  XXV 
GROWTH  OF  TREES  IN  HEIGHT 

281.  Purposes  of  Study  of  Height  Growth.  The  rate  of  height 
growth  in  trees  is  desired  in  order  to  determine  the  relative  ability  of 
different  species  in  a  mixed  stand  to  sm-vive  and  dominate  their  com- 
petitors. Height  growth  is  the  factor  which  largely  determines  the 
future  composition  of  mixed  even-aged  stands,  A  condition  of  sup- 
pression is  indicated  by  the  diminution  of  height  growth.  Trees  capable 
of  living  under  suppression  have  the  power  of  maintaining  a  much 
reduced  height  growth  for  a  long  period  and  of  afterwards  recovering 
and  increasing  this  rate.  In  the  second  place,  data  on  height  growth 
are  desired  to  determine  the  quality  of  site  as  a  basis  for  classifying  plots 
in  the  study  of  yields  per  acre  for  yield  tables.  The  relative  heights 
based  on  age  which  are  attained  by  trees  and  stands  are  a  close  indica- 
tion of  the  site  quality,  even  superior  to  volume  production  as  a  reliable 
index  of  site.  Finally,  height  growth  is  desired  as  a  step  in  the  deter- 
mination of  the  growth  of  trees  in  volume  whenever  the  latter  data  are 
required. 

282.  Influences  Affecting  Height  Growth.  Species.  The  juvenile 
period  following  germination  (§  2.57)  is  followed  by  a  period  of  rapid 
height  growth  which  is  maintained  until  the  tree  has  reached  from 
two-thirds  to  three-fourths  of  its  total  maximum  height.  This  period 
is  coincident  with  the  rapid  reduction  of  numbers  in  an  age  class  and 
with  the  expansion  of  the  .crowns  and  the  elimination  by  suppression 
of  those  trees  which  are  unable  to  maintain  their  position  and  crown 
spread  in  the  stand  through  being  overtopped. 

The  third  period  is  marked  by  increasing  slowness  and  finally  by 
practical  cessation  of  height  growth  and  a  marked  change  in  form  of 
crown.  In  some  hardwoods  this  is  the  result  of  division  of  the  main 
stem  into  several  branches,  and  in  conifers  it  is  characterized  by  the  loss 
of  the  habit  of  producing  annual  whorls  of  branches.  This  habit, 
however,  is  retained  by  many  species  such  as  spruce  and  fir.  When 
the  power  to  produce  annual  whorls  is  lost,  the  growth  in  height  becomes 
similar  to  that  of  branches.  The  power  of  recovery  of  height  growth, 
which  has  been  retarded  or  suppressed,  is  lost  at  an  early  age  in  intoler- 
ant species,  but  with  tolerant  species  may  be  retained  for  a  long  period. 

365 


366  GROWTH  OF  TREES  IX  HEIGHT 

Unless  trees  can  maintain  a  satisfactory  continuous  rate  of  height 
growth  individuals  so  stunted  never  attain  the  full  height  and  form 
of  an  average  mature  tree. 

The  rapidity  of  height  growth  and  the  total  heights  ultimately 
attained  are  a  specific  characteristic  which  is  retained  whether  the 
species  is  growing  in  mixture  with  other  species  having  different  rates 
of  height  growth,  or  in  pure  stands.  Competition  of  faster  growing 
species  does  not  serve  to  stimulate  the  rate  of  height  growth  of  a  species 
to  an  appreciable  extent.  Height  growth  plays  an  important  role  in 
the  survival,  dominance  and  suppression  of  competing  species. 

Quality  of  Site.  The  height  growth  of  trees  and  stands  is  directly 
affected  by  the  quality  of  the  site,  to  such  an  extent  that  the  rate  of 
growth  of  trees  in  height,  and  the  total  heights  attained  serve  as  the 
most  reliable  index  for  determining  differences  in  site  qualities  and 
formulating  a  basis  of  classification  for  sites.  This  relation  between 
height  growth  and  site  quality  is  largely  independent  of  one  of  the  factors 
which  influence  diameter  growth  of  trees  (§  270)  namely,  density  of 
stand.  Although  in  some  species,  especially  hardwoods  with  deliques- 
cent stems,  total  height  attained  is  less  for  open-grown  trees  than  for 
crowded  trees,  this  is  not  always  the  case  and  the  rate  of  height  growth 
is  usually  retained.  On  the  other  hand,  stands,  especially  of  conifers, 
which  are  so  densely  stocked  as  to  lead  to  stunting  and  starvation, 
wiU  show  a  decided  loss  of  height  growth.  One  instance  is  recorded 
in  which  a  stand  of  lodgepole  pine  70  years  old  containing  70,000  trees 
per  acre,  had  attained  a  height  of  but  10  feet. 

The  law  of  height  growth  of  trees  in  a  stand  is  to  maintain  as  far 
as  possible  an  even  rate  of  growth  for  all  the  trees  in  an  age  class  or  crown 
canopy.  There  is  considerable  differentiation  between  trees  with 
dominant,  intermediate  and  overtopped  crowns,  the  individual  rate 
of  height  growth  decreasing  progressively  with  the  loss  of  vigor  and 
dominance  of  the  crown;  but  this  differentiation  is  constantly  dimin- 
ished for  the  surviving  trees  in  an  age  class  by  the  death  of  the  over- 
topped trees  whose  rate  of  height  growth  has  slowed  down. 

When  the  growth  in  height  for  stands  is  measured,  it  is  gaged  by 
the  growth  of  dominant  or  sub-dominant  trees,  which  gives  very  con- 
sistent results.  By  thus  eliminating  the  effect  of  crown  class,  height 
growth  of  stands  becomes  almost  directly  an  expression  of  species  and 
of  site  quality. 

Crown  Class  ana  Suppression.  The  influence  of  shading,  which 
kills  overtopped  trees  in  an  even-aged  stand,  also  has  a  very  marked 
influence  on  height  growth  of  trees  of  an  age  class  growing  under  sup- 
pression or  in  the  shade  of  older  trees.  The  normal  rate  of  height 
growth  is  checked  by  shade,  and  if  it  does  not  result  in  death  the  tree 


RELATIONS  OF  HEIGHT  GROWTH  AND  DIAMETER  GROWTH     367 


survives  with  so  greatly  reduced  a  rate  of  growth  in  height  that  this 
rate  is  no  indication  of  the  capacity  of  the  species  nor  of  the  quahty 
of  the  site.  Normal  heights,  both  as  to  growth  for  a  current  period 
and  total  height  attained  at  a  given  age,  can  be  determined  only  for 
trees  which  have  grown  throughout  then-  life  cycle  free  from  suppression 
or  overtopping. 

283.  Relations  of  Height  Growth  and  Diameter  Growth.  Although 
both  growth  in  height,  and  growth  in  diameter,  are  responsive  to  site 
quahty,  they  follow  different  laws  in  response  to  density  of  stand  and 
crown  class.  As  the  result  of  the  tendency  for  all  trees  in  even-aged 
stands  of  intolerant  species  either  to  maintain  the  average  height  growth 
of  the  stand  or  to  die,  the  relation  between  diameters  and  heights  for 
individual  trees  is  not  consistent.  The  diameter  growth  of  dominant 
trees  is  relatively  faster  than  the  height  growth,  while  the  height  growth 
of  the  trees  in  danger  of  being  overtopped,  although  a  little  slower  than 
that  of  these  dominant  trees,  is  still  relatively  faster  than  their  diam- 
eter growth  which  falls  off  in  proportion  not  to  height  but  to  spread 
of  crown.  For  this  reason  a  dominant  tree  of  a  given  height  will  be  a 
stout  tree  with  low  form  quotient  (§171)  while  a  suppressed  tree  in 
the  same  stand  will  be  slender  and  cylindrical. 

These  relations  are  emphasized  when  trees  of  different  stands  are 
compared  on  the     basis    of  diameter.      Dominant    trees    of    a    given 
diameter  will  be  comparatively  short,  while  suppressed  trees  of  this 
diameter  will  be 
tall  and  slender. 
When   the    ages 
of  these  trees  are 
compared,      the 
short    dominant 
tree  is  found  to 
be  a  young  tree, 
compared     with 
the     suppressed 
tall  tree,  which  is 
much  older. 

These  rela- 
tions      between 
height  and  diam- 
eter    of     stands  ^^^   76.— Heights  of  trees  based  on  diameter  in  three  even-aged 
and      trees      are       stands  compared  with  heights  of  dominant,  intermediate  and 
shown  in  Fig.  76.       suppressed  trees  of  different  diameters. 
Within  a   given 
age  class,  the  curves  indicate  the  somewhat  slower  growth  in  height 


BO 





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368 


GROWTH  OF  TREES  IN  HEIGHT 


(1)         (2)        (S)  (4)        (5> 

Rings      Height  Length   Years  to  Years  to' 

in  of  of  Log    Grow  in  Grow-to 

Section    Section  Feet        height   height  of 

Feet  for  Log    Section 


of  'he  suppressed  trees,  but  the  maintenance  of  nearly  the  average 
rate  for  all  surviving  trees.  But  the  dotted  lines  indicate  the  greater 
height  of  suppressed  trees  having  a  given  diameter,  when  compared 
with  dominant  trees. 

284.  Measurement  of  Height  Growth.  For  the  juvenile  period  of 
height  growth  of  seedlings  and  saplings  a  practical  method  of  measure- 
ment is  to  determine  the  total 
age  and  the  total  height  of 
dominant  trees  (§256  and  §257). 
Trees  which  will  not  survive 
should  not  be  measured  for 
height.  For  young  conifers  show- 
ing annual  whorls,  the  exact 
height  growth  for  each  year  may 
})e  determined  by  measuring  the 
length  of  the  whorl.  This  method 
is  used  in  measuring  the  annual 
height  growth  of  coniferous  plan- 
tations (§258). 

On  older  trees  height  growth 
should  be  measured  by  analyzing 
the  growth  of  individual  trees. 
Total  height  growth  for  a  given 
tree  is  obtained  when  its  height 
and  total  age  are  known,  and  a 
composite  growth  ciuve  may  be 
built  up  as  suggested  for  seed- 
lings, by  obtaining  these  data  for 
a  number  of  trees  of  different 
ages  on  the  same  site  quality, 
plotting  the  heights  on  the  basis 
of  age  and  drawing  an  average 
curve  of  height  on  age.  But  a 
more  accurate  method  is  possible 
when  each  tree  has  been  cut  into 
several  sections,  the  age  of  which 
can  be  determined  from  ring 
counts.  In  this  case  as  many 
points  for  a  curve  of  height 
growth  are  found  as  there  are 
sections  cut,  and  these  points 
form  a  true  growth  curve  for  the  tree.  Diameter  growth  begins,  at 
a  given  section,  in  the  year  in  which  the  tree  reaches  the  height  of  this 


53 

1 

70 

16 

1 

26 

26 

37 

i 

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44 

33 

33 

A 
\ 

37 

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8 

7 

64 

17 

16 

8 

4 

68 

9 

12 

1      I 

/• 

'\ 

\^-i 

70 

^  z 

1 

3 

V^ 

Age 

Age 

of  Seedling,  3  Years 
ofTreej  70  Years 

Fig.  77. — Method  of  determining  the 
growth  in  height  of  a  tree  from  the 
ages  of  upper  sections,  or  ring  counts. 
The  difference  in  age  between  consecu- 
tive sections  indicates  the  period  re- 
quired to  grow  in  height  from  the  lower 
to  the  upper  section. 


MEASUREMENT  OF  HEIGHT  GROWTH 


369 


section.  The  number  of  rings  shown  by  the  section,  when  subtracted 
from  the  total  age  of  the  tree  (age  of  stump  plus  seedling  age)  gives 
the  years  required  to  grow  to  this  height.  The  process  as  shown  in 
Fig.  77  consists  of  the  following  steps: 

1.  Determine  age  of  tree  from  stump  plus  seedling  age  (§  257). 

2.  Count  the  rings  at  each  successive  upper  section,  and  measure 

length  of  section  to  get  height  from  ground.     Include 
height  of  stump. 


§6 

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48 
40 

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X 

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11 
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IG 

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8 

* 

Trees 
9 

averaged  f 
6 

)r  each  dec 
4 

ide® 
3 

4 

2 

-10  "3 


- 10  i 


10 


20 


30 


50 


60 


40 
Age,  Years 

Fig.  78. — Alternate  methods  of  averaging  the  heights  of  trees,  for  a  curve  of  height 

based  on  age.     Original  data  plotted.     For  curve 0 average   age 

at  fixed  heights  is  found.     For  curve © average  height  for  each  decade. 

The  prolonged  curve is  made  necessary  by  dropping  out  of  fast-growing 

trees  from  the  average  by  decades. 

3.  Subtract  these  counts  successively  from  total  age  of  tree,  to 

obtain  total  height  growth  at  each  section  and  age. 

4.  Subtract  the  age  of  any  section-  from  that  of  the  one  below, 

to  find  the   period   required   for  the   current  growth  in 
height  for  the  length  of  section. 

This  method  may  be  simplified  by  first  computing  the  height  growth 
curve  for  the  portion  above  the  stump,  on  all  trees,  and  afterwards 
making  the  average  correction  required  for  stump  height  and  correspond- 
ing age  of  seedUng,  on  the  final  curve  or  table. 


370 


GROWTH  OF  TREES   IN   HEIGHT 


Graphic  Method.  In  averaging  together  the  data  for  height  growth  on  the  basis 
of  age,  it  is  evident  that  few  if  any  points  will  fall  at  the  same  age,  even  if  taken 
at  the  same  height  above  ground.  For  this  reason,  the  most  convenient  method  of 
determining  an  average  rate  of  height  growth  based  on  age  is  to  plot  the  original 
data  for  each  tree,  and  draw  a  curve  based  on  ocular  inspection  of  the  result  assisted 
by  weighting  the  points  or  calculating  the  position  of  the  average  point  if  the  data 
are  not  sufficiently  abundant  to  dispense  with  this  step.  In  this  graph,  age  is  placed 
on  the  horizontal  scale  and  height  in  feet  on  the  vertical  scale. 

It  is  not  practicable  to  determine  the  arithmetical  average  height  at  each  separate 
age  previous  to  plotting  the  data.  This  is  best  done  from  the  graph.  The  height 
growth  of  ten  trees,  which  were  sectioned  at  8-foot  intervals  above  the  stump 
is  shown  in  Fig.  78.  Stump  height  is  omitted.  The  heights  at  each  8-foot  section 
fall  on  the  same  horizontal  line,  i.e.,  have  the  same  ordinate.  The  total  or  final 
heights  represent  the  height  of  the  tree. 

Two  methods  of  averaging  the  data  are  shown.  By  the  first,  all  points  falling 
in  the  same  decade  are  averaged  for  the  points  marked  O .  The  number  of  points 
used  is  indicated  at  base  of  Fig.  78.  This  method  is  based  on  age,  but  in  some  decades 
the  same  tree  enters  twice  while  in  others  it  does  not  appear.     The  depression  of  the 

curve  at  final  decade  is  caused  by 
the  dropping  out  of  eight  of  the  ten 
trees  from  the  average. 

The  second  method  is  to  aver- 
age the  age  at  each  8-foot  point. 
This  average,  marked  (8*,  is  then 
based  not  on  age  but  on  height,  but 
is  plotted  on  age.  Since  all  ten  trees 
enter  this  average  at  each  of  three 
points,  the  curve  is  more  regular 
than  the  first.  There  is  not  the 
same  objection  to  interchanging  the 
basis  of  this  curve  between  age  and 
height  as  outlined  above,  as  there 
is  in  studying  diameter  growth, 
since  the  rate  of  height  growth 
-Method  of  correcting  curve  of  height  j^^^  ^^^^  ^^^^^  ^^  ^^  more  con- 
growth  based  on  stump,  by  addmg  height  ^ig^ently  a  function  of  age  and  vice 
and  age  of  seedling,  thus  givmg  height  ^^^^^^  ^^^  ^j^^  ^^^^  q^^jj^^  ^^  ^.^^^ 
growth  of  tree  based  on  its  total  age.  ^^.j^  j^^.  diameter    growth  two  or 

more  additional  variables  influence  the  rate  of  growth  (§  296  and  §  270). 

The  height  growth,  as  read  from  the  above  curve,  may  be  shown  in  a  table  based 
on  total  age  and  height  of  tree,  by  adding  average  stump  height  (of  1  foot),  and  seed- 
ling age  (of  2  years)  to  the  curve,  and  reading  the  corrected  values  from  the  pro- 
longed curve,  as  shown  in  Fig.  79. 

The  values,  read  for  even  decades  are  given  in  Table  LVII:  ^ 

>  The  averaging  of  the  above  data  to  obtain  the  weighted  average  points  may  be 
simplified,  after  the  points  are  plotted,  by  the  following  method.  For  the  first 
decade,  average  heights  include  7  trees,  each  8  feet  or  points  above  the  base  of  the 
graph,  or  "  up  "  and  1  tree  16  feet  "  up  "  or  a  total  of  72  points  "  up";  average  for 
8  trees,  9  points  "up."  Average  age  includes  3  trees  4  years  or  points  to  right  of 
the  left  margin  of  the  graph,  or  "  over,"  2  trees  5  years  "  over,"  1  tree  6  years,  1 
tree  7  years  and  1  tree  8  years,  a  total  of  43  years,  average  5.4  points  "  over," 


<cgN 


Fig.  79. 


MEASUREMENT  OF  HEIGHT  GROWTH 


371 


TABLE  LVH 

Height  Growth  of  Chestnut  Oak,  Milford,  Pike  Co.,  Pa. 

Basis,  Ten  Trees 


Age. 

Height. 

Height. 

Years 

Feet 

s 

Feet 

2 

1 

40 

35 

10 

10 

50 

41 

20 

19 

60 

46 

30 

28 

70 

50 

The  total  height,  based  on  total  age,  of  these  ten  trees  is  shown  by  the  last  ten 
points.  It  is  evident  that  with  a  sufficient  number  of  trees  of  all  ages,  a  height  curve 
based  on  age  could  be  constructed  without  analyzing  the  trees  above  the  stump  sec- 
tion, but  it  is  equally  evident  that  such  analyses,  as  shown  in  the  figure,  not  only 
multiply  the  weight  of  each  tree  by  the  number  of  sections  taken  but  substitute 
actual  growth  of  given  trees  for  composite  growth  by  comparison  of  different  trees. 
Such  a  history  or  record  of  growth,  whether  it  is  of  diameter,  height  or  yields  per  acre, 
(§  266  and  §  326),  is  the  most  reliable  basis  of  growth  data. 

Current  HeigH  Growth.  The  current  or  periodic  height  growth 
for  the  last  decade  or  two  may  be  required  to  complete  the  data  for 
determining  the  current  volume  growth  of  trees.  This  should  be  meas- 
ured on  felled  trees  by  cutting  back  the  tip  until  a  section  is  found 
containing  the  required  number  of  rings.  For  determining  growth 
for  short  periods  this  is  a  simple  process.  Only  on  young  trees  should 
the  last  period  of  growth  be  determined  by  counting  back  the  number 
of  whorls  from  the  tip  In  older  timber  and  especially  on  standing 
trees,  it  is  impossible  to  secure  accuracy  by  this  method. 

285.  The  Substitution  of  Curves  of  Average  Height  Based  on 
Diameter  for  Actual  Measurement  of  Height  Growth.  In  studies 
intended  to  determine  the  volume  growth  of  trees,  especially  of  seed 
trees  and  young  timber  left  on  cut-over  lands,  a  method  has  been  sought 

data  are  identical  with  the  original  figures,  the  advantage  lying  in  the  graphic  classi- 
fication of  the  data  for  averaging.  But  for  the  next  and  subsequent  decades  the  base, 
for  age,  can  be  shifted  to  the  right  by  one  decade,  so  that  the  points  "  over  "  include 
only  the  fractional  decade,  while  for  height  the  base  can  be  raised  to  exclude  that 
portion  of  the  graph  which  includes  no  points.     Thus,  for  the  third  decade  there  are 

9  points,  whose  weights  vary  from  1  to  10  years  or  points.  For  age,  the  basis  or 
zero  is  20  years  and  the  points  "  over  "  are  1,  2,  3,  6,  6,  7,  8,  9  and  10,  or  a  total  of 
52,  average  5.8  points  "  over  "  or  25.8  years.     For  height  the  base  may  be  taken  at 

10  feet  and  the  points  "  up  "  are  then  6,  14,  14,  14,  22,  22,  22,  22,  30,  a  total  of  166 
points  "  up,"  average  18.4  points  up,  or  28.4  feet.  In  plotting,  where  two  or  more 
dots  fall  on  the  same  point,  a  numeral  must  be  written  in,  as  indicated,  to  show  the 
weight  of  the  point. 


372  GROWTH  OF  TREES  IN  HEIGHT 

b}^  which  this  volume  growth  can  be  predicted  by  a  study  of  diameter 
growth  and  by  the  determination  of  the  resultant  volume  of  the  tree 
from  its  average  height  and  volume  as  shown  in  a  volume  table.  In 
order  to  save  the  expense  of  determining  the  actual  growth  in  height 
of  these  trees,  recourse  is  had  to  the  relation  between  height  and  diam- 
eter as  expressed  by  a  curve  of  heights  based  on  diameter  such  as  is 
illustrated  in  Fig.  76.     The  process  is  as  fo'lows: 

1.  The  increase  in  diameter  for  a  given  period  for  a  tree  of  a  certain 
diameter  is  predicted  or  determined;  e.g.,  the  tree  may  grow  from  a 
10-inch  to  a  12-inch  diameter. 

2.  The  average  curve  of  height  on  diameter  shows  the  heights  of 
a  10-inch  and  12-inch  tree  respectively. 

3.  It  is  then  erroneously  assumed  that  the  10-inch  tree  will  grow 
in  height  by  the  amount  of  this  difference,  that  is,  that  it  will  have, 
when  12  inches  in  diameter,  the  height  of  a  12-inch  tree.  The  fallacy 
of  this  reasoning  is  clearly  evident  when  applied  to  any  single  tree  or 
to  any  stand  of  a  given  age.  If  the  tree  or  stand  is  young  and  the  curve 
of  height  on  diameter  has  been  prepared  for  trees  of  this  class  or  age 
in  the  vicinity,  the  tree  will  grow  much  faster  than  the  difference  in 
height  indicated  by.  this  curve,  and  the  same  is  true  of  the  trees  in  an 
even-aged  stand.  But  for  old  or  mature  even-aged  stands,  the  reverse 
may  be  true  and  the  trees  may  grow  more  slowly  than  the  difference 
shown.  Such  a  curve  is  not  a  growth  curve  at  all,  but  a  curve  showing 
the  average  heights  attained  by  trees  which  may  be  all  of  the  same 
age.  Only  when  the  curve  of  height  based  on  diameter  includes  trees 
of  all  ages  as  well  as  diameters,  does  it  approach  the  form  of  a  true 
growth  curve,  as  shown  by  the  dotted  curves  in  Fig.  76.  To  do  this 
it  must  harmonize  two  variables,  namely,  diameter  and  age.  In  general, 
small  trees  are  young  trees  and  large  trees  are  old  trees.  If  sufficient 
data  have  been  included,  covering  wide  enough  ranges  both  of  diameter 
and  of  age,  and  the  measurements  are  taken  on  the  same  site  quality, 
a  rough  average  is  obtained  in  which  the  height  of  a  tree  of  given  diam- 
eter is  correlated  with  the  age  of  tree  of  the  same  diameter.  The  more 
nearly  this  general  result  is  obtained,  the  more  reliable  will  be  the  aver- 
age results  of  applying  this  curve  in  predicting  the  growth  in  height 
through  the  medium  of  the  growth  in  diameter  to  trees  or  stands  of  all 
ages,  and  thus  avoiding  a  direct  study  of  height  growth.  It  is  obvious 
that  for  special  problems  on  specific  classes,  ages  and  stands  of  trees, 
no  such  generalized  curve  should  be  depended  upon,  but  a  few  measure- 
ments of  height  growth  on  the  trees  in  question  will  give  results  whose 
accuracy  justifies  the  expense. 

The  height  curve  of  even-aged  stands  is  determined  either  from  the 
height  growth  of  the  maximum  or  dominant  trees  in  the  stand,  or  from 


REFERENCES  373 

that  of  trees  containing  the  average  volume  of  the  stand.  It  has  been 
found  that  the  relation  between  dominant  and  average  trees  in  height 
growth  is  very  consistent,  and  either  basis  furnishes  an  index  to  the 
growth  rate,  which  may  be  used  later  in  classifying  the  plots  on  a  basis 
of  site  for  the  construction  of  yield  tables. 

On  account  of  its  uniformity  for  a  given  site  quality,  average  height 
growth  may  be  determined  from  the  analysis  of  from  five  to  twenty- 
five  average  or  dominant  trees  with  very  satisfactory  results. 

References 

Relation  between  Spring  Precipitation  and  Height  Growth  of  Western  Yellow  Pine, 

G.  A.  Pearson,  Journal  of  Forestry,  Vol.  XVI,  1918,  p.  677. 
Relation  between   Height  Growth  of  Larch  Seedlings  and  Weather  Conditions, 

D.  R.  Brewster,  Journal  of  Forestry,  Vol.  XVI,  1918,  p.  861. 


CHAPTER  XXVI 
GROWTH  OF  TREES  IN  VOLUME 

286.  Relation  between  Volume  Growth,  Form  and  Diameter  Growth. 

The  growth  of  trees  in  volume  is  the  product  of  the  growth  in  height 
and  the  growth  in  area  at  different  portions  of  the  stem,  which  is 
expressed  in  diameter  growth.  The  exact  form  of  the  tree  and  the  rela- 
tion between  diameter  and  resulting  area  and  volume  growth  at  dif- 
ferent heights  from  the  ground  are  the  result  of  mechanical  laws  of 
resistance  to  stresses.  The  form  of  the  tree  is  intended  to  resist  wind 
pressure  in  order  to  maintain  its  upright  position  and  not  be  snapped 
off  or  blown  over.  As  was  shown  in  Chapter  XVI  this  pressure  is 
directly  caused  by  the  force  of  the  winds  acting  on  the  crown  and 
focused  in  the  center  of  area  of  the  crown  exposure  (§172).  Growth 
in  diameter  will  be  distril^uted  in  response  to  this  strain  to  give  the 
maximum  resistance  with  the  minimum  of  material. 

As  the  form  of  crown  and  its  position  with  respect  to  the  bole  changes, 
the  point  of  average  pressure  shifts  and  the  form  of  the  tree  will  be 
modified  by  a  more  rapid  diameter  growth  at  the  points  requiring 
strengthening.  An  increase  in  the  stress  to  which  the  tree  is  exposed 
will  also  cause  changes  in  the  distribution  of  growth.  Trees  which 
have  grown  in  a  protected  stand  and  are  exposed  by  cutting  will  either 
blow  over  or  will  rapidly  strengthen  their  resistance  by  laying  on 
increased  growth  at  the  base  or  stump  where  the  effect  of  this  change 
in  exposure  is  most  evident.  The  upper  form  of  the  tree,  being  influ- 
enced by  crown,  does  not  change  appreciably.  Trees  in  a  leaning 
position  continually  add  most  of  the  diameter  growth  on  the  under  side. 

Where  the  growth  in  volume  of  a  tree  on  cut-over  areas  is  judged 
from  the  growth  in  diameter  on  the  stump,  without  correction,  a  rate 
of  from  50  to  100  per  cent  in  excess  of  the  true  volume  growth  may  be 
obtained.  S\ich  measurements  should  therefore  be  taken  at  B.H. 
where  the  effect  of  this  increase  is  not  felt,  or  else  growth  measurements 
taken  on  the  stump  must  be  carefully  compared  with  measurements 
at  upper  points  on  the  tree. 

287.  Tree  Analysis,  its  Purpose  and  Application.  The  analysis  of 
an  individual  tree  by  the  measurement  of  diameter  growth  at  upper 
sections,  in  order  to  determine  its  volume  growth,  is  termed  tree  analysis, 
(synonym,  stem  analysis,  §  254) .     This  process  enables  one  to  determine 

374 


SUBSTITUTION  OF  VOLUME  TABLES  FOR  TREE  ANALYSIS  373 

the  upper  dimensions  and  volume  of  trees  of  a  smaller  size  than  those 
which  exist  in  a  given  stand.  This  is  an  advantage  in  case  such 
smaller  sizes  are  lacking,  but  where  present  they  may  be  directly  meas- 
ured. The  volume  which  trees  produce  at  given  ages  can  thus  be 
obtained  in  one  of  two  ways,  either  by  measuring  trees  of  different 
ages  directly  for  volume  or  by  analyzing  a  single  tree  or  a  number  of 
trees  in  order  to  determine  the  past  growth  in  volume.  The  latter 
method  alone  will  bring  out  the  changes  which  take  place  in  form,  as 
described  above,  due  to  altered  conditions.  In  applying  such  growth 
figures  to  answer  the  fundamental  question  of  growth  studies,  namely, 
what  is  the  rate  of  growth  in  volume  per  acre,  annually  or  for  a  given 
period,  not  only  must  the  growth  of  average  rather  than  individual 
trees  be  determined,  but  the  relations  of  these  average  trees  to  the 
number  of  trees  which  will  survive  on  an  acre  at  different  ages  must 
also  be  known  (§  275).  Since  the  recording  and  working  up  of  growth 
measurements  to  determine  total  volume  growth  is  slow  and  expensive, 
only  a  few  trees  may  be  taken.  It  is  necessary  that  these  trees  have 
the  average  form  quotient  for  the  stand  to  which  their  results  will  be 
applied.  This  means  either  a  careful  selection  or  a  chance  of  incurring 
an  error  of  from  10  to  15  per  cent  by  the  accidental  selection  of  trees 
which  depart  from  this  average  in  form. 

288.  Substitution  of  Volume  Tables  for  Tree  Analysis.  The  growth 
of  an  average  tree  is  determined  by  the  average  growth  in  D.B.H., 
the  average  height  growth  and  the  average  growth  in  diameter  at 
upper  sections,  of  which  the  most  important  is  the  diameter  growth 
at  one -half  of  the  height.  The  growth  of  upper  diameters  is  usually 
accompanied  by  a  change  in  form,  caused  by  a  change  in  the  length  and 
position  of  the  crown.  This  is  illustrated  in  Fig.  80  (§  290)  for 
which  tree  both  butt  swelling  and  upper  diameters  increased  faster 
than  growth  at  8  feet. 

Relying  upon  the  maintenance  of  a  consistent  tree  form  for  average 
trees,  a  method  is  in  common  use  as  a  substitute  for  the  analysis  of 
trees  to  determine  their  volume  growth.  This  method  depends  upon 
the  use  of  volume  tables  to  determine  the  volume  of  trees  whose  height 
and  diameter  are  known.  Since  a  standard  volume  table  expresses 
the  actual  volume  of  average  trees  much  more  accurately  than  it  can 
1)6  obtained  by  the  analysis  of  a  few  sample  trees,  the  substitution 
of  a  volume  for  the  average  tree  taken  from  this  table  enables  the  investi- 
gator to  concentrate  his  effort  on  determining  average  growth  in  D.B.H. 
and  in  height.  The  actual  measurement  of  height  growth  involves 
the  counting  of  rings  for  determination  of  age  of  upper  sections  on  at 
least  a  few  trees  (§  284),  but  dispenses  with  the  measurement  of  diameter 
growth  on  these  upper  sections,  and  requires  from  one-fifth  to  one-tenth 


376 


GROWTH  OF  TREES  IN  VOLUME 


as  many  trees  as  are  required  for  the  study  of  average  diameter  growth 
on  account  of  the  greater  consistency  of  height  growth  based  on  age. 
From  a  curve  of  growth  in  diameter,  based  on  age  (§  267  and  §  268), 
the  diameters  of  the  average  trees  at  different  ages  are  determined. 
From  a  second  curve  of  height  based  on  age  (§284),  the  heights  of  the 
same  average  trees  for  different  ages  are  found.  Since  diameter  and 
height  determine  the  volume  as  classified  in  these  standard  volume 
tables,  the  requisite  volume  is  interpolated  from  the  values  in  the  table 
for  the  nearest  ^o-inch  in  diameter  and  foot  in  height.  The  successive 
volumes  found  in  this  way  indicate  the  growth  laid  on  by  the  average 
tree.  This  may  be  expressed  in  whatever  unit  of  volume  is  represented 
by  the  volume  table  employed.  This  method  is  almost  universally 
substituted  for  volume  growth  analysis  wherever  figures  on  average 
volume  growth  of  trees  are  desired.  This  method  is  illustrated  by 
Table  LVIII.i 

1  The  method  of  interpolation  is  illustrated  as  follows.  The  60-year-old  tree  is 
6.6  inches  in  D.B.H.  and  46  feet  high.  The  values  in  the  standard  table  from 
which  to  interpolate  are,  in  cubic  feet. 


D.BH. 
Inches 

Heights 

40  Feet             50  Feet 

Cubic  Feet 

6 

7 

4.2 
5.7 

5.0 
6.6 

The  difference  for  1  inch  is  1.5  cubic  feet  for  40-foot  trees,  and  for  .6  inch,  is 
.9  cubic  foot,  giving  for  6.6  inches,  5.1  cubic  feet.  The  average  difference  between 
40-  and  50-foot  trees  is  .85  cubic  foot.  For  46-foot  trees  it  is  .6  times  .85  =  .51  cubic 
foot.  Then  5.1 -|-. 51  =  5.61  rounded  off  to  5.6  cubic  feet  as  the  interpolated  volume 
sought.  These  interpolations  are  more  expeditiously  made  from  graphic  plotting 
of  the  values  in  the  volume  table. 

One  drawback  to  the  use  of  volume  tables  as  a  substitute  for  actual  growth  analy- 
sis is  illustrated  in  the  attempt  to  measure  growth  at  successive  decades  on  sample 
plots  for  scientific  purposes.  Even  here,  if  a  single  volume  table  is  carefully  pre- 
pared, combining  aU  age  classes,  the  transition  in  form  from  young  to  old  trees  is 
blended  with  the  volumes  shown  in  the  table  for  small  and  large  trees,  but  where,  as 
for  instance  with  Western  yellow  pine,  separate  volume  tables  were  made  for  black 
jack  or  young  trees  and  for  yellow  pine  or  old  trees  which  differed  by  about  10  per 
cent  in  the  average  volume  due  to  difference  in  form,  the  application  of  a  different 
volume  table  to  trees  passing  from  one  age  class  to  the  other  caused  a  jump  of  10 
per  cent  in  the  volume  due  apparently  to  growth,  but  in  reality  due  to  the  irregular 
distribution  of  this  growth  by  separation  of  form  classes  in  these  tables. 


MEASUREMENTS  REQUIRED  FOR  TREE  ANALYSES 


377 


TABLE  LVIII 

Growth  of  Chestnut  Oak 

In  Cubic  Volume,  from  Diameter  and  Height  Growth  and  Use  of  a  Standard 

Volume  Table 


Corresponding  * 

Age. 

D.B.H. 

Height. 

volume  from 

table  by 
interpolation. 

Periodic 
growth. 

Years 

Inches 

Feet 

Cubic  feet 

Cubic  feet 

10 

1.2 

10 

20 

2.5 

19 

30 

3.8 

28 

1.3    , 

1.35 
1.55 
1.40 

40 

5.0 

35 

2.65 

50 

5.9 

41 

4.2 

60 

6.6 

46 

5.6 

70 

7.2 

50 

7.0    ' 

*  Cubic  volumes  taken  from  Frothingham's  table  for  chestnut  oak  in  Bui.  96  Forest  Service, 
"Second  Growth  Hardwoods  in  Connecticut."  Height  from  Table  LVII,  §284.  Diameter  from 
growth  of  the  same  ten  trees  used  in  this  table. 


136 
30 
26 

\ 

}\ 

,10y 

ears 

V 

\ 

7\ 

10  1 

\ 

ears 

'1.0 

V 

I', 

10  \ 

A 

21  y 

'Kl5 
10 

\ 

\ 

\ 

1 

r'lo 

\  J 

. , 

I, 

yea 

3. 

^ 

0 

V\*\ 

6  \ 

10 

\ 

10  \io\ 

^y 

12      3     4      5     6 
Diameter,  inches 

Fig.  80. — Stem  analysis  of  a 
tree  36  years  old,  by  dec- 
ades, counting  in  from 
outer  ring,  based  on  stump. 
Stump  is  shown  below 
point  marked  0. 


289.  Measurements  Required  for  Tree 
Analyses.  The  data  required  in  a  tree 
analysis,  in  addition  to  those  taken  for 
volume  and  itemized  in  §  134  and  §  135, 
are, 

1.  Age  of  each  section  (height  above 
stump  and  length  given). 

2.  Growth  on  average  radius  from  center 
to  outer  ring,  by  decades. 

3.  Where  needed,  width  of  sap  and 
number  of  rings  in  sapwood. 

290.  Computation  of  Volume  Growth  for 
Single  Trees.  The  method  of  computing 
the  growth  in  volume  for  a  given  tree  is 
best  shown  by  graphic  illustration.  Fig. 
80  shows  the  dimensions  of  a  chestnut  oak 
36  years  old  at  the  stump,  and  the  size 
which  this  tree  had  when  26,  16  and  6 
years  old. 

To  correlate  the  growth  of  upper  section 
for  the  same  decades,  these  decades  are 
counted  from  the  circumference  inward,  as 
shown,  with  the  odd  rings  at  the  center. 
Diameter  growth  for  each  decade  is  then 


378 


GROWTH  OF  TREES  IN  VOLUME 


measured  from  center  outward, 
are  given  in  the  following  table: 


The  full  data  for  this  tree  analysis 


TABLE  LIX 
Stem  Analysis  of  a  Tree 


Species,  Chestnut  Oak. 
Date,  1912. 
Total  Height,  40  feet. 
Width  Crown,  14  feet. 
Tree  Class,  Suppressed. 


Locality,  Milford,  Pike  Co.,  Pa. 
D.B.H.,  4  inches.        Height  Stump,  1  foot. 
Merch.  Length,  20  feet. 
Length  Crown,  17  feet. 


Height 

Length 

Diameter, 

Width 

Diameter, 

above 

of 

outside 

bark, 

inside 

Age. 

stump. 

section. 

bark. 

single. 

bark. 

Feet 

Feet 

Inches 

Inches 

Inches 

Years 

Stump 

0 

1 

6.05 

0.5 

5.05 

36 

1 

8 

8 

3.95 

.3 

3.35 

31 

2 

16 

8 

3.5 

.2 

3.1 

24 

3 

24 

8 

2.3 

,15 

2.0 

17 

4 

32 

8 

1.0 

.05 

.9 

10 

Tip 

39 

7 

Distance  in  inches  on  average  radius  from  center  to  ring,  by  decades.     The 
first  column  shows  the  number  of  years  in  the  first  fractional  decade. 


(1) 

(2) 

(3) 

(4) 

(6) 

0.5 

1.3 

2.1 

2.5 

(1) 

0.05 

0.65 

1.25 

1.7 

(4) 

0.25 

1.05 

1.55 

(7) 

0.55 

1.0 

(10) 

0.45 

In  addition,  for  a  group  of  trees  analyzed,  the  site,  density  of  stand, 
character  of  trees  shown,  conditions  of  cutting  or  other  factors  whose 
influence  on  growth  is  to  be  determined,  are  recorded.  With  diameter 
at  each  decade  for  each  section  recorded,  the  total  volume  of  the  tree 
and  its  volume  at  each  decade  in  the  past,  e.g.,  for  36,  26,  16  and  6 
years,  is  obtained  by  methods  indicated  in  Chapter  III,  using  the 
Smalian  or  the  Huber  formula  for  cubic  contents. 

But  one  detail  is  lacking — the  actual  height  which  the  tree  had 
at  the  above  decades,  in  case  the  former  tip  falls  between  two  of  the 
sections  counted.  This  tip  contains  a  very  small  per  cent  of  total 
volume,  and  for  merchantable  contents  would  be  ignored.  But  for 
accurate  studies  of  total  cubic  contents  the  height  is  obtained  by  assum- 
ing that  the  height  growth  maintained  the  same  rate  per  year  as  shown 


SUBSTITUTING  AVERAGE  GROWTH  IN  FORM  OR  TAPERS    379 

for  the  entire  section  concealing  the  tip;  e.g.,  in  Fig.  80  the  third  sec- 
tion took  24—17  =  7  years  to  grow  8  feet.  The  tip  contains  4  rings, 
or  4  years'  growth.  Hence  its  height  is  y  of  8  feet  =  4.5  feet.  For  the 
second  section  the  period  required  was  31  —  24  =  7  years.  The  tip 
has  1  ring,  hence  its  height  is  y  of  8  ft.  or  1.1  ft.  or 

/  Age  of  tip  \ 

Length  of  tip=  I  — : . zv — ~      )  Length  of  section. 

\ Years  to  grow  length  ot  section/ 

The  age  of  any  one  tree  will  probably  fall  at  an  odd  j'ear  instead 
of  an  even  decade  and  the  age  of  the  average  tree  whose  volume  is 
calculated  will  fall  on  one  of  these  odd  years;  e.g.,  for  the  chestnut 
oak  ah)ove  analyzed  which  took  2  years  to  grow  to  stunip  height,  the 
table  and  figures  above  will  show  the  age  of  a  tree  8,  18,  28  and  38  years 
in  age.  To  find  the  volume  of  the  tree  at  even  decades,  as  10,  20,  30 
years  instead  of  odd  years,  the  volumes  as  determined  are  now  plotted 
on  cross-section  paper  on  which  age  is  placed  on  the  horizontal  scale 
and  volume  on  the  vertical  scale.  From  these  curves  the  volumes 
for  even  decades  can  be  read.  Bj-  averaging  these  volumes  on  the 
basis  of  age  the  average  growth  in  volume  is  obtained  for  all  the  trees 
analyzed. 

291.  Method  of  Substituting  Average  Growth  in  Form  or  Tapers, 
for  Volume.  The  taper  measurements  or  diameters  determined  from 
Fig.  80  thus  enable  one  to  ascertain  the  volume  of  the  tree  at  different 
ages  expressed  in  any  unit.  In  this  it  does  not  differ  from  taper  tables 
discussed  in  §  167  except  that  age  is  now  the  basis  of  the  dimen- 
sions shown. 

The  advantage  of  recording  the  tapers  for  the  individual  tree  rather 
than  its  separate  volumes  at  different  ages  applies  equally  to  the  average 
of  a  number  of  trees  analyzed  for  volume  growth.  For  this  reason 
the  method  of  computing  volumes  directly  for  each  tree  has  given  way 
entirely  to  the  method  described  below  by  which  the  average  tapers 
or  dimensions  of  all  of  the  trees  studied  are  first  determined.  From 
the  average  tree  thus  plotted,  the  volumes  can  then  be  found  for  any 
of  the  desired  units,  such  as  cubic  feet,  board  feet  in  an}-  given  log 
rule,  standard  ties  or  poles,  for  each  age  or  decade.  This  method 
reduces  the  work  of  computing  volumes  to  a  single  average  tree  for 
each  tree  class. 

The  first  requirement  of  this  method  is  a  curve  of  average  growth 
in  height  based  on  age  (§  284).  This  establishes  the  year  or  age  in  the 
life  of  the  tree  at  which  the  diameter  growth  of  each  upper  section 
at  a  given  height  originates  and  marks  the  zero  or  origin  of  the  curve 
for  this  section  when  plotted  on  the  age  of  the  tree  (§  269).  Second, 
a  separate  curve  of  diameter  growth  based  on  age  is  constructed  for 


380  GROWTH  OF  TREES  IN  VOLUME 

all  sections  which  fall  at  the  same  height  above  the  ground.  The  sum 
of  the  age  or  period  required  for  the  average  tree  to  reach  this  height, 
plus  the  age  or  period  represented  by  the  growth  of  the  section  equals 
the  age  of  the  tree  regardless  of  the  height  of  section.  It  is  evident 
then  that  the  average  curve  of  growth  in  diameter  for  any  of  these 
sections  can  be  plotted  on  a  single  sheet  of  cross  section  paper  whose 
horizontal  scale  represents  the  age  of  the  tree  and  whose  vertical  scale 
represents  the  diameter  of  any  cross  section.  A  cross  section  which 
does  not  begin  to  grow  in  diameter  for  17  years  will  diminish  to  zero 
and  the  curve  representing  its  growth  will  intersect  the  base  or  zero 
diameter  at  17  on  the  horizontal  scale  representing  age  of  tree. 

In  Fig.  70  (§  269)  a  curve  of  stump  diameter  based  on  the  age  of  the 
tree  was  shown  as  intersecting  this  base  at  the  age  represented  by  the 
seedling.  On  this  same  sheet  a  curve  representing  the  D.B.H.  and  one 
showing  the  diameter  at  the  top  of  the  first  16-foot  log  were  indicated 
with  their  points  of  intersection.  On  a  single  vertical  line  the  points 
shown  were  the  diameters  of  a  tree  of  a  given  age  and  indicated  the 
D.B.H.,  D.I.B.  at  stump  and  D.I.B.  at  top  diameter  of  first  log  for 
this  age.  But  to  get  a  curve  showing  these  three  dimensions  for  trees 
of  different  ages  in  the  illustration  given,  the  points  were  not  taken 
from  the  growth  of  one  tree,  but  by  the  measurement  of  several  trees 
differing  in  age,  stump  diameter  and  corresponding  D.B.H.  and  upper 
tapers.  The  connection  of  the  points  for  these  separate  trees  which 
differ  on  the  basis  of  age,  gives  the  curves  showing  the  increase  in  the 
■  upper  diameters  or  tapers  for  trees  of  different  ages. 

The  method  of  plotting  the  upper  diameters  showing  the  growth 
of  an  average  tree  at  the  different  ages  of  its  life  is  identical  with  this 
previous  method,  with  the  exception  that  instead  of  these  ages  being 
represented  by  the  final,  present  or  outer  dimensions  of  separate  trees, 
they  include  the  past,  interior  dimensions  as  well,  by  the  measurement 
of  past  growth.  Even  though  the  growth  is  an  average  of  many  trees, 
the  method  still  remains  the  same  since  each  decade's  growth  is  a  com- 
posite of  the  actual  growth  or  internal  dimensions  of  a  number  of  trees. 
The  method  of  plotting  the  data  is  as  follows: 

1.  Prepare  and  plot  a  curve  of  average  height  based  on  age  on  a 
separate  sheet. 

2.  Prepare  on  separate  sheets,  curves  of  average  diameter  growth 
for  all  cross  sections  falling  at  each  separate  height,  as  for  instance  a 
curve  for  sections  falling  at  8  feet,  16  feet,  etc.,  including  one  for  the 
stump  section.  It  is  assumed  that  the  height  of  seedlings  based  on 
age  has  been  determined  and  that  D.B.H.  has  been  correlated  with 
stump  D.I.B. 

3.  After  determining  the  initial  or  zero  year  for  each  of  the  curves 


SUBSTITUTING  AVERAGE  GROWTH  IN  FORM  OR  TAPERS 


381 


of  diameter  growth,  including  the  stump  section,  transfer  or  assemble 
each  of  these  curves  on  a  single  sheet  whose  zero  represents  the  zero 
3^ear  of  the  tree's  age. 

In  Fig.  81  the  curve  of  stump  growth  from  Table  LIX  is  plotted 
with  the  zero  at  2 
years,  age  of  seed- 
ling of  stump  height. 
This  is  usually  as- 
sumed to  be  also 
the  origin  of  the 
D.B.H.  curve.  For 
the  curve  of  diam- 
eter growth  at  8  feet, 
the  period  required 
to  grow  to  this 
height  by  Fig.  81, 
or  by  interpolation 
in  Table  LIX  is  7 
years  plus  2  j'ears 
for  seedling.  The 
zero  is  placed  at  9 
years.  Since  the 
first  fractional  dec- 
ade averaged  6  years 
on  these  sections,  the 
first  diameter  is  plot- 
ted above  9+6=15  j'ears,  and  subsequent  decades  at  25,  35 
etc.,  as  indicated  by  the  points. 

The  height  growth  for  section  3  at  16  feet  took  15+2  =  17  j^ears. 
The  first  fractional  decade  was  6  j^ears.  The  points  are  plotted  above 
23,  33,  43  years.  In  this  way  each  upper  section  is  plotted  on  the  sheet 
representing  the  age  of  the  average  tree.^ 

To  read  this  record  for  the  purpose  of  determining  the  volume  in 
any  given  unit  for  a  tree  of  a  given  age,  the  dimensions  of  a  tree  of  the 
required  age  fall  in  the  vertical  line  intersecting  this  age.  For  instance, 
a  tree  40  years  old  will  have  its  diameter  inside  bark  at  the  16-foot 
cross  section  indicated  in  Fig.  81  as  2.4  inches.  Reading  upwards 
as  the  diameter  increases,  the  next  lower  cross  section  has  a  diameter 
of  3.4  inches  and  D.B.H.  is  4.8  inches.  Since  the  height  or  distance 
between  these  cross  sections  cannot  be  shown  on  this  diagram,  but 


>  • 

y^ 

f 

A 

Y 

Z' 

#. 

/ 

/ 

/ 

W} 

A 

/ 

// 

/  \ 
/ 

A 

f 

/ 

<H 

/  \ 
/ 

// 

f 

^y 

.' 

/ 

/. 

n 

'A 

/ 

/ 

40 
,  years 


Fig.  81.— Diameters  at  8-foot  points,  for  an  average  tree 
at  different  ages,  or  growth  analysis.  Chestnut  Oak, 
IMilford,  Pike  Co.,  Pa. 


years. 


1  In  the  above  figure,  D.  B.  H.  outside  bark  exceeds  D.  I.  B.  at  stump  up  to 
about  7  inches.     This  frequently  occurs  on  small  thick-barked  trees. 


382  GROWTH  OF  TREES  IN  VOLUME 

only  diameter  based  on  age,  it  is  necessary  to  indicate  upon  the  curves 
the  height  which  each  curve  represents. 

This  series  of  curves  can  be  used  only  to  determine  the  diameters 
at  the  definite  points,  as  8,  16,  24  feet,  etc.,  for  which  curves  have  been 
drawn.  It  corresponds  with  Fig.  32  (§  168)  for  taper  curves.  To 
obtain  the  growth  in  form  for  the  tree  at  intervening  points,  these 
curves  should  be  replotted  in  the  form  shown  for  a  single  tree,  in  Fig.  80. 

From  the  average  tree  thus  shown,  the  growth  by  decades  in  any 
form  or  length  of  product  can  be  directly  computed,  to  any  required 
diameter  limit. ^ 

292.  Substitution  of  Taper  Tables  for  Tree  Analyses.  Just  as  the 
above  method  substitutes  the  form  of  the  average  tree  at  different 
ages  for  the  direct  calculation  of  the  volume  at  these  ages,  so  it  is  pos- 
sible to  go  one  step  further  and  to  substitute  the  entire  form  or  taper 
of  trees  of  different  diameters,  heights  and  ages,  just  as  was  done  in 
Fig.  70  on  the  curve  of  stump  diameter  growth,  for  D.B.H.  and  top 
of  first  log.  To  make  this  substitution,  the  diameter  and  height  of 
average  trees  are  first  determined  for  each  decade  in  age.  Second, 
from  a  table  of  average  tapers,  the  form  or  taper  of  trees  of  the  cor- 
responding diameters  and  heights  are  taken.  This  may  be  done  by 
interpolation  in  case  the  required  diameter  or  height  falls  between 
inch  diameter  classes  or  5-  to  10-foot  height  divisions  expressed  in  taper 
table.  The  tapers  thus  borrowed  are  assumed  to  be  those  of  the  tree 
at  the  different  ages. 

This  method  has  the  same  advantages  and  drawbacks  as  the  sub- 
stitution of  the  volumes  from  a  volume  table  for  the  actual  volume 
of  sample  trees  as  described  in  §  242.  The  average  tapers  are  taken 
in  most  instances  from  a  much  larger  number  of  trees  than  could  be 
analyzed  for  form  at  the  different  decades  of  their  growth.  These 
tapers  therefore  probably  represent  quite  closely  the  average  form  of 
the  tree  of  these  sizes  and  ages.  On  the  other  hand,  this  average,  just 
as  for  volumes,  may  depart  from  the  actual  average  of  the  trees  to  be 
measured  in  case  the  data  do  not  coincide  in  origin  and  the  trees  differ 
in  average  form  quotient. 

The  best  check  upon  the  accuracy  of  substitution  of  taper  tables 
for  tree  analyses  is  to  test  the  form  quotient  both  of  the  taper  tables 
and  of  the  trees  desired.  A  considerable  departure  in  this  form  quotient 
indicates  that  the  tapers  do  not  represent  the  average  sought. 

1  This  method  of  graphic  plotting  of  average  growth  in  diameter  at  eaeh  upper 
section  was  devised  by  A.  J.  Mlodjiansky  (Measuring  the  Forest  Crop,  Bui. 
No.  20,  Division  of  Forestry,  U.  S.  Dept.  Agr.,  1898).  The  method  of  assembling 
all  the  curves  on  the  same  sheet  was  devised  by  H.  S.  Graves  (Forest  Mensura- 
tion, 1906,  p.  295). 


REFERENCES  383 


References 


Difficulties  and  Errors  in  Stem  Analysis,  A.  S.  WUliams,  Forestry  Quarterly,  Vol.  I, 

1903,  p.  12. 
Pitch  Pine  in  Pike  Co.,  Pa.,  John  Bentley,  Jr.,  Forestry  Quarterly,  Vol.  Ill,   1905, 

p.  14. 
Stem  Analyses,  John  Bentley,  Jr.,  Forestry  Quarterly,  Vol.  XII,  1914,  p.  158. 
A  Simplified  Method  of  Stem  Analysis,  T.  W.  Dwight,  Journal  of  Forestry,  Vol.  XV, 

1917,  p.  864. 
Mechanical  Aids  in  Stem  Analyses,  E.  C.  Pegg,  Journal  of  Forestry,  Vol.  XVII, 

1919,  p.  682. 


CHAPTER  XXVII 
FACTORS  AFFECTING  THE  GROWTH  OF  STANDS 

293.  Enumeration  of  Factors  Affecting   Growth   of   Stands.     The 

rate  of  growth  per  acre  or  total  vokiine  production  of  stands  is  the  result 
of  five  classes  of  factors,  namely,  site,  form,  treatment,  density,  and 
composition. 

Under  site  are  included  all  factors  of  local  environment  such  as  soil, 
exposure  and  altitude,  which  influence  growth  (§  294). 

The  term  form  alludes  to  age,  and  the  forms  of  stands  distinguished 
in  yield  studies  are  even-aged  and  many-aged  (§  259). 

Treatment  refers  to  the  sHvicultural  management  of  the  stand, 
in  the  form  of  thinnings,  and  protection;  untreated  stands  are  those 
grown  under  natural  conditions  (§  300). 

Density  means  primarily  the  completeness  of  crown  cover,  but  this 
factor  is  also  influenced  by  the  number  of  trees  per  acre  (§  301). 

Under  composition,  pure  and  mixed  stands  are  distinguished.  Pure 
stands  are  those  in  which  a  single  species  comprises  80  per  cent  or  more 
of  the  volume.  Mixed  stands  are  those  made  up  of  two  or  more  species, 
none  of  which  amounts  to  80  per  cent  of  the  volume.  Stands  may  be 
alluded  to  as  pure  if  80  per  cent  or  more  is  composed  of  trees  of  the 
same  genus,  such  as  pure  pine  or  pure  oak  stands. 

Natural  enemies  such  as  insects  and  fungi,  and  climatic  factors 
such  as  tornadoes  and  ice  storms  reduce  the  density  of  stocking  and 
lower  the  rate  of  growth,  thereby  widening  the  gap  between  average 
and  fully  stocked  stands. 

294.  Site  Factors,  or  Quality  of  Site,  In  estimating  the  volume 
of  stands,  the  forest  type  is  made  a  distinct  unit  of  area  for  the  purpose 
of  increasing  the  probability  of  accuracy  in  obtaining  an  average  stand 
per  acre,  or  in  securing  a  curve  of  average  height  on  diameter  (§  225 
and  §  227).  In  the  measurement  of  growth  and  yields,  not  only  is 
the  forest  type  also  a  fundamental  factor,  since  it  determines  the 
species  and  composition  of  the  stand,  whose  capacity  for  growth  under- 
lies the  results  obtained,  but  these  types  must  be  further  subdivided 
into  site  classes. 

The  rate  of  growth  per  year  or  total  yield  for  a  given  period  for 
different   species  depends   directly  upon  the   combination  of  factors 

384 


VOLUME  GROWTH  A  BASIS  FOR  SITE  QUALITIES  385 

which  influence  this  growth,  chief  among  which  are  quaHty  and  depth 
of  soil,  average  moisture  contents,  slope  and  exposure,  altitude  and 
climate.  Site  factors  cause  a  variation  in  total  possible  yields  of  from 
200  to  300  per  cent.  Hence  for  a  given  stand  or  area  the  yield  cannot 
be  predicted  within  a  reasonable  degree  of  accuracy  unless  the  quality 
of  site  is  taken  into  account.  This  difference  in  yield  on  good  and  on  poor 
sites  is  caused  by  the  more  rapid  growth  in  height,  diameter,  and  volume, 
of  the  trees  in  the  stand,  when  growing  on  more  favorable  sites.  Fewer 
trees  may  mature  on  good  sites  than  on  poor,  because  of  the  larger 
sizes  and  crown  spread  attained,  but  the  sum  of  their  volumes  will 
exceed  those  of  the  trees  maturing  on  the  poorer  sites.  When  the 
period  of  years  required  to  produce  these  yields  is  considered,  and  the 
mean  annual  growth  is  computed  (§  245)  it  will  be  seen  that  the  more 
rapid  growth  on  good  sites  produces  even  more  striking  differences  in 
the  annual  rate  of  growth  between  poorer  and  better  sites.  These 
differences  are  further  increased  when  the  value  of  the  yield  is  compared 
with  the  cost  of  production,  so  that  it  becomes  of  utmost  importance 
in  forestry  to  determine,  for  any  large  area  of  forest  land,  the  acreage 
embraced  in  each  of  several  grades  or  qualities  of  site. 

295.  Volume  Growth  a  Basis  for  Site  Qualities.  Forest  types  some- 
times show  abrupt  transition  from  one  to  another,  corresponding  to 
sharp  differences  in  soil  moisture;  but  more  often  the  change  is  gradual 
and  the  separation  of  areas  in  each  type,  as  made  in  the  field,  is  arbitrary. 
The  differences  in  site  quality  within  a  type  form  an  unbroken  series 
of  gradations,  which  must  be  separated,  on  a  purely  arbitrary'  basis, 
into  a  convenient  number  of  site  classes,  whose  average  yields  may 
be  expressed  in  tables.  In  European  practice  five  qualities  are  recog- 
nized when  a  few  species  occupy  a  wide  range  of  conditions.  In  America 
three  qualities  have  so  far  sufficed  to  cover  the  range  of  a  single  species. 

The  problem  of  classifying  site  qualities  is  two-fold.  First,  the 
plots  whose  yields  are  measured  to  determine  the  average  rates  of 
growth  for  different  sites  must  be  separated  into  the  predetermined 
site  classes.  Second,  some  convenient  means  must  be  found  to  apply 
this  site  classification  to  forest  lands  during  a  forest  survey  in  order 
that  the  total  area  may  be  subdivided  on  this  basis  for  the  pi'ediction 
of  growth  on  the  forest. 

The  most  direct  method  of  classifying  plots  measured  for  yield  is 
by  the  rate  of  growth  per  year  actually  produced,  i.e.,  the  total  yield 
based  on  age  of  the  stand.  This  has  been  the  basis  of  most  of  the  yield 
tables  constructed  in  America,  and  might  suffice  were  it  not  for  the 
four  other  factors  which  modify  the  yields  per  acre  independent  of  site; 
namely,  form  of  stand,  treatment,  degree  of  stocking,  and  composition 
of  stand. 


386  FACTORS  AFFECTING  THE  GROWTH  OF  STANDS 

The  influence  of  these  variable  factors  is  tremendous,  and  it  has 
usually  been  considered  necessary  to  eliminate  them  by  constructing 
yield  tables  for  given  fixed  conditions  only,  such  as  for  even-aged 
stands,  artificially  grown  and  thinned,  of  normal  or  full  stocking,  and 
of  pure  species.  Where  these  conditions  do  not  apply,  as  for  instance 
in  mixed  stands  of  broken  density  in  forests  of  all  ages,  it  has  often 
been  considered  impossible  to  determine  the  rate  of  growth  per  acre. 

296.  Height  Growth  a  Basis  for  Site  Qualities.  Although  it  may 
be  possible,  by  rigid  selection,  to  eliminate  these  four  variables  and  thus 
base  the  site  qualities  upon  the  rate  of  growth  or  the  total  yield  per  acre 
based  on  age,  yet  when  it  comes  to  reversing  the  process  and  applying 
this  standard  of  site  classes  to  the  classification  of  lands  on  a  larger 
area,  the  remaining  variables  are  present  and  must  be  dealt  with. 
This  problem  may  be  summed  up  as  follows: 

1.  The  factors  of  site,  such  as  climate,  and  soil,  are  too  complicated 
to  be  directly  measured  in  the  field  as  a  means  of  site  classification. 
Results  expressed  in  forest  growth,  rather  than  causes,  must  be  used 
as  the  indicator  of  site. 

2.  Volume  as  a  site  indicator  is  incomplete  without  the  determina- 
tion of  age.  For  most  conditions  the  relative  volume  based  on  age 
is  too  variable  and  difficult  of  determination  to  serve  as  a  field  basis 
of  classification  of  large  areas. 

3.  Dimensions  of  typical  dominant  trees  in  a  stand  may  serve  as 
the  required  indicator,  since  the  tree  unit  is  independent  of  the  variables 
of  age,  form,  composition  and  density  which  affect  the  stand. 

4.  The  dimensions  which  may  serve  for  this  purpose  are  diameter 
and  height.  Of  these,  height  alone  is  a  reliable  index  of  site  quality 
since  it  is  affected  but  little  by  varying  density  or  degree  of  stocking, 
or  by  the  treatment  of  the  stand.  Height  based  on  age  is  a  more 
reliable  basis  than  volume  on  age  for  stands  of  varying  degrees  of  stock- 
ing, and  for  both  wild  or  unmanaged  forests  and  thinned  or  managed 
stands.  This  reduces  or  eliminates  two  of  the  five  variables,  namely, 
treatment,  and  density  of  stand.  Height  growth  is  retarded  by  shade 
to  a  marked  degree;  hence  in  forests  of  all  ages,  and  in  mixed  stands 
of  several  species,  height  based  on  total  age  ceases  to  be  a  reliable 
index,  since  the  factor  of  economic  age  is  introduced. 

Total  height  or  height  at  maturity  remains,  even  in  mixed  stands, 
a  distinguishing  characteristic  of  different  site  qualities.  The  growth 
of  dominant,  unsuppressed  trees,  a  few  of  which  may  be  found  in  almost 
every  stand,  may  be  ascertained  in  a  very  few  tests  and  will  hold  good 
for  the  stand  or  site.  Thus  the  remaining  two  variables,  form  and 
composition,  may  be  eliminated  by  selection  of  dominant  trees  or  fully 
mature  trees. 


OTHER  POSSIBLE  BASES  FOR  SITE  QUALITIES 


387 


Site  qualities,  whether  three  or  five  in  number,  must  be  adapted 
to  the  range  of  actual  yields  of  the  species  to  be  measured.  Different 
species  require  a  different  range  of  site  factors.  The  conifers  thrive 
in  soils  too  poor  for  hardwoods;  hence  quality  I  for  pines  may  be  quality 
II  for  oaks. 

The  adoption  of  a  common  standard  of  site  index  for  species  with  the 
same  range  of  soil  requirements  is  desirable.  One  suggestion  is  to 
classify  the  trees  of  the  country  into  groups,  based  on  their  total  growth 
in  height  at  a  definite  age.  This  principle  is  illustrated  by  the  follow- 
ing table,  in  which  four  site  classes  are  made  for  each  group,  based 
on  even  gradations  of  total  height  for  dominant  trees  of  the  same  age. 

TABLE  LX 

Standards  of  Site  Classification  Based  on  the  Height  of  Tree  at  100  Years 


Site 

Standard  a. 

Standard  b. 

Standard  c. 

Feet 

Feet 

Feet 

I 

110 

90 

70 

II 

90 

75 

60 

HI 

70 

60 

50 

IV 

50 

45 

« 

A  standardization  of  this  character  serves  the  double  purpose  of 
coordinating  the  j-ield  tables  for  species  of  similar  growi:h  habits,  and 
furnishing  the  simplest  basis  for  site  classification  during  forest  survey. 


297.  Other  Possible  Bases  for  Site  Qualities.  Medwiedew's  Method.  A 
method  of  site  classification  suggested  by  Medwiedew,  a  Russian,  and  applied  by 
Hanzlik  to  Douglas  fir  is  as  follows : 

A  site  factor  is  calculated  by  the  formula, 


Site  factor  = 


cXh 


when  c= basal  area  on  the  average  acre; 
/i  =  average  height  of  stand; 
n  =  age  of  stand. 

These  so-called  site  factors  may  then  be  grouped  to  represent  different  site 
qualities,  all  factors  falling  between  certain  limits  indicating  quality  I,  etc.  This 
basis  is  not  consistent  as  an  indication  of  site,  since  it  is  nothihg  but  the  mean  annual 
growth  of  the  stand  in  a  different  form.     If /  =  form  factor,  then,  c/i/= total  cubic 

chf 
volume,  and  —  =  mean  annual  growth  of  stand.     As  mean  annual  growth  varies 

n 
with  age  as  well  as  site,  it  cannot  be  substituted  for  either  volume  or  height  as  an 
absolute  basis  of  classification. 


388  FACTORS  AFFECTING  THE  GROWTH  OF  STANDS 

A  still  more  impracticable  plan  is  to  base  site  factors  on  the  current  annual 
growth  of  a  stand.  ^ 

298.  The  Form  of  Stands.  Even-aged  versus  Many-aged.  There 
is  an  essential  ditfercnce  in  the  character  of  even-aged  stands  and  those 
composed  of  all  ages  on  the  same  area,  and  this  difference  constitutes 
one  of  the  greatest  difficulties  in  determining  the  rate  of  growth  or  yields. 
It  has  been  shown  (§  274)  that  the  competition  between  individual  trees 
made  necessary  by  the  expansion  of  their  crowns  and  growing  space 
occurs  in  an  even-aged  stand  between  trees  of  the  same  age  class.  Except 
around  the  borders  of  this  age  class  there  can  be  no  expansion  of  the 
areas  occupied  by  the  total  stand  belonging  to  this  age  class.  The 
factor  of  area  can  therefore  be  standardized  in  yield  tables.  Since 
the  yield  of  even-aged  stands  is  composed  of  the  volumes  of  trees  which 
have  remained  dominant  throughout  the  life  of  the  stand,  the  rate  of 
growth  of  the  individual  trees  is  a  maximum  both  in  height  and  diameter 
and  the  mean  annual  growth  resulting  on  an  acre  is  the  maximum  for 
the  site  when  measured  for  the  period  required  for  the  growth  of  the 
average  tree  from  seedling  to  maturity. 

The  conditions  are  entirely  different  in  many-aged  stands,  the  dif- 
ference being  greatest  for  species  which  may  be  subjected  to  a  long 
period  of  suppression  and  yet  retain  the  power  to  survive  and  recover. 
In  these  stands  several  different  age  classes  are  brought  into  competi- 
tion not  merely  with  trees  of  their  own  age,  but  with  older  and  younger 
trees.  The  older  trees  have  the  advantage  of  the  younger  in  appropriat- 
ing space  vacated  by  the  death  of  veterans  or  by  the  removal  of  trees 
for  any  cause.  The  young  trees  growing  under  partial  shade  are  held 
back  in  height  growth,  diameter  growth  and  consequent  volume  growth. 
The  economic  space  occupied  by  the  younger  age  classes  growing  under 
partial  shade  may  be  defined  as  the  actual  percentage  of  the  total  grow- 
ing space  as  represented  by  the  available  light,  moisture  and  soil  fer- 
tility which  is  appropriated  by  these  young  trees  to  the  exclusion  of 
its  use  by  other  age  classes.  This  proportion  of  space  so  used  is  exceed- 
ingly small  and  may  be  negligible,  yet  the  reproduction  may  survive 
as  scattered  individuals  for  many  years.  When  old  trees  die,  the  space 
released  is  not,  as  in  the  case  of  even-aged  stands,  occupied  entirely 
by  reproduction,  but  is  distributed  among  all  of  the  trees  so  placed 
that  they  may  avail  themselves  of  it  by  expanding  their  crowns.  A 
portion  only  of  released  space  is  taken  by  additional  reproduction. 

1  "  Concerning  Site,"  Carlos  G.  Bates,  Journal  of  Forestry,  XVI,  1918,  p.  383. 
Not  only  is  this  basis  impractical  of  measurement  and  classification  in  the  field,  but 
it  varies  with  age  of  the  stand  to  a  much  greater  degree  than  does  mean  annual 
growth,  hence  is  not  trustworthy  as  a  means  of  separating  sites,  though  the  postulate 
that  the  best  sites  are  capable  of  yielding  the  largest  current  annual  growth  is  per- 
fectly true. 


THE  FORM  OF  STANDS.     EVEN-AGED  \^RSUS  MANY-AGED      389 

The  result  of  these  two  factors  is  that  the  area  of  an  age  class  is  at  first 
small,  its  growth  retarded  and  mortality  heavy,  but  with  advancing 
age,  the  area  or  per  cent  of  total  area  occupied  by  this  class  increases 
until  it  reaches  a  maximum  at  a  period  when  the  stand  is  at  maturity 
and  before  the  loss  of  veterans  begins  to  leave  holes  in  the  canopy. 

TABLE  LXI 

Average  Crown  Spread  of  Loblolly  Pine  in  the  Forest,  at  Vredexburgh, 

Ala. 


Age. 

Diameter  of 

Per  cent  of 

Per  cent  of 

crown. 

increase  in 

mcrease  in 

Trees  per  acre 

Years 

Feet 

diameter 

area 

30 

1.3  0 

40 

L5.5 

19 

42 

140 

50 

19.0 

46 

113 

116 

60 

22.0 

69 

186 

88 

70 

24.5 

88 

255 

70 

80 

27.0 

108 

332 

59 

This  law  of  expansion  is  illustrated  in  Fig.  82. 


4  Acres 

I        I  Area  occupied  by  Crowoa 
^^  Area  not  occupied  by  Crowna 

Even-aged 
stand. 


Single  age-class  in 
Many-aged  forest. 


Fig.  82. — Possible  expansion  of  area  occupied  by  crowns  of  trees  of  a  given  age 
class  in  a  many-aged  forest,  contrasted  with  limited  expansion  possible  in 
crown  area  in  an  even-aged  stand.  Loblolly  Pine,  Ala.  Dotted  lines  show 
possible  expansion  of  7  per  cent  in  even-aged  stand.  Shaded  area  shows  pos- 
sible expansion  of  stand  of  332  per  cent  in  many-aged  forest. 

On  the  left,  in  Fig.  82  an  even-aged  stand  occupies  a  square  area  of  4  acres,  417 
feet  square.  During  its  growth,  cro^^Ti  expansion  is  effected  by  a  reduction  in  the 
number  of  trees  from  140  at  40  years,  to  59  at  80  years,  with  much  more  rapid  reduc- 
tion i^revious  to  40  years.  The  only  expansion  of  area  possible  for  the  age  cla.ss  is 
around  the  edges  of  the  square.  The  trees  can  extend  their  crowns  an  average  of 
14  feet,  or  7  feet  on  one  side,  in  the  50-j'ear  period  (27-13  feet).  This  gives  a  final 
area  in  square  feet  of  43 1^  or  an  expansion  of  7  per  cent. 


390  FACTORS  AFFECTING  THE  GROWTH  OF  STANDS 

By  increasing  the  area  of  the  stand,  this  possible  expansion  of  area  becomes  less. 
By  reducing  the  area,  the  per  cent  of  expansion  possible  becomes  greater,  since  a 
greater  per  cent  of  the  total  number  of  crowns  are  so  placed  as  to  be  able  to  utilize 
the  increased  space.  The  maximum  possible  expansion  occurs  when  there  are  but 
59  trees  per  acre  at  30  years,  equally  spaced,  and  unobstructed  by  older  age  classes, 
in  which  case  the  area  actually  utilized  by  this  age  class  expands  332  per  cent  or  is 
432  per  cent  of  its  original  area,  and  the  stand  becomes  fully  stocked  at  80  years. 
This  expansion  of  actual  are  is  shown  on  the  right,  in  Fig.  82. 

This  second  process  is  what  takes  place  in  a  forest  composed  of  stands  of  many 
different  ages.  In  the  case  of  even-aged  stands,  thinning  or  removal  of  trees  simply 
permits  the  remainder  to  grow,  with  no  change  in  area  for  the  class,  and  the  removal 
of  the  final  crop  is  followed  by  reproduction  which  in  turn  occupies  the  entire  original 
area.  But  with  many-aged  stands,  when  the  final  crop  is  removed,  which  takes  place 
on  any  acre  in  several  different  cuttings,  the  area  so  released  is  reproduced  only  in 
part.  The  remainder  is  absorbed  by  the  crown  spread  of  the  intermediate  age 
classes  which  thus  increase  their  total  area  in  the  manner  shown  by  Fig.  82. 

In  the  illustration,  this  stand  at  30  years  occupies  but  one-fourth  of  the  total 
area  of  the  4  acres.  The  remainder  can  be  occupied  by  older  timber,  which  in  the 
50-year  period  is  removed  as  it  matures.  By  assuming  this  4  acres  to  be  but  a  part 
of  a  larger  area,  and  to  be  distributed  over  the  area  coinciding  with  the  distribution 
of  the  single  age  class  in  question,  the  conditions  of  a  many-aged  forest  are  visualized. 
This  factor  of  crown  expansion  and  competition  between  different  age  classes  is  the 
basis  of  the  differences  between  the  increment  of  many-aged  and  even-aged  stands. 
It  explains  suppression,  economic  age,  and  increased  growth  after  cutting.  The 
actual  amount  of  expansion  and  rate  of  increase  due  to  this  factor  will  be  consider- 
ablj'  less  in  all  instances  than  the  per  cents  given  in  table  LXI  since  only  a  portion 
of  the  maximum  space  required  by  each  tree  of  the  class  for  expansion  is  available 
at  all,  and  but  a  part  of  this  can  be  taken  from  other  age  classes.  Summed  up, 
this  factor  represents  an  additional  rate  of  increment  to  be  added  to  that  which  an 
even-aged  stand  of  like  volume  would  show,  and  caused  by  the  fact  that  the  volume 
of  the  age  class  in  the  many-aged  forest,  while  occupying  only  a  certain  per  cent  of 
the  area  of  the  forest,  is  thereby  distributed  over  a  much  larger  area  into  which  its 
crowns  can  expand. 

299.  Annual  Increment  of  Many-aged  Stands.  The  rate  of  growth 
per  year  based  on  a  unit  of  area  for  many-aged  forests  does  not  repre- 
sent production  of  a  single  age  class,  but  of  the  sum  of  all  the  age  classes 
on  the  area,  averaged  for  a  long  period.  If  desired  for  a  single  age 
class,  this  rate  or  yield  per  acre  should  not  be  based  on  the  area  occupied 
by  the  timber  at  maturity  divided  by  the  total  ages  of  the  trees  com- 
posing this  stand,  for  this  would  greatly  under-estimate  the  rate  of 
mean  annual  growth.  The  error  can  be  expressed  and  corrected  in 
one  of  three  ways:  (1)  either  the  age  used  as  a  divisor  must  be  shortened 
to  represent  the  economic  age  of  dominant  trees  growing  in  even-aged 
stands,  or  (2)  the  area  occupied  by  the  mature  crop  must  be  reduced 
to  represent  the  average  area  for  the  stand  during  its  life,  which  is 
practically  impossible,  or  (3)  to  the  yield  for  the  period  represented 
by  the  total  life  of  the  trees  in  the  stand  as  actually  shown  by  ring 
counts,  must  be  added  the  additional  yields  from  other  crops  of  timber 


THE  EFFECT  OF  TREATMENT  ON  GROWTH  391 

which  this  same  area  produced  during  the  period  when  the  final  crop 
was  only  occupying  a  portion  of  it.  The  latter  problem  may  be  illus- 
trated best  by  the  yield  or  rate  of  growth  per  year  of  stands  which 
have  come  up  to  spruce  following  poplar  or  white  birch  on  a  burn. 
In  the  period  requii-ed  to  produce  a  mature  crop  of  spruce,  a  crop 
of  poplar  and  birch  has  also  been  produced.  The  mean  annual  growth 
for  the  whole  period  must  include  the  total  yield  of  both  species. 

Owing  to  the  difficulty  of  adjusting  these  yields  on  one  of  these 
three  bases,  it  is  customary  to  employ  a  substitute  method  of  determin- 
ing the  rate  of  growth,  not  for  the  total  period  by  any  of  these  adjust- 
ments, but  for  a  partial  period,  measuring  the  current  periodic  growth 
based  upon  trees  or  stands  which  have  already  reached  a  given  diameter 
or  average  age.  This  will  be  discussed  in  Chapter  XXXI.  Its  effect 
is  to  eliminate  most  of  the  uncertainty  attending  the  adjustment  of 
the  factor  of  competition  in  many-aged  stands,  but  it  introduces  the 
question  as  to  whether  the  current  growth  measured  represents  the 
true  mean  or  average  for  the  site  over  a  complete  period  of  crop  pro- 
duction. 

300.  The  Effect  of  Treatment  on  Growth.  The  fact  that  the  growth 
of  individual  trees  demands  expansion  of  their  crowns  influences 
not  merely  the  yield  per  acre  which  may  be  attained,  but  more  especi- 
ally the  dimensions  of  the  individual  trees  in  the  stand.  Since  the 
production  of  lumber  and  of  certain  piece  products  and  the  value  of 
products  grown  on  a  given  acre  depend  much  more  largely  upon  dimen- 
sions and  sizes  and  vipon  quality  than  upon  total  cubic  volume,  yields 
attained  in  board  feet  are  profoundly  influenced  by  the  number  of  trees 
brought  to  maturity  in  stands  of  equal  degrees  of  crown  density  or 
stocking.  It  has  been  commonly  assumed  that  a  normal  or  fully 
stocked  stand  simply  meant  one  which  showed  a  complete  crown  density 
throughout  its  life  regardless  or  independent  of  the  number  of  trees 
which  composed  it.  This  conception  neglects  the  fundamental  idea 
of  the  tree  as  an  individual.  Stands  which  are  fully  stocked  when 
young,  so  that  crown  density  is  early  established,  usually  become  over-: 
stocked  almost  immediately.  The  normal  number  of  trees,  to  attain 
best  results  or  highest  yields,  is  least  on  good  sites  with  strong  growing 
species,  rapid  height  growth  and  correspondingly  rapid  diameter  growth, 
and  increases  as  the  sites  become  poorer.  The  danger  of  over-stocking 
and  stagnation  of  both  height  and  diameter  growth  increases  with 
poor  sites,  even-aged  stands,  and  tendency  to  abundant  reproduction. 
These  natural  tendencies  are  affected  tremendously  by  artificial  control. 
All  operations  such  as  planting,  in  which  the  initial  spacing  is  fixed, 
and  subsequent  thinning  l)y  which  the  resultant  number  of  trees  per 
acre  at  each  decade  is  determined,  have  a  dii'ect  effect  upon  the  diam- 


392  FACTORS  AFFECTING  THE  GROWTH  OF  STANDS 

eter  growth  of  the  remaining  stand,  which  in  stands  continually  under 
management  may  be  maintained  at  an  almost  constant  rate  until 
the  maturity  of  the  stand. 

It  has  been  found  that  in  stands  originally  stocked  with  only  part 
of  the  normal  number  of  trees  for  smaller  ages,  as  the  age  of  such  stands 
advances  and  the  number  of  trees  required  in  a  stand  of  maximum  or 
normal  density  decreases,  the  poorly  stocked  stand  tends  to  approach 
and  to  equal  the  yield  per  acre  of  the  stand  which  has  been  normally 
stocked  throughout  its  life.  There  is  therefore  a  universal  tendency 
under  natural  conditions  for  stands  to  approach  a  full  crown  cover  as 
well  as  for  the  more  densely  stocked  stands  to  become  over-stocked. 
This  tendency  must  be  recognized  in  dealing  with  density  factors  or 
per  cents  in  prediction  of  yield  and  forms  a  conservative  factor  in  the 
prediction  of  growth  for  partly  stocked  empirical  or  average  stands. 
Ideal  conditions  for  growth  are  found  in  stands  which  have  been  main- 
tained at  a  normal  number  of  trees  per  acre  as  well  as  a  normal  crown 
density  through  repeated  thinnings.  Not  only  is  the  total  volume 
produced  per  acre  and  the  rate  of  growth  greatly  increased  by  a  proper 
balance  between  thinnings  and  the  remaining  stand,  but  the  maturity 
of  the  stand  is  hastened  and  its  rotation  may  be  reduced  if  desired. 

301.  Density  of  Stocking  as  Affecting  Growth  and  Yields.  In 
spite  of  the  tendency  of  natural  stands  to  approach  normal  density  of 
stocking  through  the  expansion  of  their  crowns,  the  attainment  of 
normality  or  full  stocking  under  natural  conditions  of  growth  is  seriously 
interfered  with  by  many  agencies.  Natural  spacing  or  stocking  is 
largely  a  matter  of  chance  and  fails  over  extensive  areas.  Much  of 
the  reproduction  may  be  destroyed  during  these  early  years  by  grazing, 
fires,  frost  or  drought.  Saplings  and  poles  may  be  further  destroyed 
by  fire,  insects  and  disease.  Later  on,  insects,  disease,  fire  and  wind 
continue  to  make  gaps  in  the  age  class  and  crown  density.  Most  of 
these  detrimental  factors  are  reduced  under  protection  and  the  average 
density  greatly  improved,  yet  forests  covering  wide  areas  ordinarily 
can  not  be  brought  to  a  perfect  or  full  condition  of  crown  cover  or  stock- 
ing, no  matter  how  intensive  the  care  which  is  bestowed  upon  them. 

The  yields  of  forests  are  desired  on  the  basis  of  their  actual  average 
production  and  not  upon  the  small  per  cent  of  stands  showing  maximum 
or  perfect  conditions  of  density  and  numbers  per  acre.  This  gives 
rise  to  the  problem  of  applying  tables  of  yield  to  these  conditions,  first 
as  to  the  selection  of  areas  or  plots  for  the  measurement  of  yields,  and 
second,  as  to  whether  the  area  so  selected  shall  be  an  average  of  all 
conditions  of  stocking  within  the  site  class  or  shall  make  no  attempt 
to  attain  this  empirical  average. 

It  has  been  generally  accepted  that  the  best  method  of  obtaining 


COMPOSITION  OF  STANDS  AS  TO  SPECIES  393 

yields  is  to  select  plots  which  show  a  faii-ly  complete  crown  density, 
not  seriously  reduced  by  avoidable  factors  of  damage,  and  to  con- 
struct the  table  of  yields  entirely  from  such  plots.  This  is  supposed 
to  give  the  normal  relation  between  yields  at  different  ages  for  well- 
stocked  stands.  There  remain  many  variable  factors,  the  chief  of 
which  is  the  number  of  trees  per  acre  in  the  plots  measured.  It  has 
been  suggested  that  the  age  or  ages  at  which  the  final  yield  is  to  be 
harvested  shall  be  taken  to  indicate  the  normal  number  of  trees  per 
acre  and  that  stands  of  lesser  age  having  this  number  or  more  trees, 
while  not  showing  the  full  yield  for  these  ages  may  be  regarded  as  fully 
stocked,  if  not  to  be  cut  until  the  final  age.  The  onh'  difference  between 
such  stands  and  stands  Avhich  remain  fully  stocked  would  be  found  in 
the  thinnings  in  the  interval  and  in  the  quality  and  limbiness  of  the 
timber.^ 

Yield  tables  based  on  a  given  standard  such  as  described  may  be 
discounted  to  predict  the  average  degree  of  stocking  for  average  areas, 
which  are  known  as  empirical  yields.  In  some  instances  efforts  have 
been  made,  by  collecting  data  on  large  areas,  to  obtain  these  empirical 
yields  or  averages  directly  in  the  field  instead  of  by  discount  from 
yield  tables.  In  either  one  or  the  other  of  these  forms,  the  empirical 
or  actual  average  is  the  final  result  desired,  and  the  normal  or  standard 
yield  table  is  but  the  means  to  this  end.  The  arguments  in  favor  of 
obtaining  a  normal  or  standard  3'ield  table  by  the  selection  of  plots 
are  that  the  variables  represented  in  the  average  or  empirical  stocking 
by  differences  in  form  or  mixed  ages,  differences  in  density  and  dif- 
ferences in  composition  of  the  forest,  are  eliminated  from  the  table, 
which  is  confined  to  showing  differences  in  yield  based  on  site  qualities 
and  age.  The  relations  of  more  than  two  variables  can  not  be  accu- 
rately set  forth  in  a  single  table. 

302.  Composition  of  Stands  as  to  Species.  Stands  composed  of 
a  mixture  of  species  maj'  vary  in  yield  from  pure  stands.  Species  may 
differ  considerabty  in  their  capacity  for  growth  and  yields  even  on  the 
same  site.  They  vary  in  height  growth  and  consequently  are  affected 
differently  by  the  factor  of  suppression  when  in  mixed  stands.  The 
rate  of  survival  and  the  dimensions  vary  so  that  the  composition  of 
the  stand  changes  with  its  growth.  Finally,  the  original  composition, 
independent  of  these  later  changes,  varies  greatly.  For  these  reasons  the 
prediction  of  yields  in  stands  of  mixed  species  has  always  been  regarded 
as  extremely  difficult.  Approximate  rather  than  accurate  results  must 
be  accepted.  Recent  investigations  indicate  that  for  certain  character- 
istic types  and  mixtures  of  species  naturally  growing  together,  yields 

1  The  Use  of  Yield  Tables  in  Predicting  Growth,  E.  E.  Carter,  Proc.  Soc.  Am. 
Foresters,  Vol.  IX,  No.  2,  p.  177. 


394  FACTORS  AFFECTING  THE  GROWTH  OF  STANDS 

determined  for  the  mixed  stands  do  not  differ  very  widely  from  those 
of  pm'e  stands  (§  314). 

References 

Universal  Yield  Tables,  Fricke  (Based  on  height  classes);  Review  Forestry 
Quarterly,  Vol.  XII,  1914,  p.  629. 

Classifying  Forest  Sites  by  Height  Growth,  E.  H.  Frothingham;  Journal  of  Forestry, 
Vol.  XIX,  1921,  p.  374. 

A  Generalized  Yield  Table  for  Even-aged  Well-stocked  Stands  of  Southern  Upland 
Hardwoods,  W.  D.  Sterrett,  Journal  of  Forestry,  Vol.  XIX,  1921,  p.  382. 

Concerning  Site,  F.  Roth,  Forestry  Quarterly,  Vol.  XIV,  1916,  p.  3. 

Site  Determination  and  Yield  Forecasts  in  the  Southern  Appalachians,  E.  H.  Froth- 
ingham, Journal  of  Forestry,  Vol.  XIX,  1921,  p.  14. 


CHAPTER  XXVIII 
NORMAL   YIELD    TABLES    FOR   EVEN-AGED    STANDS 

303.  Definition  and  Purposes  of  Yield  Tables.  A  yield  table  is 
intended  to  show  the  yields  per  acre  which  can  be  expected  from  stands 
of  timber  at  given  ages  or  for  given  periods,  in  terms  of  a  given  unit 
of  volume  or  of  product. 

A  complete  yield  table  will  show  yields  for  successive  decades 
or  five-year  periods  covering  the  range  of  age  of  a  species.  Ordinarily, 
yield  tables  do  not  show  the  loss  in  yields  per  acre  during  the  decadent 
period  in  over-mature  stands,  but  they  can  be  constructed  so  as  to  do 
so.  In  forests  under  management,  the  maximum  ages  shown  are  those 
of  the  oldest  stands  before  cutting. 

Yield  tables  are  used  primarily  to  predict  the  yield  of  existing 
stands,  hence  they  are  assumed  to  represent  the  actual  development 
of  individual  or  typical  stands  throughout  their  life  cycle.  This  they 
do  not  always  do,  since  naturally  stocked  areas  tend  constantly  to  pass 
from  a  condition  of  under-stocking  to  one  of  over-stocking.  It  follows 
that  the  most  reliable  yield  tables  are  those  constructed  for  stands 
grown  under  management,  where  thiimings  have  controlled  the  incre- 
ment. 

Yield  tables  are  the  fundamental  data  required  for  the  determination 
of  the  value  of  forest  lands  and  the  profits  of  forestry,  the  appraisal 
of  damages  to  forest  property,  the  choice  of  a  rotation  or  average  age 
at  which  timber  should  be  cut,  the  advisability  of  thinnings,  the  choice 
of  species,  and  the  relative  profit  from  expenditures  for  all  forestry 
operations  on  different  sites.  An  accurate  or  even  an  approximate 
knowledge  of  yields  per  acre  and  the  average  rate  of  growth  per  year 
tends  to  place  forestry  on  a  business  basis  rather  than  one  of  blind 
speculation. 

304.  Standards  for  Yield  Tables.  Yield  tables  undertake  to  set 
standards  in  which  the  variables  affecting  yield  are  eliminated.  The 
basis  of  all  yield  tables  is  a  separation  into  site  qualities,  with  separate 
average  yields  for  each  quality,  since  the  fundamental  variable  is  site 
quality. 

Form  of  stand  requires  separate  yield  tables  for  even-aged  stands, 
and  many-aged  stands  (§  252). 

395 


396  NORMAL  YIELD  TABLES  FOR  EVEN-AGED  STANDS 

The  factor  of  density  of  stocking  (§  273)  separates  yield  tables  into 
Normal  or  Index  tables  which  are  based  on  an  average  full  or  maximum 
stocking,  and  Empirical  tables,  which  represent  the  actual  average 
density  of  stocking  on  a  given  area  including  partially  stocked  and 
unstocked  portions. 

Composition  of  the  forest  is  distinguished  by  constructing  tables 
for  pure  stands  (§  314)  separately  from  mixed  stands. 

The  most  important  distinction  is  probably  that  made  between 
natural  stands  and  those  grown  under  management.  Owing  to  the 
great  influence  of  treatment  upon  growth  and  yields,  the  standard 
of  normality  (see  above)  is  entirely  different  for  natural  and  for  arti- 
ficially grown  stands,  and  yield  tables  based  on  the  yields  of  planted, 
thinned  and  managed  forests  must  be  made  to  replace  the  present 
normal  yield  tables,  when  the  material  for  such  measuremients  becomes 
available  in  sufficient  quantity  to  furnish  a  proper  basis. 

Normal  or  index  yield  tables  serve  their  chief  purpose  as  a  standard 
of  comparison,  since  most  stands  will  produce  either  larger  or  smaller 
yields  than  those  shown  (§  250).  This  function  is  better  served  if 
the  standard  of  normality  set  by  the  table  is  not  abnormally  high, 
but  is  made  to  conform  to  the  results  possible  of  attainment  on  the 
average  acre  of  the  site  class,  with  reasonably  thorough  protection  from 
destructive  agencies  and  reasonably  full  stocking. 

305.  Construction  of  Yield  Tables,  Baur's  Method.  There  are  two 
methods  possible  in  the  preparation  of  yield  tables.  The  first,  known 
as  Baur's  method  ^  is  based  on  the  measurement  of  the  present  volume 
and  age  of  numerous  plots  which  are  then  classified  as  to  site  and  age 
and  form  the  basis  of  curves  of  average  yields  based  on  age  for  from 
three  to  four  site  classes.  This  method  corresponds  with  the  defini- 
tion of  a  yield  table  cited  in  §  249  since  it  does  not  pretend  to  trace 
the  past  history  of  these  individual  stands;  yet  the  use  to  which  such 
a  table  is  put  is  to  predict  from  these  average  curves  the  growth  of  a 
given  stand  by  decades.  For  original  stands  under  natural  conditions, 
this  method  is  universally  used.  The  second  method  is  to  re-measure 
established  plots  at  stated  intervals  to  determine  the  volume  of  growth, 
diminution  in  number  of  trees  per  acre  and  other  changes  in  the  stand. 
While  more  accurate,  the  collection  of  such  data  must  await  the  growth 
of  the  timber  and  the  method  is  best  applied  to  stands  under  manage- 
ment. 

Yield  tables  can  be  constructed  by  Baur's  method  on  the  basis  of 
from  50  to  200  plots  dependent  on  the  range  of  site  qualities  and  condi- 
tions of  growth.     The  aim  is  usually  to  get  at  least  100  plots. 

1  Die  Holzmesskunde,  Franz  Baur,  Professor  of  Forestry,  University  of  Munich, 
Bavaria,  1891. 


STANDARD  FOR  "NORMAL"  DENSITY  OF  STOCKING         397 

306.  Standard  for  "  Normal "  Density  of  Stocking.  In  selecting 
plots  for  a  yield  table,  in  natural  stands,  it  is  neither  possible  nor  advis- 
able to  seek  areas  which  show  the  maximum  theoretical  density  of 
stocking,  either  as  to  crown  canopy  or  number  of  stems  per  acre.  Nor 
should  any  effort  be  made  to  select  plots  which  represent  the  empirical 
average  of  stocking.  The  standard  should  be  to  exclude  from  the  plots 
all  larger  blanks  caused  by  destructive  agencies  or  failure  of  stocking 
and  to  select  areas  reasonably  well  stocked,  with  comparatively  complete 
crown  canopy.  This  standard  of  selection  should  be  such  that  a  suf- 
ficient number  of  plots  can  be  readily  obtained  from  the  larger  areas, 
without  refinements  either  in  size  or  in  location.  If  too  high  a  standard 
is  set,  the  plots  conforming  to  this  standard  will  be  found  to  be  either 
located  exclusively  on  the  better  portions  of  each  site,  or  the  area  of 
the  plots' will  be  too  small  for  safe  results.  In  natural  stands  this  ten- 
dency will  lead  to  the  selection  of  plots  containing  too  great  a  number 
of  trees,  which  will  result  later  in  over-stocking. 

The  average  yield  obtained  from  plots  selected  on  this  basis  is 
termed  the  normal  yield,  though  it  may  be  exceeded  by  the  best  plots, 
or  by  stands  grown  under  management. 

307.  Age  Classes.  The  area  of  a  plot  should  include  but  one  age 
class.  Where  stands  are  actually  even-aged  over  considerable  areas, 
plots  are  easily  and  rapidly  located.  Where  there  is  difficulty  in  dis- 
tinguishing the  age  classes,  and  in  locating  areas  which  exclude  all 
trees  but  those  belonging  to  the  class  desired,  it  may  be  necessary  to 
include  a  few  scattered  trees  of  a  different  age  class  in  order  to  obtain 
plots  of  a  suitable  size.  The  net  area  of  the  plot  can  then  be  found 
by  deducting  the  space  occupied  by  these  trees,  which  can  be  based 
on  the  area  covered  by  their  crown  spread,  modified  in  open  stands 
to  include  a  proper  proportion  of  the  gaps  in  the  crown  cover. 

Stands  whose  period  of  reproduction  is  from  ten  to  thirty  years, 
depending  on  site  and  climatic  factors,  but  which  may  still  be  classed 
as  even-aged  stands  ( §  259)  will  be  measured  as  such  and  their  average 
age  determined. 

308.  Area  of  Plots.  The  value  of  a  single  plot  in  indicating  normal 
yield  increases  with  its  size,  within  the  limit  which  permits  of  securing 
a  uniform  stocking  and  crown  cover  conforming  with  the  standard 
sought.  Since  one  plot  represents  but  a  single  age  and  one  shade  of 
site  quality,  and  the  cost  of  measurement  increases  with  size,  it  is  better 
to  limit  the  size  of  plots  for  a  yield  table  and  obtain  a  greater  number 
more  widely  distributed. 

The  size  of  plots  should  increase  with  the  size  and  age  of  the  trees 
to  be  measured.  The  greatest  danger  in  measuring  small  plots  is 
failure  to  coordinate  the  quantitative  site  factors  utilized  in  producing 


398  NORMAL  YIELD  TABLES  FOR  EVEN-AGED  STANDS 

the  3'ield  with  the  area  measured.     This  error  is  best  illustrated  by  the 

measurement  of  an  isolated  clump  of  trees  with  w^ide  crown  and  root 

spread.      A  plot  laid  out  to  include    their  boles  will  have  too  small 

an  area,  and  an  excessive  yield  (Fig.  83). 

In  dry  regions  especially,  root  spread  exceeds  that  of  crowns  and 

cannot  be  determined  accurately.     The  effect  of  these  errors  is  especially 

noticeable  when  the  size  of  the  plots  is  small,  the  yield  per  acre  varying 

inversely  with  area  of  plots.     By  increasing  the  size  of  the  plot,  the 

proportional  influence  of  a  faulty  location  of  its  boundaries  is  lessened, 

and  when  coupled  with  care  in  making  these  boundaries  inclusive  of 

crown  space  and  probable  root  space  of  the  trees  measured,  the  error 

is  negligible.     Just  as  for  other  sample  plots  ('§  243),  it  is  better  to 

have  a  smaller  plot  surrounded  by  a  control  strip  of  similar  timber  than 

to     extend     the 

r^ — ^^"^ — -^^^  /"^"^-'---s..,^  boundaries  to  in~ 

/         \^  I      'I  xV/i  /  /  \  elude  the  whole 

Yj/j-'  [     \(  v  1     1/  J  ^^  ^  stand  to  be 

/^  ^"\  I        1^  measured,  and  it 

I  \|       I  is  usually  possi- 

iL^ 1 1 Wll  H  \\ ble,  in  regions  of 

|_  ^7 c~^ ' ]  average  rainfall, 

„      „„     T,  ,  ,.     ,    ,  .  .  ,  ,  to  have   such   a 

)i\G.  83. — Keiation  between  growing  space  occupied  by  crowns 

or  roots  of    trees   and  size  of  plot   measured  to  secure    control     Strip. 

yield  per  acre.  The  size  of  plots 

^— Too  small  an  area.  under  the  above 

B — Correct  for  humid  region  or  site.  principles     will 

C — Approximately  correct  for  arid  region.  vary     from     y?- 

acre,  for  dense 
young  stands,  to  5  acres  for  veteran  scattered  timber  in  dry  regions. 
Ordinary  sizes  run  from  ^  to  2  acres.  Since  these  boundaries 
should  be  accurately  run,  plots  should  be  square  or  rectangular, 
and  since  the  area  contributing  to  the  growth  of  single  trees  is 
in  theory  a  circle,  rectangular  plots  should  not  be  too  narrow;  their 
short  dimension  should  be  at  least  four  times  the  average  width  of 
cro\/ns  of  the  trees  measured.  For  the  same  reason  plots  should  never 
be  triangular  or  have  sharp  angles.  Unless  intended  for  permanent 
location  and  re-measurement,  the  corners  of  plots  are  marked  tempora- 
rily by  any  convenient  means,  and  their  side  lines  blazed  or  marked 
so  as  to  exclude  all  trees  falling  outside  of  the  boundary. 

309.  Measurements  Required  on  Each  Plot.  Dimensions  of  Trees. 
A  diameter  limit  is  determined,  dependent  on  minimum  merchantable 
sizes.  All  trees  above  this  are  measured  at  B.H.  and  recorded  in  diam- 
eter classes  of  1  inch  or  2  inches.     Since  these  plots  are  for  the  purpose 


MEASUREMENTS  REQUIRED  ON  EACH  PLOT  399 

of  measuring  yields  they  are  selected  in  stands  which  have  reached 
merchantable  sizes.  Plots  on  which  a  portion  only  of  the  trees  are 
merchantable  may  require  the  counting  of  the  remaining  stand  and  its 
classification  as  to  size.  Dead  trees  are  recorded  by  diameter.  Species 
are  separately  tallied. 

The  height  of  trees  for  a  yield  table  should  be  taken  separately 
on  each  plot.  Several  tr.^es  of  different  diameters,  whose  heights  are 
average  for  the  stand  should  be  measured  and  recorded  together  with 
their  diameters,  the  number  varying  with  the  stand,  from  5  to  15. 
Where  merchantable  and  not  total  height  is  desired,  the  satisfactory 
determination  of  heights  for  the  plot  is  made  much  more  difficult  by 
the  variation  in  top  diameters  and  the  danger  of  error  in  judging  heights. 
Such  a  yield  table,  while  practical,  is  less  reliable  than  one  based  on 
total  heights.  Total  height  should  always  be  recorded  regardless  of 
whether  merchantable  height  is  used,  since  it  is  required  for  a  permanent 
standard  of  site  quality. 

Where  the  merchantable  height  unit  is  used  it  may  be  better  to  tally 
the  merchantable  length  of  every  tree  on  the  plot  than  to  rely  on  a  few 
trees  measured  by  the  hyj^someter.  This  introduces  the  element  of 
ocular  guess. 

Age  and  Volume  of  Stand.  The  age  of  each  plot  is  separately 
determined  by  methods  discussed  in  Chapter  XXIII.  The  common 
method  of  determining  the  volume  on  the  plot  is  by  standard  volume 
tables,  based  on  diameter  and  height.  This  assumes  that  the  variation 
of  the  trees  on  each  plot  as  to  shape  or  form  quotients  from  the  average 
form  for  this  species  or  region,  is  not  sufficient  to  require  separate 
determination.  Since  trees  must  either  be  felled  or  cut  into,  to  deter- 
mine age,  except  when  the  increment  borer  will  suffice,  and  since  the 
trees  selected  for  this  purpose  would  be  average  in  volume  for  the  stand 
or  for  diameter  groups  within  it,  these  sample  trees  are  sometimes  used 
to  determine  the  volume  of  the  stand.  This  method  is  useful  when  no 
reliable  volume  table  exists,  and  when  cubic  volume  is  sought.  The 
additional  accuracj^  attained  in  measuring  the  volume  of  the  sample 
trees  for  the  plot  itself  is  offset  by  the  possibility  that  the  trees  cut 
may  vary  from  the  true  average  of  the  stand.  The  methods  of  deter- 
mining the  size  of  such  sample  trees  for  felling  are  described  in  §  241. 

Crown  Classes.  Each  tree  on  the  plot  is  usually  tallied  in  the  crown 
class  in  which  it  falls,  as  classified  in  §  274. 

Description  of  Plot  or  Site.  Since  in  the  preparation  of  a  yield  no 
effort  is  made  to  classify  the  plots  into  site  qualities  by  inspection  of 
the  site  factors  in  the  field,  the  description  of  the  plot  should  be  brief, 
and  serve  merely  to  explain  the  results  obtained  and  check  their  value. 
The  points  to  be  covered  are  the  following: 


400  NORMAL  YIELD  TABLES  FOR  EVEX-AGED  STANDS 

1.  Location  of  plot.  Region,  watershed  or  block,  section  or  forty. 
Relocation  is  not  contemplated  from  this  description. 

2.  Density  of  crown  cover.  This  has  in  some  studies  been  used 
in  an  attempt  to  reduce  the  area  to  a  fixed  standard  of  density;  e.g., 
a  stand  showing  .9  crown  density  would  be  considered  as  the  equivalent 
of  but  .9  of  a  full  yield  on  the  plot.  The  element  of  judgment  thus 
introduced  is  dangerous  and  had  best  be  omitted. 

3.  Altitude: 

Absolute — approximate. 

Relative — with  respect  to  nearest  stream,  when  it  affects  the 
quality  of  site. 

4.  Aspect — as  affecting  exposure. 

5.  Degree  of  slope. 

6.  Geological  formation. 

7.  Soil,  kind,  depth,  consistency  and  degree  of  moisture. 

8.  Origin  of  stand,  whether  from  sprouts  or  from  seed. 

9.  History  of  stand. 

10.  Condition  of  stand  with  respect  to  evidence  of  damage  caused 
by  fire,  insects,  wind  or  other  agencies  should  be  especially  noted. 

11.  Exposure  to  winds,  degree  and  character. 

12.  Amount  and  character  of  tree  reproduction  on  the  ground. 

13.  Herbaceous  and  shrubby  vegetation  under  the  timber. 

Record  of  Data  for  each  plot.  The  data  of  permanent  value  for  each 
plot  are, 

1.  Area,  in  acres. 

2.  Age. 

3.  Total  number  of  living  trees,  by  species. 

4.  Number  of  living  trees  above  merchantable  diameter  limit,  by 

species.     (This  may  be  shown  for  two  diameter  limits,  as  for 
cordwood  and  saw  timber  units.) 

5.  Average  diameter  (from  diameter  of  tree  of  average  basal  area, 

or  volume)  (§  242). 

6.  Height  of  dominant  trees,  or  dominant  height  of  stand;    total; 

merchantable. 

7.  Total  basal  area  at  B.   H.   of   trees  per  acre,  in  square  feet. 

This  is  a  valuable  index  to  density  of  stocking. 

8.  Yield  per  acre,  in  cubic  feet,  total. 

9.  Yield  per  acre,  in  merchantable  units,  to  given  top  diameters 

and  stump  heights. 

10.  Dead  standing  trees,  number  or  per  cent. 

11.  Density  of  crown  cover. 

12.  Description  of  plot. 


TABLE  WITH  SITE  CLASSES  BASED  ON  HEIGHT  GROWTH     401 

310.  Construction  of  Yield  Table  with  Site  Classes  Based  on  Height 
Growth.  There  are  two  possible  bases  on  which  to  sepai-ate  site  quality, 
namely  yields  or  rate  of  growth,  and  total  height  or  height  growth. 
In  choosing  between  these  as  the  basis  of  site  quality,  not  only  must 
the  construction  of  the  table  be  considered  but  also  its  later  application 
in  the  field.  Whichever  basis  is  used,  the  range  of  growth  for  a  species 
or  region  must  be  divided  arbitrarily  into  site  classes,  once  its  maximum 
and  minimum  limits  are  determined.  When  volume  or  yield  is  chosen 
as  the  direct  basis  of  site  classes,  regular  and  consistent  results  may  be 
obtained  by  eliminating  most  of  the  variables  in  the  choice  of  plots. 
But  when  these  results  are  later  used  as  a  means  of  determining  site 
qualities  in  the  field  on  the  basis  of  mean  annual  rate  of  growth  per  year 
or  total  yield  based  on  age,  the  system  breaks  down. 

On  the  other  hand,  if  the  division  of  plots  into  site  qualities  is  based 
on  height  growth  as  indicated  in  §  296  not  only  are  the  original  plots 
apt  to  be  separated  more  accurately  into  their  true  site  classes  since 
variations  in  volume  due  to  over-  or  under-stocking  as  reflected  in  the 
board  foot  or  other  unit  are  minimized,  but  the  division  of  a  large 
area  in  the  field  into  site  classes  for  the  application  of  the  growth  data 
in  predicting  yields  is  made  possible  in  strict  conformity  with  the 
standard  used  in  the  table  itself  (§  345). 

While  volume  has  been  made  the  direct  basis  of  many  European 
yield  tables,  yet  in  these  regulated  and  fully  stocked  stands  most  of 
the  variables  are  reduced  to  reasonable  proportions.  Under  our  con- 
ditions of  abnormal  and  accidental  stocking,  with  the  maximum  of 
damage  to  the  stands  during  growth,  the  variations  from  the  factor 
of  density  of  stocking  due  to  variable  number  of  trees  per  acre,  even 
in  stands  of  full  crown  cover,  is  so  great  as  to.  discourage  most  investi- 
gators on  first  attempt. 

The  steps  in  the  construction  of  a  yield  table  based  on  height  are 
as  follows: 

1.  On  cross-section  paper  on  which  age  is  plotted  on  the  horizontal 
scale,  and  height  on  the  vertical  scale,  place  the  average  height  for  each 
plot  above  the  age  of  the  stand.  These  heights  may  be  the  heights  of 
the  dominant  trees  (§  296).  These  points  will  fall  in  a  comet-shaped 
band  increasing  with  age. 

2.  Draw  a  curve  indicating  the  maximum  height  growth,  and  one 
for  minimum  height  growth  as  in  Fig,  84. 

3.  Decide  upon  the  number  of  site  classes  to  use.  These  will  depend 
largely  on  the  total  range  of  heights  found  for  trees  of  a  given  age,  and 
the  possibility  of  convenient  subdivisions  not  too  small  to  be  serviceable, 
i.e.,  large  enough  to  overcome  the  slight  variations  in  height  based  on 
age  which  may  be  due  to  density  of  stand  instead  of  site. 


402 


NORMAL  YIELD  TABLES  FOR  EVEN-AGED  STANDS 


4.  Divide  the  space  between  the  maximum  and  minimum  curves,  on 
each  ordinate,  into  arbitrary  spaces  of  equal  magnitude,  corresponding 
to  the  number  of  site  classes  established,  and  connect  the  points  so  found 
by  curves. 

5.  The  numbered  plots  whose  height  falls  in  each  division  of  the 
chart  are  assigned  to  the  indicated  site  quality.  Owing  to  variables 
affecting  yield,  some  of  the  plots  in  a  lower  site  class  may  exceed  the 
growth  of  plots  whose  site  class  is  better. 


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100 


Fig.  84. — Method  of  separating  plots  into  three  site  quahties  based  on  the  height 
attained  by  dominant  trees  in  the  stand,  plotted  on  age  of  stand.  Jack  Pine, 
Minnesota. 


The  height  of  dominant  trees  on  131  plots  of  jack  pine,  plotted  on 
the  basis  of  age,  is  shown  in  Fig.  84.  By  this  method  (Baur's),  the 
positions  of  the  maximum  and  minimum  curves  determine  that  of  the 
curves  separating  the  site  qualities.  One  or  two  plots  with  abnormally 
rapid  or  slow  growth  must  not  be  permitted  to  influence  unduly  the 
position  of  these  outer  curves.  With  height,  the  true  position  of  the 
boundary  curves  can  be  found  with  greater  certainty  than  if  volume  is 
used  originally  as  the  basis  of  classification.  In  this  figure,  the  average 
heights  of  qualities  I,  II  and  III  at  100  years  were  taken  as  90,  75  and 


TABLE  WITH  SITE  CLASSES  BASED  ON  HEIGHT  GROWTH     403 

60  feet,  following  the  suggestion  of  Roth  as  an  example  of  class  C  in 
height  classification  (Table  LV,  §  296),  and  with  these  guiding 
points  the  curves  limiting  the  three  classes  were  drawn  by  Baur's 
method. 

6.  The  yield  of  all  plots  in  a  single  site  class  are  then  plotted  on 
cross-section  paper  whose  base  or  horizontal  scale  is  age,  and  whose 
vertical  scale  is  volume.     From  these  data,  a  curve  of  average  yield 


100   110   120   130   140   150   160   170   180 
Age.  Years 


Fig.  85. — Curves  of  yield  obtained  by  averaging  the  yields  of  plots  whose  height 
growth  has  placed  them  in  the  same  site  class.  The  final  curves  smooth  off 
irregularities  in  these  averages.  Second  growth  Western  Yellow  Pine,  California. 
S.  B.  Show. 


based  on  age  may  be  drawn  from  which  the  yields  for  the  site  class 
for  each  decade  or  five-year  period  are  read.  A  separate  curve  is  plotted 
for  each  site  class.  The  jdeld  table  finally  shows  the  average  yields 
based  on  age  for  each  separate  site  class. 


404  NORMAL  YIELD  TABLES  FOR  EVEN-AGED  STANDS 

When  constructed  on  this  basis,  yields  for  different  site  classes 
increase  at  a  greater  ratio  than  do  the  indicating  heights. 

In  drawing  the  curve  of  yield  based  on  age  for  a  single  site  class, 
it  is  best  to  first  obtain  the  average  yield  for  a  given  decade  by  arith- 
metical means  and  connect  these  averages  by  straight  lines.  Even  if 
each  plot  were  normal,  the  averages  at  different  points  might  fall  above 
or  below  the  mean  for  the  site  as  the  plots  happened  to  be  on  the  better 
or  poorer  portions  of  this  site  class — and  to  this  factor,  the  natural  vari- 
ation in  density  or  yield  is  added. 

7.  For  this  reason,  the  average  curves  so  constructed,  for  each 
site  class,  should  now  be  assembled  on  a  single  sheet,  as  shown  in  Fig. 
85.  The  curves  of  yield  based  on  age  can  then  be  harmonized  for  all 
site  classes  by  the  same  principle  as  used  for  volume  tables  (§  140).^ 

311.  Rejection  of  Abnormal  Plots.  As  shown  in  §  304,  the  intent 
of  this  table  is  to  estal)lish  a  standard  of  yield,  termed  normal  or  index, 
with  which  the  yields  of  any  existing  stand  may  be  compared.  After 
the  separation  based  on  height  growth  is  effected,  the  yields  of  plots 
in  the  same  site  class  will  show  great  variation,  due  to  the 

Natural  range  of  site  quality  within  the  arbitrary  boundaries 

established ; 
Number  of  trees  per  acre  in  the  natural  stocking; 
Completeness  of  the  crown  canopy. 

The  eccentric  behavior  of  the  averages  plotted  in  Fig.  85  indicates  the 
effect  of  these  variations  in  yield.  The  question  arises  as  to  whether 
all  of  the  plots  should  be  included  in  these  averages  or  certain  plots 
rejected  as  abnormally  stocked.  A  method  of  correcting  the  yields 
by  a  factor  of  density  of  crown  has  been  generally  rejected  as  unsatis- 
factory (§  309).  The  area  of  plots  is  accepted  as  measured.  There 
are,  then,  two  possibilities  of  rejection;  first,  by  ocular  selection  in  the 
field,  which  eliminates  those  plots  which  are  incompletely  stocked; 
second,  by  further  inspection  of  the  plotted  volumes  based  on  age. 

Baur's  rule  for  rejection  of  plots  is  quoted  by  Graves  as  follows: 
"Stands  which  have  the  same  age  and  average  height  are  compared, 
and  all  are  considered  normal  whose  basal  area  lies  within  a  range  of 
15  per  cent;  that  is,  the  basal  area  of  the  best  and  poorest  stocked  stands 
must  not  differ  more  than  15  per  cent."  ^  The  application  of  this  rule 
rests  upon  the  interpretation  of  the  term  "  average  height."  Where 
from  three  to  five  site  classes  are  made  as  in  Fig.  85,  and  a  curve  of 
average  height  is  found  for  each  site  class,  which  would  fall  midway  of 

iThe  yields  shown  in  Fig.  85  are  from  an  unpublished  manuscript  by  S.  B. 
Show,  U.  S.  Forest  Service,  California,  for  second  growth  Western  yellow  pine. 
"  Graves'  Forest  Mensuration,  p.  319. 


REJECTION  OF  ABNORMAL  PLOTS  405 

the  limits  shown  in  the  figure,  the  rule  has  been  applied  in  this  country 
to  all  plots  whose  heights  classify  them  with  a  given  site.  The  natural 
variation  in  volume  for  plots  within  one  site  class  is  greater  than  15  per 
cent,  independent  of  abnormalities — hence  if  all  plots  which  vary  7^ 
per  cent  above  or  below  the  average  volume  for  the  site  at  that  age  are 
rejected,  about  half  of  the  plots,  although  normal,  may  he  thrown  out. 
If  this  rule  is  to  be  correctly  applied  as  a  test  of  normality,  the  arbitrary 
permitted  variation  of  15  per  cent,  if  used  at  all,  should  first  be  corrected 
by  finding  what  the  normal  yield  of  the  particular  plot  should  be,  based 
on  its  actual  height.  If  height  for  the  plot  is  midway  between  quality 
I  and  II,  normal  yield  is  also  midway  between  the  averages  for  these 
qualities.     The  steps  necessary  would  be  as  follows: 

1.  Draw  curves  of  average  height  as  shown  in  Fig.  84,  and  curves 
of  average  volume  as  shown  in  Fig.  85. 

2.  Determine  the  per  cent  of  variation  above  or  below  average  height, 
for  each  plot,  and  subtract  or  add  the  same  per  cent  from  the  volume  of 
the  plot.  This  gives  the  corrected  volume  of  the  plot  based  on 
average  height  for  the  site, 

3.  Compare  the  corrected  volume  of  the  plot  with  the  average  volume 
for  the  site.  If  it  falls  above  or  below  the  calculated  normal  by  more 
than  the  desired  per  cent  of  error  the  plot  can  be  thrown  out. 

4.  After  testing  the  normality  of  all  plots,  re-compute  the  average, 
using  only  those  plots  accepted  as  conforming  to  the  standard. 

If  15  per  cent  is  a  proper  standard  of  variation  for  forests  under 
management,  it  is  probable  that  even  with  the  above  method  this  per 
cent  is  too  small  as  a  criterion  of  normality  for  natural  stands.  It 
should  be  possible,  by  eye,  to  select  plots  of  which  at  least  95  per  cent 
will  be  suitable  for  inclusion  in  obtaining  the  average  results  for  a  stand- 
ard yield  table.  With  a  range  of  basal  area  increased  to  25  per  cent 
for  plots  of  the  same  height  based  on  age  as  indicated,  it  is  probable  that 
only  distinctly  abnormal  plots  wiU  be  rejected. 

In  constructing  volume  tables  it  is  not  customary  to  reject  trees 
after  they  have  been  measured  for  volume,  since  rejection  can  take 
place  in  the  selection  of  the  tree.  With  plots  for  yield  tables,  the  desire 
to  secure  a  theoretically  normal  or  uniform  standard  may  easily  lead 
to  too  rigid  a  rejection  of  plots  which  are  entirely  suitable  for  the  aver- 
age sought.  Maximum  yields,  on  the  basis  of  site  alone,  should  never 
be  sought  by  these  average  curves  of  yield,  since  the  best  portions  of 
the  site  will  exceed  the  average.  Again,  such  tables,  if  made  for  natural 
stands,  should  show  what  can  reasonably  be  expected  in  stands  repro- 
duced naturally  and  not  thinned,  on  the  average  acre  for  site.  A  con- 
sistent average  showing  the  probable  progress  of  a  fully  or  normally 
stocked  acre  by  decades,  and  not  an  abnormal  maximum  yield,  is  the 


406  NORMAL  YIELD  TABLES  FOR  EVEN-AGED  STANDS 

object  sought  both  in  field  selection  of  plots  and  in  their  further  sifting 
in  the  office  for  the  preparation  of  normal  yield  tables  for  natural 
growth. 

312.  Construction  of  Yield  Table  with  Site  Classes  Based  Directly 
on  Yields  per  Acre.  The  main  objection  to  the  direct  classification 
of  site  on  the  basis  of  yield  or  volume  on  age  by  Baur's  method  is  the 
impossibility  of  using  this  basis  later  as  a  means  of  classifying  forest 
lands  into  site  qualities  from  field  examination.  Furthermore,  yield 
alone  gives  an  unsatisfactory  basis  for  correlating  yield  tables  for  given 
species  when  made  for  different  regions,  or  for  correlating  the  yields 
of  different  though  similar  species.  It  is  this  need  of  standardization 
that  has  led  to  the  adoption  of  height  growth  rather  than  volume  as 
the  basic  standard. 

A  further  objection  to  the  direct  use  of  yields  lies  in  the  method  of 
plotting,  and  the  testing  of  plots  for  normal  density.  By  this  method, 
the  volumes  of  all  plots,  based  on  age,  are  entered  on  the  same  sheet  as 
shown  in  Fig.  86.  The  drawing  of  the  maximum  and  minimum  curves 
is  the  next  step.  There  is  no  way  by  which  the  abnormality  of  the  plots 
can  be  first  tested  as  with  heights.  So  the  elimination  consists  wholly 
of  drawing  these  boundary  lines  to  exclude  certain  plots  whose  yield 
is  so  much  greater  or  smaller  than  the  remainder  that  their  inclusion 
would  unduly  influence  the  position  of  these  limiting  curves. 

The  third  step  is  to  divide  the  space  thus  blocked  off  into  equal 
bands  by  the  method  used  for  height,  i.e.,  by  dividing  the  distance 
on  each  ordinate  into  equal  parts,  and  connecting  the  points  so  estab- 
lished. 

Finally,  a  curve  is  drawn  exactly  midway  of  each  space  as  described 
for  height  (§  310),  and  the  values  are  read  from  this  curve  at  each  decade 
to  form  the  table  of  yield  based  on  age. 

By  this  method  yields  increase  with  site  quality  by  exact  intervals. 
No  averages  are  attempted,  and  the  result  is  entirely  independent  of 
height  and  is  influenced  principally  by  the  maximum  and  minimum- 
yields  rather  than  the  general  weight  of  the  plots  studied. 

Using  as  the  basis  the  plots  which  have  been  classed  as  belonging 
to  each  separate  site  by  either  of  the  above  methods,  curves  showing 
the  average  at  different  ages  can  also  be  prepared  for  the  following 
additional  data: 

Number  of  trees  per  acre; 

Total, 

Above  a  minimum  diameter. 
Average  diameter. 
Average  height  of  dominant  trees. 
Total  basal  area. 


YIELD  TABLES  FOR  STANDS  GROWN  UNDER  MANAGEMENT    407 


313.  Yield  Tables  for  Stands  Grown  under  Management.     Normal 

yield  tables  for  stands  grown  under  management  may  be  constructed 
by  the  above  methods,  whenever  plots  are  available  which  have  been 
under  proper  management,  but  may  in  the  course  of  time  be  checked 
and  finally  supplemented  entirely  if  desirable  by  the  yields  of  plots 
which  have  been  measured  at  intervals  of  from  five  to  ten  years. 


4000 

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10  20  30  40  50  GO  70  80 

Age,  Years 

Fig.  86. — Curves  of  yield  based  directly  on  cubic  volume  plotted  on  age.     Jack 
Pine,  Minnesota. 

WTiere  a  series  of  plots,  differing  in  age  by  ten  years,  is  available, 
the  measurement  a  decade  later  on  these  plots  will  give  fragments  of 
a  curve  of  growth  which  may  be  pieced  together.  The  greater  the 
period  over  which  these  re-measurements  extend,  the  more  nearly  do 
these  fragmentary  curves  form  a  complete  series. 

It  may  be  expected  that  yields  on  areas  under  treatment  will  exceed 
the  so-called  normal  yields  used  as  a  standard  for  natural  growth. 


408  NORMAL  YIELD  TABLES  FOR  EVEN-AGED  STANDS 

The  latter  tables  thus  become  the  basis  or  minimum  from  which  such 
increased  yields  may  be  computed  for  fully  stocked  areas. 

314.  Yield  Tables  for  Stands  of  Mixed  Species.  Practically  all 
stands  are  composed  of  more  than  one  species,  though  some  conifers 
as  Western  yellow  pine  and  lodgepole  pine  grow  in  practically  pure 
stands.  So  prevalent  is  the  mixture  that  a  stand  which  is  composed 
of  80  per  cent  and  over  in  volume  for  the  given  age  class  of  a  single 
species  is  termed  a  pure  stand  of  that  species.  There  may  exist  a  large 
number  of  trees  in  an  under-story  of  different  species,  and  yet  the  volume 
of  the  trees  of  other  species  in  the  main  stand  may  not  exceed  20  per 
cent. 

In  even-aged  stands  composed  of  two  or  more  species  in  mixture, 
two  methods  have  been  proposed  for  the  determination  of  yields.  One 
is  to  prepare  yield  tables  for  pure  stands  of  each  species,  and  then  to 
determine  the  per  cent  of  these  species  in  the  mixed  stand.  The  further 
yield  of  such  a  stand  is  predicted  by  applying  the  per  cent  thus  indicated, 
to  each  yield  table,  and  taking  the  sum  of  the  two  partial  yields  as  the 
yield  of  the  mixed  stand. 

In  applying  these  tables  on  this  basis  to  get  yields  for  the  future 
from  young  stands,  the  question  of  survival  may  affect  the  result,  in 
case  one  species  tends  to  crowd  out  another.  But  when  stands  are 
even-aged,  the  association  is  apt  to  be  of  species  which  customarily 
grow  in  mixture  and  maintain  their  places  in  the  stand.  The  yields, 
however,  will  be  for  the  per  cent  of  future,  not  of  present  mixture. 

"V^Hiere  species  differ  radically  in  their  characters,  and  grow  in  a 
mixed  stand,  such  as  a  hardwood  species  with  conifers,  there  is  apt  to 
be  greater  variation  in  yields,  but  with  trees  of  similar  habits,  such 
as  mixed  sprout  hardwoods  or  mixtures  of  two  or  more  conifers,  the 
stand  behaves  much  as  it  would  for  pure  stands. 

For  all  such  even-aged  mixed  stands,  it  is  possible  to  prepare  yield 
tables  by  disregarding  the  per  cent  of  mixture,  or  recording  it  merely 
as  a  descriptive  item,  and  proceeding  as  if  the  stand  were  pure. 

An  example  ^  of  a  yield  table  for  mixed  stands  of  second-growth  hardwoods  in 
New  England  is  given  below.  The  conchisions  based  on  this  study  were,  first,  that 
in  spite  of  wide  variation  in  percentages  of  species  in  mixture,  for  a  given  age,  site, 
and  density,  the  volumes  in  board  feet,  cubic  feet  and  cords  were  constant,  and, 
second,  that  the  volumes  of  trees  of  given  height  and  diameter  in  cords  and  cubic 
feet  were  the  same,  regardless  of  species. 

1  Bulletin  of  the  Harvard  Forest  No.  1.  Growth  Study  and  Normal  Yield  Tables 
for  Second-Growth  Hardwood  Stands  in  Central  New  England.  By  J.  Nelson 
Spaeth,  Cambridge,  Mass.,  1921, 


YIELD  TABLES  FOR  STANDS  OF  MIXED  SPECIES 


409 


TABLE  LXII 

Normal  Yield  per  Acre  in  Cubic  Feet  and  Cords  of  Better  Second-growth 
Hardwood  Stands  in  Central  New  England 


SITE   CLASS  I 

(All  trees  2  inches  in  diameter  and  over) 


Age 

Trees 

Basal 

Height 

D.B.H. 

• 
Volume 

Vclume 

Forest 

in 

per 

area 

in 

in 

per  acre. 

per  acre. 

form 

Years 

acre 

Sq.  ft. 

Feet 

Inches 

Cu.  ft. 

Cords 

factor 

20 

1250 

66.0 

27.1 

3.11 

1041 

15.80 

0.582 

25 

1120 

90.8 

33.0 

3.86 

1625 

23.71 

.542 

30 

1010 

107.2 

37.5 

4.41 

2150 

29.75 

.501 

35 

900 

119.9 

41.5 

4.94 

2628 

34.96 

.503 

40 

800 

130.2 

45.0 

5.46 

3058 

39.63 

.520 

45 

700 

139.7 

48.2 

6.05 

3495 

44.03 

.520 

50 

610 

148.0 

50.7 

6.69 

3898 

48.00 

.520 

55 

525 

155.7 

53.1 

7.37 

4298 

51.84 

.520 

60 

450 

162.5 

55.4 

8.14 

4677 

55.50 

.520 

65 

390 

169.0 

57.8 

8.91 

5068 

59.25 

.520 

70 

340 

175  1 

59.8   • 

9.72 

5462 

62.75 

.522 

75 

300 

180.9 

61.9 

10.51 

5833 

66.18 

.521 

80 

270 

186.3 

64.0 

11.25 

6200 

69.50 

.520 

site   CLASS  II 

(All  trees  2  inches  in  diameter  and  over) 


Age 

Trees 

Basal 

Height 

D.B.H. 

Volume 

Volume 

Forest 

in 

per 

area. 

m 

m 

per  acre. 

per  acre. 

form 

Years 

acre 

Sq.  ft. 

Feet 

Inches 

Cu.  ft. 

Cords 

factor 

25 

1360 

59.8 

27.8 

2.84 

982 

14.65 

0.593 

30 

1235 

77.9 

31.8 

3.40 

1380 

20.40 

.557 

35 

1125 

91.1 

34.8 

3.86 

1798 

25.48 

.567 

40 

1030 

101.6 

37.4 

4.25 

2180 

29.53 

.574 

45 

940 

110  3 

39.8 

4.66 

2534 

33.04 

.577 

50 

855 

117.9 

41.5 

4  94 

2828 

35.98 

.580 

55 

775 

124.6 

42.8 

5.43 

3118 

38.55 

.584 

60 

700 

130.7 

44.2 

5.85 

3375 

41.08 

.584 

65 

630 

136.6 

45.3 

6.31 

3638 

43.42 

.587 

70 

565 

142.2 

46.8 

6.79 

3895 

45.61 

.592 

75 

500 

147.7 

47.0 

7.36 

4146 

47.75 

.598 

80 

440 

153.0 

47.6 

7.78 

4390 

49.80 

.601 

The  percentage  of  species  in  mixture  in  the  stands  comprising  the  above  tables  is 
shown  in  Table  LXIII. 


410 


NORMAL  YIELD  TABLES  FOR  EVEN-AGED  STANDS 


TABLE  LXIII 

Percentage  of  the  Various  Species  in  Mixture  from  Table  LXII  Classified 
AS  TO  Type  and  Site  Class 


Maple 

BmcH 

Better  Hwdl^^^^^;; 

.    . 

Ch't-   Bass- 

Pop- 
lar 

Ash, 
white 

Misc.* 

i  nut  i  wood 

Red 

Hard  Gray 

Paper 

Yel. 

Qiial,      I 

27 

15 

3 

0 

2 

8 

2 

6 

9 

7 

15 

6 

Qual.     II 

20 

12 

6 

0 

8 

10 

7 

5 

3 

8 

14 

7 

Inf.     Hwd. 

2 

24 

2 

38 

3 

4 

0 

1 

0 

15 

1 

10 

*  Under  miscellaneous  are  included  all  species  whose  combined  representation  in  the  plots  of 
any  one  type  or  site  class  is  less  than  5  per  cent  of  the  total  number  of  trees.  These  species 
are:  white  oak,  black  cherry,  pignut  hickory,  white  pine,  hemlock,  elm,  butternut,  hop  horn- 
beam, black  birch,  flowering  dogwood,  and  shad  bush. 

By  either  of  the  above  two  methods  of  constructing  yield  tables  for 
mixed  stands,  the  yield  of  the  entire  stand  is  taken  as  the  standard  of 
yields.^ 

The  classification  of  mixed  stand  may  be  greatly  simplified  by  group- 
ing together  all  plots  in  which  80  per  "cent  or  over  of  the  merchantable 
volume  is  made  up  of  certain  species.  In  a  study  of  the  mixed  conifer 
type  on  the  Plumas  National  Forest  in  California,  containing  Western 
yellow  pine,  sugar  pine,  Douglas  fir,  white  fir,  and  incense  cedar, 
75  per  cent  of  156  plots  were  found  to  contain  but  two  principal  species 
whose  combined  volume  was  over  80  per  cent  of  the  plot.  The  yields 
could  be  grouped  as 

1.  Yellow  pine — Douglas  fir. 

2.  Yellow  pine — Fir  (Douglas  or  white). 

3.  Douglas  fir — white  fir. 

As  indicating  the  possibilities  of  simplifying  the  problem  of  yields  of 
mixed  stands,  it  was  found  in  this  study  that  the  average  basal  areas,  for 
plots  showing  the  same  standard  of  height  growth  (§  296)  was  as  follows: 


Type 

Basic  plots 

Per  cents  of  yellow 

pine — Douglas  fir 

type 

Yellow  pine — Douglas  fir 

43 
65 
21 

100.0 
97.0 

105.1 

'  A  method  by  which  the  per  cent  of  yields  in  plots  of  mixed  species  is  recorded 
on  the  cross  section  paper,  and  the  yield  per  acre  expressed  for  different  species 
which  constitute  different  per  cents  of  the  total  stand,  is  described  in  Graves' 
Forest  Mensuration,  Chapter  XVII,  p.  332. 


REFERENCES  411 

This  result  strengths  the  conclusion  that  for  species  which  form 
part  of  the  same  crown  canopy,  differences  in  total  yield,  of  plots  with 
different  per  cents  of  mixture,  may  not  constitute  a  serious  obstacle 
to  the  construction  of  yield  tables  based  on  age.^ 

References 

Rate  of  Growth  of  Conifers  in  the  British  Isles.  Bui.  3,  Forestry  Commission, 
1920. 

Comparison  of  Yields  in  the  White  Mountains  and  Southern  Appalachians,  K.  W. 
Woodward,  Forestry  Quarterly,  Vol.  XI,  1913,  p.  503. 

Einheitliche  Schatzungstafel  fur  Kiefer,  Zeitschrift  ftir  Forest-  und  Jagdwesen,  June, 
1914,  p.  325.     Review,  Forestry  Quarterly,  Vol.  XII,  1914,  p.  629. 

The  Use  of  Yield  Tables  in  Predicting  Growth,  E.  E.  Carter,  Proc.  Soc.  Am.  Foresters, 
Vol.  IX,  1914,  p.  177. 

Yields  of  Mixed  Stands,  Schwappach,  Untersuchungen  in  Mischbestanden,  Zeit- 
schrift fiir  Forest-  und  Jagdwesen,  Aug.,  1914,  p.  472.  Review,  Forestry 
Quarterly,  Vol.  XIII,  1915,  p.  98. 

1 A  Preliminary  Study  of  Growth  and  Yield  of  Mixed  Stands,  S.  B.  Show  and 
Duncan  Dunning,  U.  S.  Forest  Service,  San  Francisco,  Cal.,  1921.  Unpublished 
manuscript. 


CHAPTER  XXIX 

THE  USE  OF  YIELD  TABLES  IN  THE  PREDICTION  OF  GROWTH 
IN  EVEN-AGED  STANDS,  WITH  APPLICATION  TO  LARGE 
AGE  GROUPS 

315.  Factors  Affecting  the  Probable  Accuracy  of  Yield  Predictions. 

If  the  average  yield  on  Quality  I  site  for  a  species  is  taken  as  100  per 
cent,  and  but  three  qualities  are  distinguished,  the  relative  yields  shown 
for  Qualities  II  and  III  may  be  as  low  as  72  and  45  per  cent  of  that  on 
Quality  I,  respectively.^  This  means  gaps  of  28  and  27  per  cent  in  the 
series  between  the  points  arbitrarily  marked  by  the  average  curves 
expressed  in  the  yield  table.  The  use  of  five  qualities  of  site  reduce 
these  intervals  to  about  15  per  cent.  For  young  stands,  or  areas  just 
growing  up  to  timber,  this  is  as  close  a  prediction  as  can  be  expected. 
If  the  site  is  properly  classified,  its  future  yield  if  normally  stocked  will 
differ  by  an  extreme  of  one-half  of  the  above  interval,  either  above 
or  below  the  standard.  Once  the  site  is  identified  by  the  use  of  average 
height  based  on  age,  the  future  yields  can  be  predicted  by  use  of  the 
yield  table,  either  for  bare  land  or  for  partly  grown  young  stands, 
provided  the  degree  of  stocking  agrees  with  that  incorporated  in  the 
table. 

The  larger  part  of  the  area  of  any  natural  forest  is  not  comparable 
with  these  conditions.  The  variables  of  density  of  stocking,  form  of 
age  classes,  and  composition  of  species  must  all  be  dealt  with  before 
yields  on  any  considerable  area  can  be  predicted  within  the  desired  mar- 
gin of  accuracy.  The  degree  of  accuracy  attainable  in  prediction  of 
yields  in  our  wild  forests  is  not  yet  known  even  approximately  since 
for  many-aged  forests  and  mixed  stands,  yield  tables  based  on  age 
have  not  been  attempted  until  recently  (§  314).  This  much  can  be 
said — the  degree  of  accuracy  attainable,  and  hence  required,  is  greatest 
for  short  periods,  i.e.,  for  the  current  growth  of  a  decade  or  two,  and 
diminishes  as  the  length  of  the  period  increases.  But  the  relative 
importance  of  accuracy  also  diminishes  with  the  length  of  the  period, 
thus  permitting  the  use  of  yield  tables  based  on  averages. 

1  Norway  Pine  in  the  Lake  States,  U.  S.  Dept.  Agr.,  1914,  Bui.  139,  p.  15. 

412 


ACTUAL  OR  EMPIRICAL  DENSITY  OF  STOCKING  413 

316.  Methods  of  Determining  Actual  or  Empirical  Density  of 
Stocking.  For  even-aged,  pure  stands,  but  one  variable  is  present 
in  addition  to  site  quality,  that  of  the  density  of  stocking.  As  this 
variable  is  the  result,  first,  of  the  intrusion  of  small  areas  of  unstocked 
land  into  the  timbered  area,  which  it  may  not  pay  to  exclude  in  mapping 
(§  306)  and  second,  of  the  uninterrupted  play  of  natural  agencies  of 
destruction  operating  on  stands  which  are  themselves  originally  the 
result  of  chance  at  the  time  of  reproduction,  the  problem  is  to  arrive 
at  an  average  yield  per  acre  which  expresses  not  so  much  the  capacity 
of  the  site  as  the  accidental  product  of  these  various  conditions.  This 
average  will  in  all  cases  be  less  than  the  standard  or  normal  yields  for 
the  same  area,  sometimes  by  as  much  as  50  per  cent.  Evidently  the 
determination  of  site  quality  is  but  the  first  step  in  predicting  the  yields 
of  existing  stands  from  such  a  standard  table,  and  without  correction 
these  predictions  may  range  from  50  to  100  per  cent  too  high  except 
on  small  tracts,  such  as  plantations  or  managed  forests,  whose  density 
factor  is  known  to  coincide  closely  with  the  yield  table. 

Use  of  Empirical  Yield  Tables.  There  are  two  methods  of  over- 
coming this  difficulty.  The  first  is  an  attempt  to  arrive  directly  at 
the  average  yields  based  on  age  for  the  larger  area,  or  to  make  an  empir- 
ical jaeld  table  (§  303)  which  will  reflect  the  degree  of  stocking  present. 
This  applies  the  principle  used  in  timber  estimating  in  determining  the 
volume  of  the  average  acre  (§  209).  But  the  operation  is  more  dif- 
ficult, as  it  involves  the  separation  of  the  entire  area  into  stands  based 
on  age,  whose  area  is  known,  and  the  combining  of  these  data  into  a 
yield  table  subnormal  in  character  and  representing  a  purely  arbitrary 
percentage  of  standard  yields.  In  the  preparation  of  such  a  table,  the 
curves  of  yield  are  affected  by  the  varying  per  cents  of  stocking  of  dif- 
ferent age  classes  and  areas  so  that  practically  the  entire  area  must  be 
analyzed  to  obtain  the  true  average,  and  then  the  table  will  be  incorrect 
in  its  prediction  of  yield  for  any  specific  age  class  or  stand  which  differs 
from  this  arbitrary  average  stocking.  The  table  will  be  correct  only 
for  the  tract  on  which  it  is  made  since  empirical  density  varies  with 
every  forest  and  block.  Empirical  yield  tables  on  this  basis  have  the 
same  drawbacks  as  volume  tables  for  defective  trees  which  express 
the  net  contents  only  (§  151). 

Use  of  Normal  Yield  Tables  by  Reduction.  The  better  plan,  and 
the  one  which  will  probably  be  universal^  used,  is  to  depend  upon  a 
standard  normal  yield  table  (just  as  upon  a  volume  table  for  sound 
trees  only)  and  to  ascertain  the  relation  or  percentage  of  deduction  from 
this  table,  which  applies  to  the  specific  stand  or  larger  area  for  which 
yield  is  desired.     For  even-aged  stands,  the  application  of  the  yield 


414  THE  USE  OF  YIELD  TABLES 

table  to  the  larger  area  involves  the  same  steps  for  this  area  as  are 
required  in  the  construction  of  the  normal  yield  table  itself,  or  for  the 
preparation  of  an  average  empirical  yield  table.  These  are  as 
follows: 

1.  Determine  the  volume,  the  area  occupied,  and  the  age  of  each 
separate  age  class. 

2.  From  these  data  in  turn  compute  the  volume  per  acre  for  the  given 
age. 

3.  Determine  the  relative  density  by  dividing  this  unit  volume  by 
the  yield  of  an  acre  of  the  same  age  from  the  yield  table;  this  is  expressed 
as  a  per  cent  of  the  standard  yield  for  that  age.  Per  cent  density  can 
thus  be  found  separately  for  each  age  class,  or  for  each  separate  stand 
if  desired. 

317.  Application  of  Density  Factor  in  Prediction  of  Growth  from 
Yield  Tables.  Future  yield  can  now  be  predicted  for  all  stands  from 
the  same  yield  table,  by  applying  the  reduction  per  cent  to  this  table 
which  is  required  by  the  stand  or  age  class  in  question. 

Influence  of  Number  of  Trees  per  Acre.  There  is  one  valid  objec- 
tion to  this  assumption  that  relative  density  as  expressed  at  a  given 
age  in  terms  of  volume  will  remain  constant  for  future  yields  and  that 
is  that  under  the  laws  of  growth  of  stands  partially  stocked  this  stand 
will  tend  to  become  fully  stocked  (§  301).  A  knowledge  of  the  number 
of  trees  per  acre  required  for  full  stocking  at  the  age  of  cutting  is  also 
obtained  from  a  normal  yield  table,  and  this  knowledge  may  be  directly 
applied  in  determining  the  per  cent  of  density  in  immature  stands, 
not  on  the  basis  of  crown  cover  existent  but  of  the  ultimate  yield  to 
be  expected  from  the  trees  which  will  probably  survive.  In  the  same 
way,  for  older  stands,  when  volume  per  acre  is  less  than  that  in  a  nor- 
mal stand,  but  the  number  of  trees  per  acre  is  sufficient,  the  reduction 
can  be  lessened  as  applied  to  these  partially  stocked  stands  as  long  as 
the  trees  are  so  distributed  as  to  utilize  the  area;  e.g.,  in  one  case, 
a  50  per  cent  average  stocking  may  represent  100  per  cent  stocking  on 
50  per  cent  of  the  area,  with  the  rest  blank.  No  correction  should 
be  made.  In  another  case  the  entire  area  is  covered  with  a  stand  whose 
volume  is  50  per  cent  of  normal,  but  trees  are  well  placed.  In  this  case 
the  yield  will  probably  be  normal  at  the  age  at  which  the  normal  num- 
ber of  trees  per  acre  drops  to  about  the  average  number  now  present  in 
the  natural  stand. 

The  former  or  simpler  method  is  of  course  extremely  conservative 
and  allows  a  margin  for  the  continuance  of  natural  losses  by  fire,  wind, 
insects  and  diseases,  while  the  latter  may  be  applied  to  more  intensively 
managed  and  better  protected  forests. 


PREDICTION  OF  GROWTH  FROM  YIELD  TABLES 


415 


This  method  is  illustrated  below  based  on  a  standard  yield  table,  §  314. 
Second-growth  Hardwoods  in  Central  New  England 
Site  Class  I 


Prediction  op 

Actual 

Standard 

Yield  63  Per  Cent 

Area. 

Age. 

Yield. 

Yield, 
per 

Yield 
per 

Reduction. 

OF  Standard  in 

acre. 

acre. 

10  Years. 

20  Years. 

Acres 

Years 

Cords 

Cords 

Cords 

Per  cent 

Cords 

Cords 

10 

25 

150 

15 

23.71 

63 

22 

27,7 

This  assumes  no  increase  in  the  density  factor  with  age  and  is  the  most  conserva- 
tive method. 

Assuming  that  future  yield  will  be  influenced  by  the  number  of  trees  and  their 
distribution,  the  future  yields  as  shown  may  be  increased  as  follows : 


Number  of      Normal 
trees        i  number  in 

per  acre  now     10  years 

1 

Reduction 

per  cent  in 

10  years 

Yield  in 

10  years. 

Cords 

Normal 

number  in 

20  years 

Reduction 

per  cent  in 

20  years 

Yield  in 

20  years. 

Cords 

600 

900 

mi 

23.3 

700 

86 

37.8 

This  basis  gives  the  maximum  possible  yields  to  be  expected  by  contrast  to  the 
first  method,  since  it  does  not  contemplate  the  loss  of  any  of  the  original  six  hundred 
trees,  and  assumes  that  these  trees  are  distributed  at  equally  spaced  intervals  over 
the  area. 

Somewhere  between  these  two  predictions  the  actual  future  yield  will  be  found. 

Use  of  Basal  Areas.  Basal  area  may  be  substituted  for  yields  in 
determining  the  percentage  relations,  and  as  a  basis  for  predicting 
yields  in  cubic  feet.  If  in  the  above  example  the  basal  area  at  twenty- 
five  years  is  57.2  square  feet  per  acre,  the  reduction  per  cent  is  63  and 
the  same  prediction  of  future  yield  is  obtained,  which  can  be  modified 
by  comparing  the  number  of  trees  per  acre  in  the  same  way. 

These  illustrations  bring  out  the  function  of  a  yield  table  as  dis- 
tinguished from  that  of  merely  stating  the  yields  of  stands.  When  the 
total  age  of  any  given  stand  is  determined  in  addition  to  its  volume, 
the  rate  of  growth  per  year  for  that  stand  can  then  be  found,  or  its  past 
yield.  But  the  whole  purpose  of  a  yield  table  is  to  predict  the  future 
yields  of  stands.  A  standard  yield  table  gives  a  means  of  predicting 
this  future  yield,  by  indicating  first  the  yield  relation  as  to  density  of 


416  THE  USE  OF  YIELD  TABLES 

the  stand  in  question  with  the  standard  jaelds,  the  second,  the  rate  of 
growth  for  future  decades,  which  can  be  reduced  to  fit  the  existing 
stand. 

318.  Separation  of  the  Factors  of  Volume,  Age  and  Area.  The 
difficulties  surrounding  the  prediction  of  j'ields  lie  in  the  fact  that  this 
requires  for  any  stand  the  determination  of  three  factors:  volume,  which 
can  always  be  measured;  age,  which  can  be  determined  for  a  given  tree 
but  is  difficult  to  find  for  an  entire  stand  of  mixed  ages;  and  area,  which 
can  be  measured,  provided  the  boundaries  of  the  age  class  are  known 
or  defined.  The  trouble  arises  entirely  from  the  mixture  of  trees  of  dif- 
ferent age  classes  on  the  same  area,  the  overlapping  of  crowns  and  root 
spread,  and  the  shifting  of  total  areas  occupied  by  each  separate  age 
class  in  successive  periods  (§  298  and  §  299).  Thus  two  of  the  essential 
factors,  age 'and  area  lose  their  clear  definition.  These  two  factors 
are  interdependent  in  such  forests.  Age  classes  cannot  be  confined 
to  stands  of  a  single  age  but  must  include  an  age  group.  The  area 
occupied  by  such  a  group  will  be  influenced  by  the  numl^er  of  separate 
ages  included  in  the  group. 

It  has  been  shown  previously  in  this  chapter  that  the  area  occupied 
by  a  given  age  class,  when  determined  by  mapping,  determines  the 
relative  density  of  stands  whose  age  is  known.  The  yield  table  expresses 
an  arbitrary  standard  yield  on  1  acre  at  a  given  age,  representing 
100  per  cent  density  at  each  age.  (This  means  that  the  table  is  accepted 
as  standard,  but  does  not  necessarily  represent  the  maximum  yields 
possible  on  an}^  acre,  which  maj^  exceed  this  standard,  by  from  15  to 
20  per  cent.)  When  both  area  and  age  are  determinable  for  a  stand, 
the  exact  relation  as  to  density  or  yield  when  compared  with  the  standard 
can  be  found  for  each  stand  separately.  Wlien  neither  can  be  found 
with  accuracy,  the}'  must  be  found  by  such  means  as  is  possible,  and  the 
results,  while  not  as  accurate,  will  be  serviceable  and  worth  attaining. 
The  general  method  of  solving  this  problem  is  to  work  from  the  known 
to  the  unknown,  accepting  averages  and  approximations  when  exact 
determination  is  impossible. 

319.  Determination  of  Areas  from  Density  Factor.  One  of  the 
simplest  and  most  useful  applications  of  this  principle  is  in  the  deter- 
mination of  the  area  occupied  by  each  of  several  age  classes,  whose 
age  and  volume  are  known  but  wiiich  have  not  been  or  cannot  be  mapped 
separately. 

The  total  area  of  the  tract  can  always  be  determined.  If  for  any 
reason  it  is  impossible  to  map  the  area  of  each  age  class,  these  areas  may 
still  be  found  by  proportion  if  we  arc  willing  to  assume  that  the  average 
density  of  the  entire  stand  can  be  applied  separately  to  each  age  class. 
While  admittedly  less  accurate  than   the  separate   determination   of 


DETERMINATION  OF  AREAS  FROM  DENSITY  FACTOR        41' 


density  by  classes,  yet  the  total  error  is  probably  very  small.     The 
method  is  as  follows: 

The  standard  density,  or  100  per  cent,  as  expressed  in  the  jdeld 
table,  calls  for  a  definite  volume  per  acre,  differing  with  each  age. 

The  total  volume  and  age  of  each  age  class  in  the  forest  are  known. 

By  dividing  this  volume  by  the  standard  volume  on  1  acre  of  the 
required  age  from  the  yield  table,  the  area  which  would  be  required  by 
the  age  class  if  stocked  at  100  per  cent  density  is  found. 

The  sum  of  the  areas  found  in  this  manner  for  all  the  age  classes 
would  be  the  total  area  of  the  forest  if  the  density  of  stocking  were 
100  per  cent. 

Since  the  total  area  actually  stocked  is  known  for  this  sum  or  total 
of  age  classes,  but  not  for  each  age  class  separately',  it  follows  that, 
Actual  per  cent  of  density  for  total  area 


Area  100  per  cent  stocked 
Total  area 


100, 


and,  assuming  this  per  cent  for  each  class, 

...  ,  /  Area  100  per  cent  \ 

Area  m  each  age  class  =  l   ^     ,     ,  •  ,       ) , — r^, r— . 

\stocked  m  age  class/  per  cent  of  density 


100 


ILLUSTRATION 
Second-growth  Hardwoods  in  Central  New  England 


Age. 

Volume. 
Cords 

Yield  of  1  acre  from 
table. 
Cord.s 

Area  of  100  per  cent 

stocked. 

Acres 

20 
30 
40 
50 

1738 
5593 
3854 
1008 

15.80 
29.75 
39.63 
48.00 

Total 

110 

188 
97 
21 

416  acres 

Actual  area  624  acres. 


416 
Density  per  cent  ^77  =  665  which  will  be  assumed  to  apply  to  each  of  the  four 

age  classes  represented. 

To  determine  the  area  in  each  age  class;  ' 

100 
Ratio  to  fully  stocked  area  —  =  1.5. 
66 1 


418 


THE  USE  OF  YIELD  TABLES 


Age  class. 
Years 


Area  100  per  cent 

stocked. 

Acres 


Actual  area  in  age 


Acres 


20 

110 

165 

30 

188 

282 

40 

97 

145.5 

50 

21 

31.5 

Total 

416 

624 

This  method  of  obtaining  the  area  of  separate  age  classes  makes 
possible  the  prediction  of  yields  from  yield  tables  based  on  age  for 
long  periods  with  considerable  accuracy,  where  without  such  separation 
this  would  not  be  possible  and  yields  could  be  predicted  only  for  the 
current  decade  or  two. 

320.  Application  to  Forests  Having  a  Group  Form  of  Age  Classes. 
Forests  composed  of  species  which  are  intolerant  and  fire-resistant 
tend  to  form  groups  of  approximately  even  age.  A  yield  table  based 
on  age  can  be  obtained  for  such  species,  which  will  serve  as  a  100  per 
cent  standard.  But  it  is  very  difficult  to  separate  the  forest  itself  into 
its  component  age  classes  by  mapping  the  areas  which  they  occupy, 
and  equally  difficult  to  determine  in  a  practical  manner  the  average 
actual  age  of  the  stand  on  such  areas  even  if  mapped.  But  the  forest 
can  still  be  separated  into  these  age  classes  based  on  area  and  age, 
permitting  the  application  of  this  yield  table  to  predict  its  growth, 
provided  proper  use  is  made  of  the  laws  of  averages.  (In  timber  estimat- 
ing, it  is  permissible  to  employ  averages  known  to  be  subject  to  error 
because  it  is  not  practicable  to  attain  mathematical  accuracy  on  account 
of  expense.) 

The  problem  here  is, 

1.  To  determine  the  trees  which  belong  to  each  age  class  so  that  the 
volume  of  the  class  may  be  found. 

2.  To  determine  the  age  of  the  age  class. 

3.  To  find  its  area.  Given  the  first  two  of  these  elements,  the 
method  of  finding  the  third  has  already  been  shown  (§319). 

By  reference  to  §  275  it  is  seen  that  diameter  is  an  indicator  of  the 
age  of  trees,  but  that  a  given  age  class  will  include  a  wide  range  of  diam- 
eters. Where  stands  are  composed  of  trees  of  many  different  ages  so 
that  it  is  not  possible  to  ascertain  the  age  of  a  given  stand  by  felling 
one  or  two  trees,  nor  to  map  the  separate  areas  in  the  forest  which  are 
occupied  by  these  age  classes,  the  only  alternative  in  obtaining  age 
is  through  the  use  of  average  diameters.     The  diameters  can  be  meas- 


VOLUME  AND  AREA  FOR  TWO  AGE  GROUPS  419 

ured.  In  timber  estimating,  a  stand  table  can  be  made  giving  the  range 
and  distribution  of  diameters  in  the  stand.  The  substitution  of  diam- 
eters for  ages  thus  furnishes  a  means  of  separating  age  classes  in  forests 
of  mixed  ages. 

Choice  of  Methods.  There  are  tnree  gradations  in  the  possible 
applications  of  this  method. 

1.  Diameter  is  used  merely  to  determmc  the  age  of  an  average  tree, 
but  the  forest  is  separated  into  actual  age  classes  as  nearly  as  possible, 
rather  than  diameter  classes  (§321). 

2.  Diameter  is  used  as  the  basis  of  separation  into  classes,  whose 
average  age  is  then  determined  on  the  basis  of  these  diameters  (§  323). 
These,  as  shown  (§275),  are  not  true  age  classes  since  they  do  not 
include  all  the  trees  of  a  given  age. 

3.  Diameter  is  substituted  altogether  for  age,  and  the  total  age  of 
trees  is  not  determined  for  these  classes,  but  current  growth  is  predicted 
merely  for  trees  of  given  diameters  for  short  periods.  This  method  is 
discussed  in  Chapter  XXXII. 

The  use  of  diameter  to  indicate  total  age  is  most  reliable  when  applied 
to  large  areas  and  numbers  and  to  forests  of  many  age  classes,  for  species 
and  stands  whose  actual  and  economic  age  agree,  i.e.,  which  usually 
do  not  show  a  period  of  suppression. 

321.  Determination  of  Volume  and  Area  for  Two  Age  Groups  on 
Basis  of  Average  Age.  While  the  method  to  be  described  is  limited 
in  its  application  to  two  age  groups,  yet  even  this  subdivision  will  be 
found  of  great  value  in  Mensuration  and  Regulation.  In  the  French 
many-aged  forests,  but  two  groups  are  made  in  timber  above  exploit- 
able size.  In  our  forests,  when  under  management,  the  subdivision 
into  two  groups  will  be  equally  effective. 

In  natural  stands  containing  decadent  timber,  three  groups  are 
needed  instead  of  two,  for  timber  above  the  minimum  diameter.  These 
may  be  termed  "  young  merchantable,"  "  mature  "  and  "  veteran." 

In  the  Western  yellow  pine  stands  for  which  this  method  was 
developed,  it  was  possible  to  separate  the  young  merchantable  timber 
by  the  appearance  of  bark  into  a  class  termed  "  Blackjack,"  leaving 
the  remaining  yellow  pine  timber  for  separation  into  mature  and 
veterans.  In  forests  where  this  cannot  be  done,  it  is  possible  to  first 
separate  the  young  merchantable  timber  on  a  diameter  class  basis, 
leaving  the  larger  mature  and  veteran  timber  for  division  by  this  method. 
^Vhere  the  forest  is  cut  over,  and  but  two  age  classes  are  required, 
the  method  will  separate  the  j'oung  merchantable  from  the  mature 
timber.     The  three  steps  in  this  method  are  as  follows: 

1.  A  standard  yield  table  based  on  age  for  even-aged  stands  can 
be  made  the  basis  of  separation  of  the  forest  into  two  age  groups.     This 


420  THE  USE  OF  YIELD  TABLES 

yield  table  can  be  constructed  by  standard  methods  from  selected  plots 
in  the  groups  of  which  the  forest  is  composed.  From  this  yield  table 
two  ages  are  chosen,  representing  respectively  the  3'ounger  and  the 
older  age  class.  The  development  of  the  normal  stand  as  indicated 
by  its  current  and  its  mean  annual  growth  is  the  basis  for  this  choice 
of  ages. 

2.  The  ages  thus  chosen  from  the  yield  table  must  then  be  correlated 
with  a  given  diameter  since  it  is  impossible,  in  the  forest,  to  determine 
either  the  age  or  area  of  age  classes  directly. 

This  requires  a  table  of  diameter  growth  on  the  basis  of  age,  for  the 
species  and  site  (§  267  to  §  269)  based  on  a  sufficient  number  of  trees 
to  insure  a  reliable  average.  Age  is  the  direct  basis  of  this  curve,  and 
not  diameter  (§  275).  From  this  table,  the  diameter  sought  is  indicated, 
for  each  of  the  two  age  classes. 

3.  The  total  volume  on  the  area  contained  in  the  two  age  classes 
can  be  separated  into  the  volume  in  each  age  class,  by  means  of  these 
two  trees  of  average  diameter,  representing  average  age  of  each  class. 
This  requires: 

(a)  That  the  average  volume  contained  in  a  tree  of  this  average 
diameter  be  found.  For  this  purpose,  a  curve  of  average  height  based  on 
diameter  is  constructed  for  the  site  (§  209).  With  the  height  of  a  tree 
of  the  required  diameter  thus  indicated,  its  volume  is  found  from  the 
standard  volume  table  for  the  species  and  region. 

(b)  That  the  number  of  trees  with  this  average  volume  be  found 
for  each  age  class,  which  is  required  to  make  up  the  total  volume  of  the 
combined  group.  This  number,  multiplied  by  the  average  volume 
will  give  the  volume  of  each  age  class. 

This  solution  is  simple,  when  the  total  number  of  trees  and  their  total  volume 
are  known.  Deducting  a  given  number  of  trees  of  a  given  average  volume  from  the 
group  leaves  a  residual  volume,  which  is  equivalent  to  a  fixed  number  of  trees  of  the 
average  volume  for  the  remaining  group;  i.e.,  with  total  number,  total  volume,  and 
the  average  volume  of  each  tree  of  two  groups  fixed,  there  can  be  but  one  solution  by 
which  the  number  in  each  group,  and  consequently  the  sum  of  their  volumes  equals 
the  required  or  existing  estimate  or  total  in  the  stand.  . 

If  x  =  number  of  trees  in  younger  group; 
y  =  number  of  trees  in  older  group ; 
a  =  volume  of  average  younger  tree; 
6=  volume  of  average  older  tree. 


Then 
and 


a;+?/  =  total  number  of  trees  in  stand,  c 


ax +by  =  total  volume  of  stand,  d. 
If  all  the  trees  c  had  the  volume  a  then  instead  of  a  total  volume  d, 
ax+ay  =  ac. 


APPLICATION  OF  RESULTS  TO  FOREST  421 

The  difference  between  this  volume  and  the  total  actual  stand  is  d—ac  and  repre- 
sents the  surplus  volume  in  the  older  trees,  of  which  there  are  y.     The  difference 
in  vokune  for  each  tree  is  h—a,  and  for  all  of  the  older  trees  is  {b  —  a)y. 
Then 

{b  —  a)y  =  d  —  ac; 
and 

d  —  ac 
h—a  ' 
while 

x  =  c-y. 

Having  the  values,  or  number,  of  each  group  x  and  y,  the  total  volume  is  obtained 
by  multiplying  this  number  by  the  volume  of  the  average  tree  for  the  group. 

Illustration,  Western  Yelloiv  Pine. 

Total  volume  in  group  (d)  =27,042,800 /eet  B.M. 
Total  number  of  trees  (c)  =44,423. 
Age  of  older  trees,  veterans,  chosen  as  300  years. 
Age  of  younger  trees,  mature,  chosen  as  200  years. 
Diameter,  from  curve  of  growth,  veterans,  27  inches. 

mature,  20.7  inches. 
Volume  of  average  tree  of  this  size,  veterans  805  feet  B.M. 
mature,  340  feet  B.M. 
Then 

(1)  340x+80.5;i/ =  27,042,800  feet  B.M. 

(2)  340.c+340y  =  340c. 

=  15,103,820  feet  B.M. 
Subtracting  (2)  from  (1) 

4G5i/  =  11,938,980  feet  B.M. 
?/ =  25,675  trees; 
x  =  18,748  trees. 
Volume  of  younger  class  =  6,374,320  feet  B.M. 
Volume  of  older  class       =20,668,375  feet  B.M. 

322.  Application  of  Results  to  Forest  by  Use  of  Stand  Table  and 
Per  Cent.  It  is  not  necessary  that  a  100  per  cent  tally  of  the  number 
of  trees,  and  total  volume  for  the  .site  be  obtained,  but  only  that  the 
stand  table  (§  188)  from  which  the  determination  is  made  be  representa- 
tive of  the  total  area. 

If  in  the  timber  survey,  5  per  cent  of  the  area  is  covered  and  assumed 
to  represent  the  average  stand,  the  total  count  of  trees  on  this  5  per 
cent  and  the  total  estimate  on  the  strip,  give  the  data  needed.  If, 
in  turn,  but  10  per  cent  of  the  strip  itself  or  i^  of  1  per  cent  of  the  total 
area  is  tallied,  and  this  per  cent  gives  the  run  of  sizes  of  the  timber 
without  reference  to  its  density  of  stocking,  the  data  are  still  sufficient. 

To  obtain  the  separation  of  the  total  stand  by  means  of  the  data 
from  the  smaller  area  counted,  the  volume  of  each  age  class  is  first 
expressed  as  a  per  cent  of  the  total.  These  per  cents  are  then  applied 
to  the  total  estimated  volume  on  the  entire  area. 


422  THE  USE  OF  YIELD  TABLES 

In  the  above  case,  the  per  cents  are: 
Veterans  76.4 
Mature     23 . 6 
The  total  stand  is  2,583,940,000  feet  B.M. 
The  stand  of  veterans  is  then  1,974,130,000  feet  B.M. 
and  of  mature  is  609,810,000  feet.  B.M. 
To  secure  this  division,  a  Uttle  over  1  per  cent  of  the  total  stand  was  tallied  and 
estimated  for  the  basic  data,  while  the  total  estimate  was  secured  by  ocular  means 
(§  206)  (Coconino  National  Forest). 

323.  Determination  of  Volume  and  Area  for  Age  Groups  on  Basis 
of  Diameter  Groups.  Where  the  second  alternative  is  chosen  (Method  2, 
§  320)  to  obtain  the  separation  of  age  classes,  namely,  diameter  rather 
than  age,  the  following  changes  in  procedure  are  necessary. 

1.  The  volume  of  the  so-called  age  classes  is  directly  obtained  from 
a  stand  table,  in  which  the  number  of  trees  of  each  diameter  class  must 
be  shown. 

2.  The  diameter  of  the  average  tree  is  obtained  by  first  finding  the 
average  volume  for  the  group,  and  second,  the  tree  of  this  volume 
from  a  local  volume  table  based  soliely  on  diameter,  which  is  obtained 
from  a  curve  of  average  heights  and  a  standard  volume  table. 

3.  The  age  of  a  tree  of  this  average  diameter  is  then  found,  not 
from  the  yield  table  as  before,  but  from  the  curve  of  growth  based  on 
diameter,  which  gives  directly  the  ages  of  trees  of  given  diameters. 
The  ages  indicated  will  be  those  of  the  respective  age  groups  into  which 
the  forest  has  been  separated.  As  indicated,  this  method  works  back 
from  diameters  to  age,  while  the  first  is  based  on  age  directly. 

By  either  of  these  methods,  the  area  in  each  age  class  may  now  be 
found  by  following  the  procedure  described  in  §  319.  The  age,  and 
consequent  normal  yields  for  1  acre  at  these  ages,  have  been  determined 
for  each  age  class.  The  total  normally  or  100  per  cent  stocked  area 
can  be  found,  and  from  this  the  reduction  per  cent  and  the  area  in  each 
age  class.  From  the  reduction  per  cent  an  empirical  yield  table  can 
be  computed,  which  will  be  used  as  the  basis  for  predicting  the  yields 
of  the  forest  or  site  class  as  a  whole  (§  250). 

Since  the  above-described  methods  of  determining  areas  of  age 
groups  are  based  primarily  on  the  factor  of  relative  density  of  the  stands 
as  determined  by  volume,  they  apply  only  to  the  age  groups  which 
have  already  grown  to  merchantable  sizes.  The  problem  of  determin- 
ing the  area  of  immature  age  classes  is  treated  in  §  348,  and  must  be 
considered  in  working  out  a  plan  for  growth  predictions  for  any  large 
area,  in  connection  with  the  above  methods. 

324.  The  Construction  of  Yield  Tables  Based  on  Crown  Space,  for 
Many-aged  Stands.  The  above  methods  depend  upon  the  construc- 
tion of  yield  tables  from  plots  whose  average  age  is  determined,  so  that 


THE  CONSTRUCTION  OF  YIELD  TABLES  423 

the  yields  are  given  as  for  even-aged  stands.  Since  it  is  seldom  that 
any  species  is  so  distributed  in  age  classes  and  so  free  from  major  sources 
of  damage  as  never  to  be  found  in  stands  of  even  age,  plots  based  on 
age  can  be  obtained  under  a  greater  range  of  conditions  than  is  commonly 
admitted. 

But  when  this  method  is  apparently  impracticable,  there  remains 
one  possibility  for  constructing  a  yield  table  based  on  age,  which  although 
far  from  being  accurate,  is  based  on  a  fundamental  law  of  growth  of 
stands.  It  was  shown  in  §  274  that  as  trees  develop,  they  require 
increased  crown  space,  and  that  this  expansion  of  crown  can  be  attained 
only  by  the  reduction  of  numbers  of  trees  per  acre. 

The  diameters  of  crowns  of  trees  is  an  index  of  the  growing  space 
which  they  require  though  it  seldom  exactly  measures  this  space.  But 
if  it  can  be  shown  that  the  space  occupied  by  trees  of  different  diameters 
is  'proportional  to  the  diameter  of  their  crowns,  the  relative  number 
of  trees  per  acre  of  different  diameters  which  can  stand  on  an  acre 
can  be  determined. 

To  obtain  such  data,  crowns  can  be  assumed  as  circular  in  shape, 
(though  the  actual  shape  varies  according  to  the  light  and  growing 
space  available,  especially  in  hardwoods),  and  that  the  space  occupied 
by  each  crown  is  in  proportion  to  the  square  of  its  diameter  or  width 
in  feet. 

Measurement  of  Width  of  Crowns.  To  determine  the  average  width 
of  crown  for  trees  of  different  diameters,  two  men  may  work  together. 
One  stations  himself  behind  a  plumb-bob  suspended  from  a  pole  so  to 
hang  clear  from  a  height  of  about  8  feet.  He  lines  in  the  second  man 
at  a  point  below  the  outer  edge  of  the  crown  of  the  tree,  whose  width  is 
then  measured  on  the  ground  to  the  point  intersecting  the  opposite 
edge  of  crown.  For  this  purpose  a  pole,  marked  in  feet,  can  be  used. 
The  distance  measured  must  be  at  right  angles  to  the  lines  of  sight.  A 
record  is  made  of  the  D.B.H.  and  crown  width. ^ 

Areas  of  Crowns.  To  obtain  a  true  average  of  crown  area,  each 
crown  width  must  be  squared.  The  sum  of  the  areas  so  obtained  for 
each  diameter  class  is  divided  by  the  nmnber  of  trees  in  the  class,  to 
get  the  average  area  of  the  square  for  that  class.  The  square  root, 
or  side  of  this  square  is  the  average  width  of  the  crown  for  the  class. 
Now,  if  it  be  assumed  that  the  space  occupied  by  this  diameter  squared 
represents  the  actual  growing  space  required  by  the  tree,  the  number 
of  trees  per  acre  for  the  diameter  class  is  found  by  dividing  the  area 

1  No  effort  need  be  made  to  obtain  the  area  of  each  cro^-n  by  two  or  more  measure- 
ments or  by  plotting  the  projected  area  of  the  crown.  Reliance  is  placed  on  a  large 
number  of  measurements  of  one  diameter,  rapidly  and  accurately  taken,  to  obtain 
the  true  average  diameter  of  crowns  for  each  D.B.H.  class. 


424  THE  USE  OF  YIELD  TABLES 

of  one  acre,  43,560  square  feet,  by  this  area.  This  method  is  employed 
in  finding  the  number  of  trees  per  acre  required  to  plant  an  acre,  if 
spacing  is  4,  6,  8  or  10  feet  apart  in  both  directions. 

Density  of  Crown  Cover.  In  actual  stocking,  the  absolute  number 
of  trees  cannot  be  so  simply  determined.  As  crowns  tend  to  adjust 
themselves  to  light,  they  depart  from  a  circular  form,  and  the  circular 
spacing  itself  may  permit  of  more  trees  per  acre  than  the  square.  The 
relation  of  the  area  of  an  inscribed  circle  to  a  square  is  .7854.  That 
of  an  inscribed  circle  to  a  hexagon  is  .9018. 

If  either  of  these  relations  is  consistently  maintained,  the  total 
number  of  trees  per  acre  for  full  crown  cover  may  differ,  but  the  relative 
number,  for  trees  of  different  diameters  will  remain  constant.  From 
the  number  so  found,  a  curve  of  number  of  trees  per  acre  based  on  diam- 
eter can  be  plotted.  This  is  a  standard,  intended  to  show  relative, 
not  absolute,  numbers.  For  instance,  if  the  number  per  acre  from 
such  a  table  for  a  given  diameter  is  400  trees,  a  stand  of  200  trees  per 
acre  of  this  average  diameter  would  be  50  per  cent  of  the  standard. 

Two  factors  interfere  to  prevent  the  satisfactory  application  of  such 
a  table  in  predicting  yields.  First,  the  number  of  trees  in  fully  stocked 
stands  does  not  always  decrease  in  direct  proportion  to  their  increase 
in  crown  space.  In  tolerant  species,  a  great  over-lapping  and  suppres- 
sion of  crowns  occurs,  doubling  the  number  of  trees  per  acre  over  the 
theoretical  number  indicated  by  the  spread  of  crown,  while  in  over- 
mature stands,  the  increasing  demand  for  light  and  moisture  reduces 
the  stand  per  acre  below  that  indicated  by  the  crowns.  The  relation 
is  therefore  not  consistent  except  within  rather  narrow  limits  of  age 
and  species;  and  yields  based  on  this  assumption  will  be  excessively 
large  for  over-mature  age  classes. 

The  second  factor  tends  to  offset  the  first  in  stands  not  fully  stocked — 
this  is  the  tendency  (§301  and  §  316)  to  improve  the  degree  of  stocking 
with  age.  When  a  stand  of  a  given  age  has  only  the  number  of  trees 
required  for  one  twice  this  age,  its  rate  of  mortality  will  be  very  much 
less  since  each  tree  has  more  than  enough  room  to  survive.  Hence 
the  assumption,  in  stands  not  fully  stocked,  that  the  growth  of  a  stand 
can  be  predicted  by  determining  the  per  cent  which  the  number  of 
trees  now  in  the  age  class  bears  to  the  normal  number,  will  not  be 
borne  out,  but  better  results  will  be  obtained. 

Method  of  Construction  of  the  Yield  Table.  In  stands  which 
possess  a  full  crown  cover,  but  whose  age  classes  are  distributed  in 
many-aged  form,  the  rate  of  mortality  may  be  assumed  to  hold  for 
all  classes.  An  illustration  of  the  above  method  of  constructing  a 
yield  table  for  yellow  poplar  in  Tennessee  is  given  below.^ 
1  Based  on  data  collected  by  W.  W.  Ashe. 


METHOD  OF  CONSTRUCTION  OF  THE  YIELD  TABLE 


425 


TABLE  LXIV 
Trees  per  Acre  Based  ox  Crown  Space 


D.B.H. 

Diameter  of  crown. 

Area  of  crown  based  on 

Trees  per  acre. 

Inches 

Feet 

Square  feet 

Number 

7 

11.0 

121 

360 

8 

11.6 

134 

325 

9 

12.4 

154 

283 

10 

13.3 

177 

246 

11 

13.7 

187 

233 

12 

14.4 

207 

210 

13 

15.1 

228 

191 

14 

15.8 

249 

175 

15 

16.5 

272 

160 

16 

17.2 

•       295 

148 

17 

17.9 

320 

136 

18 

18.6 

346 

126 

19 

19.4 

376 

116 

20 

20.0 

400 

109 

21 

20.7 

428 

102 

22 

21.3 

453 

96 

The  above  data  must  now  be  correlated  with  age.  The  steps  are 
as  follows: 

1.  From  a  curve  of  age  based  on  diameter,  the  diameters  at  each 
five-year  period  are  found,  and  the  number  of  trees  per  acre,  formerly 
based  on  diameter,  are  then  interpolated  for  the  fractional  diameters 
corresponding  to  these  exact  ages. 

2.  From  a  curve  of  height  growth  based  on  age  the  height  of  the 
average  tree  is  found. 

3.  From  diameter  and  height,  the  volume  of  each  tree  is  taken 
from  a  standard  volume  table  (§  288). 

4.  The  yield  per  acre  at  each  age  is  the  product  of  the  number  of 
trees  per  acre  and  this  average  volume. 

The  application  of  this  method  is  shown  in  Table  LXV,  p.  426. 

325.  Application  of  Method  to  Many-aged  Stands.  To  apply  this 
standard  ta):)le  to  the  many-aged  forest  for  the  prediction  of  j'ield, 
the  same  principles  are  used  as  were  described  in  §  316.  But  in  this 
case,  the  number  of  trees  in  given  diameter  classes  is  the  basis  of  comparison 
to  determine  the  reduction  per  cent  or  density  factor. 

It  makes  no  material  difference  whether  the  standard  table  above 
illustrated  exactly  represents  the  true  or  actually  possible  normal  yield 
of  a  pure,  even-aged  fully  stocked  stand,  provided  it  approximately 


426 


THE  USE  OF  YIELD  TABLES 


indicates  the  proportional  yields  at  different  ages,  correlated  with  the 
proportional  falling  off  in  numbers  of  trees  per  acre  at  these  ages,  both 
factors  correlated  with  diameter  of  the  average  trees,  for  it  is  evident 
that  in  such  a  forest  no  stands  will  be  found  which  are  pure,  even-aged 
or  fully  stocked  over  any  large  area;  hence  the  use  to  which  the  table 
is  put  must  be  solely  as  a  standard  to  be  discounted  by  a  reduction  per 
cent. 

TABLE  LXV 

Yields  op  Cordwood,  for  Yellow  Poplar  in  Tennessee — Based  on    Crown 
Space  and  Volumes  of  Trees  of  Given  Ages 


Age. 

D.B.H. 

Average 

Volume  * 
in  cords  of 

Trees 

Yield 

Years 

Inches 

Height. 
Feet 

160  cord  feet. 
Cords 

per  acre 

per  acre. 
Long  cords 

40 

10.5 

78 

0.148 

237 

35.1 

45 

11.8 

83 

.198 

214 

42.6 

50 

13.0 

87 

.254 

191 

48.5 

55 

14.2 

91 

.317 

172 

54.5 

60 

15.4 

94 

.381 

155 

59.0 

65 

16.5 

97 

.445 

141 

62.7 

70 

17.5 

101 

.511 

130 

66.4 

75 

18.4 

104 

.569 

121 

68.8 

80 

19.3 

107 

.630 

114 

71.8 

85 

20.2 

110 

.693 

108 

74.8 

90 

21.0 

113 

.755 

102 

77.0 

95 

21.8 

115 

.825 

97 

80.0 

100 

22.5 

117 

.880 

94 

82.7 

*rrom  volume  table  5,  p.  22,  Bulletin  106,  Yellow  Poplar  in  Tennessee,  W.  W.  Ashe,  State 
Geological  Survey  of  Tennessee,  1913. 

The  age  of  stands,  by  this  method,  is  assumed  as  the  age  of  trees 
of  given  diameters.  To  determine  this  age,  for  each  diameter  class, 
a  curve  of  growth  is  required  in  which  ages  are  averaged  on  the  basis 
of  diameter  (§  276).  Otherwise  the  ages  of  trees  of  the  larger  classes 
will  be  over-estimated. 

To  apply  this  yield  table  for  the  prediction  of  yield  in  the  forest, 
a  large  area  must  be  considered;  otherwise  the  assumed  correlation 
between  age  and  diameter  will  not  hold  good.  The  stand  table  (§  188) 
for  this  area  must  show  the  number  of  trees  of  each  diameter  class  in 
the  forest. 

One  of  the  principal  services  rendered  by  such  a  table  is  its  indication 
of  the  probable  rate  of  loss  of  numbers,  which  is  a  most  difficult  problem 
to  solve  by  any  other  method. 


YIELD  TABLES  FOR  STANDS  GROWN  UNDER  MANAGEMENT    427 

In  applying  such  a  table,  it  can  be  assumed  that  the  mortalit^^  in 
the  forest  will  be  at  the  proportional  rate  indicated  by  the  table.  The 
prediction  of  yields  will  then  be  based  on  a  stand  table  giving  the  number 
of  trees  in  each  diameter  class.  Several  methods  of  applying  the 
standard  table  are  possible,  as 

1.  Base  the  prediction  upon  the  total  number  of  trees  in  each  diam- 
eter class  or  group.  The  per  cent  of  reduction  in  numbers  is  obtained 
from  the  table.  This  per  cent  is  applied  to  the  stand  in  the  forest, 
and  the  future  growth  obtained  by  computing  the  future  volume  of 
the  remaining  trees,  as  shown  in  the  illustration. 

2,  Base  the  prediction  upon  yields.  The  number  of  trees  in  each 
diameter  class  is  divided  by  the  number  per  acre  in  the  standard  table. 
This  gives  the  area  normally  stocked  by  that  class,  from  which  its  future 
yield  is  taken  directly  from  the  standard  yield  table.  This  area  forms, 
of  course,  but  a  small  per  cent  of  the  forest,  and  is  the  total  area  occupied 
by  trees  of  the  diameter  class. 

The  forest  can  be  divided  into  age  classes,  based  on  diameter,  and 
the  area  occupied  by  each  of  these  age  classes  obtained  as  described 
in  §  316. 

At  best,  it  can  be  seen  that  this  substitution  of  standard  yields 
based  on  growing  space  per  tree  is  a  makeshift  compared  with  determin- 
ing these  relations  from  even-aged  plots  in  which  the  factors  of  site, 
tolerance  and  soil  at  different  ages  are  directly  measured. 

326.  Yield  Tables  for  Stands  Grown  under  Management.  European 
experience  with  stands  grown  under  management  has  shown,  first, 
that  the  best  results  and  heaviest  total  yields  per  acre  are  obtained 
by  several  thinnings  at  frequent  intervals,  in  which  not  only  the  trees 
which  would  otherwise  die  before  the  next  cutting  are  removed,  but  the 
remaining  crowns  are  freed  from  competition. 

Second,  that  the  proportion  of  the  total  yield  removed  as  thinnings 
under  this  system  may  equal  one-third  or  more  of  the  total  yield. 

Third,  that  the  diameter  growth  of  the  surviving  trees  can  by  proper 
thinnings  be  sustained  at  a  uniform  rate  until  the  final  crop  is  cut. 
The  development  of  each  tree  in  the  stand  proceeds  actually  at  the  rate 
of  growth  of  a  dominant  tree  which  maintains  its  crown  spread  through- 
out its  life. 

Even  where  second-growth  stands  have  sprung  up,  in  this  country, 
and  reached  sizes  suitable  for  logging,  they  have  usually  received  no 
care  in  the  form  of  thinnings.  Stagnation  sets  in  on  many  of  these 
stands,  especially  with  conifers  on  old  fields,  and  the  diameter 
growth  of  the  whole  stand  suffers.  This  occurs  even  in  plantations 
on  which  thinnings  have  been  neglected. 

The  actual  yields  and  sizes  which  may  be  grown  on  such  stands 


428  THE  USE  OF  YIELD  TABLES 

under  sustained  management  and  thinnings  may  be  roughly  approxi- 
mated by  measurements  taken  on  natural  stands  not  under  management, 
by  the  method  just  discussed,  of  computing  the  number  of  trees  per  acre 
for  given  diameters.  The  rate  of  diameter  growth  should  be  that  of 
trees  now  dominant  in  the  stand.  This  gives  the  age  of  the  diameter 
classes.  The  approximate  amount  of  material  yielded  by  thinnings  in 
such  a  forest  may  also  be  roughly  predicted  by  noting  the  number  of 
trees  which  drop  out  of  the  stand  at  each  decade,  and  computing  their 
average  diameter  and  volume. 

By  establishing  permanent  plots,  re-measured  at  intervals  of  5 
or  10  years,  and  properly  thinned,  data  will  finally  become  available 
showing  not  merely  the  yield  of  stands  grown  under  management,  at 
final  cutting,  but  the  total  yield  including  thinnings.  The  absence 
of  such  stands  precludes  the  construction  of  yield  tables  on  this  basis 
at  present  and  justifies  efforts  to  predict  such  yields  by  means  of  crown 
spread  and  number  of  trees  per  acre  in  normal  stands.  The  nearest 
approach  to  such  yield  tables  is  found  in  tables  constructed  from  second- 
growth  stands,  or  plantations,  but  it  is  seldom  that  these  stands  have 
been  repeatedly  and  properly  thinned,  hence  the  yields  shown  merely 
indicate  a  normal  possibility  for  fully  stocked,  wild  stands. 

References 

The  Measurement  of  Increment  on  All-aged  Stands,  H.  H.  Chapman,  Proc.  Soc. 

Am.  Foresters,  Vol.  IX,  1914,  p.  189. 
Yield  Table  Methods  of  Arizona  and  New  Mexico,  T.  S.  Woolsey,  Jr.,  Proc.  Soc.  Am. 

Foresters,  Vol.  IX,  1914,  p.  207. 
Yield  in  Uneven-aged  Stands,  Barrtngton  Moore,  Proc.  Soc.  Am.  Foresters,  Vol. 

IX,  1914,  p.  216. 


CHAPTER  XXX 
THE  DETERMINATION  OF  GROWTH  PER  CENT 

327.  Definition  of  Growth  per  Cent.  Growth  per  cent  is  an  expres- 
sion of  the  relation  between  growth  and  volume. 

Current  growth  per  cent  is  the  relation  of  growth  during  a  given 
year  to  the  volume  at  the  beginning  of  the  year. 

Periodic  growth  per  cent  is  the  relation  of  the  growth  during  a  period, 
to  a  basic  volume,  which  may  be  taken  as  the  mean  or  average  volume 
for  the  period  (§  328),  but  is  usually  that  at  the  beginning  of  the  period. 

Mean  annual  growth  per  cent  is  the  per  cent  which  the  mean  annual 
growth  (§  245)  for  a  given  age  bears  to  the  total  volume  at  that  age, 
and  represents  the  average  rate  of  growth  per  year,  at  which  this  volume 
has  been  produced.  Growth  per  cent  requires  for  its  determination 
a  knowledge  of  two  factors,  the  growth  for  a  period  and  the  volume 
upon  which  this  growth  was  laid.  The  primary  purpose  for  which 
growth  per  cent  is  utilized  is  to  test  the  maturity  or  ripeness  of  individual 
trees  and  of  stands  of  timber.  Those  trees  or  stands  which  show  the 
lowest  per  cent  of  increment  on  their  present  volume  compared  with 
other  trees  or  stands,  should  be  selected  for  cutting.  The  object  of 
such  selection  is  to  withdraw  from  the  forest  the  greatest  possible  volume 
of  wood  capital,  while  at  the  same  time  reducing  the  volume  of  expected 
growth  by  the  smallest  possible  amount.  If  carried  out,  the  effect  is 
to  transform  the  forest  capital  from  a  condition  in  which  the  ratio  of 
growth  to  volume  is  low,  to  one  in  which  this  ratio  is  materially  increased 
for  the  forest  as  a  whole. 

On  individual  trees  the  difference  in  volume  or  growth  for  the  decade 
may  be  found  by  analysis  (§  287  and  §  288).  For  stands,  the  difference 
is  taken  from  yield  tables  for  the  decade.  In  each  case  one  year's 
growth  is  one-tenth  of  the  growth  for  a  decade.  The  growth  per  cent 
of  average  test  trees  is  frecjuently  assumed  to  be  that  of  the  stand. 

328.  Pressler's  Formula  for  Volume  Growth  Per  Cent.  To  deter-' 
mine  growth  per  cent  as  a  means  of  judging  the  ripeness  or  maturity 
of  stands  or  trees,  the  same  methods  apply  whether  the  unit  is  the  tree 
or  the  stand.  Since  volume  growth  is  measured  for  periods  of  a  decade, 
the  growth  for  one  3'ear  is  found  by  division.  Let  n  equal  the  period 
representing  a  decade.    This  may  be  a  longer  or  shorter  period  if  neces- 

429 


430  THE  DETERMINATION  OF  GROWTH  PER  CENT 

sary.     Let  V  ofiiuil  volume  at  present,  and  v  equal  volume  n  years  ago. 

V  —  V 

Then  growth  for  one  year  equals  .     If  it  is  assumed   that  this 

n 

growth  for  n  years  is  laid  on  in  equal  annual  installments,  then  the  growth 

so  obtained  is  considered  that  of  the  current  year  or  for  any  year  during 

the  period. 

If  the  growth  per  cent  is  obtained  on  this  basis,  the  result  will  vary 

according  to  the  year  in  which  the  volume  of  the  stand  is  taken  as  the 

basis.     If  for  ten  years  ago,  then  the  formula  is. 

Growth  per  cent=  (^^)  100. 

\    vn  / 

But  if  the  per  cent  is  desired  for  the  last  or  present  year, 

Growth  per  cent  =  (  -^ — )  100. 
\  Vn  I 

For  an  average  year  midway  of  the  period,  the  capital  or  volume  is 

2    ' 
and  growth  per  cent  is 

Y-n 


100 


Y-v\  200 


F+  V  \F+ 

2 

This  is  known  as  Pressler's  formula. 

329.  Pressler's  Formula  Based  on  Relative  Diameter.  Further  modifications 
of  this  formula  by  Pressler  are  intended  to  reduce  it  to  terms  of  diameter  so  that  it 
may  be  applied  to  measurements  on  standing  trees  taken  at  B.H.  If  height  and  form 
factor  do  not  change,  then 

_  /D^-dA  200 

^~VD2+dV  ~' 

In  this  formula  D  is  the  present  D.B.H.  and  d  is  the  diameter  n  years  ago.     D—d 

is  then  designated  as  a  and  —  is  called  the  relative  diameter.     By  making  —  =  g, 
a  a 

and  substituting  aq  for  D,  and  o{q  —  l)  for  d,  he  reduced  the  formula  thus  to 

■(g-l)A200 


g2+(g-l)2/ 


for  which  expressions  values  are  computed  in  a  table. 

To  use  this  table  the  present  diameter  D  is  divided  by  twice  the  width  of  the 
rings  in  the  period  7i,  thus  indicating  the  relative  diameter.  The  values  in  the  table 
give  the  per  cent  of  volume  growth  for  the  period.  This  is  then  divided  by  the  num- 
ber of  years  in  the  period  to  get  the  current  annual  growth  per  cent.i 

1  This  table  is  given  in  Principles  of  American  Forestry,  Samuel  B,  Green,  John 
Wiley  &  Sons,  N.  Y.,  1903,  p.  178. 


SCHNEIDER'S  FORMULA  FOR  STANDING  TREES  431 

Further  modifications  of  this  formula  are  discussed  in  Graves'  Mensuration,  pp. 
306-7. 

330.  Schneider's  Formula  for  Standing  Trees.  The  most  con- 
venient formula  for  testing  the  growth  per  cent  of  standing  trees  is 
known  as  Schneider's  formula,  developed  in  1853  by  Professor  Schneider, 
Eberswalde.  This  formula  is  applied  at  B.H.  and  requires  the  deter- 
mination of  diameter,  D,  at  that  point,  and  the  number  of  rings  in  the 
last  inch  of  radius,  n.     Then 

400 

The  following  description  of  the  derivation  of  the  formula  is  taken  from  Graves' 
Mensuration,  p.  308. 

If  n  represents  the  number  of  rings  in  the  last  inch  of  radius  at  breast-height, 

then  the  periodic  annual  growth  during  n  years  is  -  inches.     Let  the  present  diameter 

n 

2 

be  represented  by  D,  then  the  diameter  last  year  was  D and  the  diameter  at  the 

n 

2 
end  of  one  year  from  now  will  be  D-[-—. 

n 

The  present  volume  of  the  tree  is ,  that  of  one  year  ago  was 

The  growth  for  the  last  year  is  then 

4         4  V        n/    •'        4   \  n       n^ 

-hf/4:D      4  \ 
4  4    \  71       nV 

400      400 

2  2 

If  the  growth  be  calculated  on  the  basis  of  d+-  instead  of  d — ,  then  the  follow- 

n  n 

ing  formula  will  result: 

400      400 

The  average  between  the  two  formula  is  taken,  namely, 
400 


Inasmuch  as  Schneider's  formula  assumes  that  there  is  no  change 
in  height  and  nor  change  in  form  factor,  the  results  are  very  conservative. 


The  growth  per  cent  is: 

irD^hf     irhfUD       4 


432  THE  DETERMINATION  OF  GROWTH  PER  CENT 

An  attempt  has  been  made  to  adapt  the  formula  to  rapid-growing 
trees  by  substituting  other  values  for  400,  but  the  resulting  formulse 
have  little  practical  value. 

331.  Use  of  Growth  Per  Cent  to  Predict  Growth  of  Stands.  Growth 
per  cent  is  sometimes  used  to  determine  the  growth  of  trees  or  stands, 
by  both  the  standard  methods,  that  of  prediction,  and  of  comparison. 
It  is  not  well  adapted  to  secure  accurate  results  by  either  method. 
Owing  principally  to  the  variability  of  the  per  cent  relation,  and  its 
direct  dependence  on  and  derivation  from  the  two  factors,  volume  and 
increment,  the  problem  of  reversing  this  process  and  deriving  increment 
from  growth  per  cent  is  apt  to  lead  to  error  through  a  mistake  either  in 
choosing  the  basis  of  volume  for  deriving  the  per  cent  figure,  or  in 
applying  this  figure  in  turn  to  the  wrong  volume  basis. 

The  method  of  prediction  of  growth  by  means  of  growth  per  cent 
consists  of  determining  this  per  cent  for  a  stand,  either  from  sample 
trees  (§  241)  or  by  direct  use  of  yield  tables  or  other  methods  of  measur- 
ing the  past  growth  for  a  decade. 

Schiffel  states,  "  If  in  any  period  of  life  the  current  annual  incre- 
ment per  cent  of  a  tree  is  to  be  calculated,  it  would  be  contrary  to  nature 
and  incorrect  to  relate  the  increment  to  any  former  dimensions  or 
volume,  but  it  must  be  related  to  the  dimensions  or  volume  of  the  previ- 
ous year." 

The  formula,  growth  per  cent  =(-77-1 — ) —     when    n=10   years, 

XV  -\-v/   n 

bases  growth  per  cent  on  volume  five  years  ago,  and  is  correct  as  an 

average  per  cent  of  the  past  ten-year  period.     If  applied  to  the  next 

decade,  and  based  on  V,  or  present  volume,  it  assumes  an  increase  in 

growth  for  this  period.     When  this  per  cent  is  applied  only  to  the  current 

year,  and  is  based  on  V  the  per  cent  is  more  conservative. 

While  individual  trees  are  growing  rapidly  in  diameter,  as  dominant 

trees,  their  growth  per  cent  for  a  time  falls  less  rapidly  than  that  of 

slower-growing  trees.     In  even-aged  stands,  growth  on  individual  trees 

is  proportional  to  their  diameters.     Growth  per  cent  in  area  is  about 

twice  the  per  cent  of  diameter  growth.     If  determined  for  the  trees 

which  will  be  retained  under  management,  this  relation  of  growth  to 

volume  may  be  fairly  consistent  in  such  even-aged,  thinned  stands. 

Hence  sample  or  average  trees  may  give  a  close  indication  of  the  growth 

per  cent  or  present  status  of  the  stand.     But  the  assumption  that  this 

growth  -per  cent  will  continue  to  be  laid  on  annually  breaks  down  at 

once;    hence  the  real  assumption  and  the  only  one  possible,  if  growth 

per  cent  is  to  be  applied  for  predictions,  is  that  the  volume  indicated 

by  this  per  cent  will  continue  to  be  laid  on  annually.     And  this  in  turn 

is  inaccurate. 


GROWTH  PER  CENT  TO  DETERMINE  GROWTH  OF  STANDS      433 

The  sources  of  inaccuracy  in  this  method  are: 

1.  Predicting  the  volume  growth  of  a  stand  from  that  of  one  or  two 
selected  or  average  trees.  The  growth  per  cent  of  a  stand  is  practically 
always  less  than  that  of  the  average  trees  which  survive,  due  to  loss 
of  numbers  and  falling  growth  rate  of  the  suppressed  class. 

2.  Applying  a  growth  per  cent  obtained  from  a  past  period  on  a 
smaller  volume,  to  the  present  volume  of  tree  or  stand,  under  the  assump- 
tion that  not  only  will  the  rate  of  growth  in  volume  continue  the  same 
but  the  per  cent  will  remain  unchanged,  when,  as  shown,  growth  per 
cents  always  fall  as  wood  capital  increases. 

3.  Assuming  that  the  growth  per  cent  as  derived  from  average 
trees,  or  even  from  sample  plots,  will  apply  to  larger  areas  and  to  dif- 
ferent proportions  of  age  classes  in  mixture,  when  in  fact,  so  doubly 
sensitive  is  this  per  cent  relation,  that  any  difference  in  average  age 
and  volume  between  the  forest  and  the  sample  areas  will  result  in  a 
large  error  in  determining  the  true  weighted  per  cent  by  this  means. 

The  possible  errors  may  be  illustrated  as  follows : 

From  a  yield  table  for  White  Pine  '  the  actual  known  yields  are, 

At  30  years 3750  cubic  feet 

40  years 6590  cubic  feet 

50  years 8035  cubic  feet 

60  years 9075  cubic  feet 

By  Pressler's  formula,  the  current  annual  growth  per  cent  for  these  decades  is, 

30  to  40  years 5 . 5  per  cent 

40  to  50  years 2 . 0  per  cent 

50  to  60  years 1 . 2  per  cent 

If  the  growth  for  the  decade  from  thirty  to  forty  years  be  taken  to  indicate  the 
current  growth  in  the  fortieth  year,  of  284  board  feet,  this  gives  a  current  growth  per 
cent  for  that  year  on  6590  board  feet,  of  4 . 3  per  cent.  Assuming  that  this  growth 
per  cent  will  continue  for  the  next  decade,  we  have  a  total  increase  of  43  per  cent  or 
2834  board  feet.     The  actual  growth  is  1445  board  feet.     The  error  is  96  per  cent 


Such  errors  are  the  result  of  use  of  the  growth  per  cent,  even  when  the  basic 
data  are  correct.  The  errors  may  be  greatly  increased  when  growth  per  cent  is 
obtained  from  single  trees  and  the  losses  in  the  stand  are  ignored,  since  too  high  a 
current  growth  per  cent  will  be  obtained. 

332.  Use  of  Growth  Per  Cent  to  Determine  Growth  of  Stands  by 
Comparison  with  Measured  Plots.  The  only  merit  which  growth  per 
cent  has  as  a  method  of  determining  growth  lies  in  the  possibility  of 
using  it  as  a  means  of  comparison.     Since  per  cent  does  not  express 

1  Forest  Mensuration  of  the  White  Pine  in  Mass.,  H.  O.  Cook,  Office  of  State 
Forester,  1908,  p.  21. 


434  THE  DETERMINATION  OF  GROWTH  PER  CENT 

absolute  quantity  but  a  relation,  the  assumption  is  that  this  relation 
once  established  for  a  given  stand  will  apply  to  other  stands  of  a  similar 
character  but  differing  in  area  and  total  volume.  Growth  per  cent 
on  sample  plots  could  for  instance  be  applied  to  determine  the  annual 
growth  on  the  stand  within  which  they  are  located. 

In  so  far  as  it  can  be  known  that  the  relation  between  the  volume 
of  the  larger  area  and  the  growth  on  this  area  is  the  same  as  on  the  stand 
sampled,  the  method  is  obviously  correct.  The  error  lies  in  applying 
such  growth  per  cent  figures  to  stands  or  areas  on  which  this  relation 
is  not  the  same,  because  the  average  age,  thrift,  or  other  conditions, 
differ  from  the  sample  area.  The  simplicity  of  assuming  that  growth 
per  cent  for  a  sample  tree,  or  for  a  sample  plot,  can  be  applied  to  large 
areas  has  led  to  its  use  as  a  substitute  for  sound  growth  data  in  many 
instances.  No  such  short  cut  will  actually  measure  the  growth  on  a 
forest  comprising  many  stands  of  different  ages,  site  quahties,  and 
densities  of  stocking. 

333.  Use  of  Growth  Per  Cent  in  Forests  Composed  of  All  Age 
Classes.  Growth  per  cent  is  a  direct  expression  of  current  growth  in 
its  relation  to  past  or  total  volume.  Hence  it  varies  with  the  current 
growth  curve.  Current  growth  per  cent  is  equal  to  mean  annual 
growth  per  cent  in  the  year  in  which  the  mean  annual  growth  culmi- 
nates  (§  245). 

In  a  forest  composed  of  stands  of  all  ages,  or  in  a  stand  composed 
of  trees  of  all  ages,  equally  proportioned  as  to  area  or  ultimate  yield, 
and  under  management,  the  current  growth  per  cent  for  the  whole 
forest  or  the  whole  stand,  when  weighted  by  volume  of  each  age  or  tree 
class,  will  be  equal  to  the  mean  annual  growth  per  cent  for  every  year, 
since  there  is  no  change  from  year  to  year  in  either  of  the  two  factors, 
total  volume  or  increment,  which  determine  it. 

For  such  a  forest  the  average  growth  per  cent  can  be  found  separately 
for  each  diameter  class.  By  weighting  each  per  cent  according  to  the 
volume  of  the  trees  in  this  class  for  the  stand,  a  composite  per  cent  is 
obtained  which  shows  the  present  status  of  the  forest,  and  is  applicable 
in  predicting  its  growth.  But  accurately  to  determine  this  per  cent, 
the  growth  itself  must  first  be  found  on  the  trees  or  plots  measured. 
If  in  determining  this  growth,  the  future  factors  are  really  considered, 
the  numbers  reduced,  and  the  rate  of  diameter  growth  and  probable 
suppression  taken  into  account,  the  result  is  a  quantitative  statement 
of  growth  for  the  next  decade  or  two  instead  of  for  the  past  decade. 
This  prediction  of  growth,  on  a  few  acres  or  a  small  per  cent  of  the  stand, 
can  then  be  reduced  to  the  form  of  a  per  cent  of  present  volume,  and 
applied,  in  this  form,  to  the  remaining  stand  as  a  convenient  means  of 
computing  growth  on  the  total  area, 


GROWTH  PER  CENT  IN  QUALITY  AND  VALUE  435 

334.  Growth  Per  Cent  in  Quality  and  Value.  Growth  in  money 
value  of  a  stand  is  treated  in  Forest  Valuation. ^  This  depends  upon 
the  three  factors  mentioned  in  §  244,  namely,  increase  in  volume,  in 
quality,  and  in  unit  price  independent  of  the  other  two  factors.  The 
growth  in  quality  differs  from  that  in  volume,  since  it  tends  in  a  measure 
to  raise  the  value  of  the  previous  growth,  especially  when  this  increased 
quality  is  due  to  increased  dimensions.  Per  cent  increase  in  value  is 
usually  computed  as  an  annual  per  cent  found  by  dividing  the  periodic 
per  cent  by  the  years  in  the  period,  and  is  applied  to  the  volume  at 
the  beginning  of  the  period,  thus  showing  simple  interest  on  the  initial 
value.  When  thus  expressed,  the  per  cent  of  increase  is  made  up  of 
the  sum  of  the  per  cents  due  to  each  of  the  three  separate  factors. 
For  young  and  immature  timber,  growth  per  cent  in  volume  forms  the 
chief  element  of  increase,  but  as  the  trees  reach  maturity  this  diminishes, 
and  is  greatly  exceeded  by  per  cent  increase  in  price  due  to  quality,  and 
to  unit  prices — so  that  the  per  cent  of  increment  in  value  may  con- 
tinue for  a  much  longer  time  than  that  of  volume. 

The  growth  in  quality  of  a  stand  can  be  measured  by  the  use  of 
graded  log  tables  (§74)  or  graded  volume  tables  (§165)  provided  it 
is  carefully  ascertained  that  these  tables  apply  to  the  trees  in  the  stands 
to  be  measured,  at  the  successive  ages. 

References 

A  Practical  Application  of  Presslcr's  Formula,  A.  B.  Recknagel,  Forestry  Quarterly, 

Vol.  XIV,  1916,  p.  260. 
Table  for  Determining  Financial  Increment  Per  Cent  for  Trees  Based  on  their 

Market  Values,  Erling  Overland,  Translated  by  Nils  B.  Eckbo,  Forestry  Quar- 
terly, Vol.  V,  1907,  p.  36. 
Increment  Per  Cent,  Schiffel,  Centralblatt  f.  g.  d.   Forstwesen,  Jan.,   1910,  p.  6. 

Review,  Forestry  Quarterly,  Vol.  VIII,  1910,  p.  377. 
Hilfstafel  zur  Zuwachserhebung,  Forstwissenschaftliches  Centralblatt,    Apr.,  1911, 

p.  200.     Review,  Forestry  Quarterly,  Vol.  IX,  1911,  p.  321. 
Relative  Increment  of  Tree  Classes,  Review,  Forestry  Quarterly,  Vol.  IX,  1911,  p. 

633. 
Zuwachsuntersuchungen   an    Tannen,    Allgemeine   Forst-   und   Jagdzeitung,    Sept. 

1907,  p.  305.     Review,  Forestry  Quarterly,  Vol.  V,  1907,  p.  431. 
Ueber  Zuwachsprocent,  Centralblatt  f.  d.  g.  Forstwesen,  Jan.,  1910,  p.  6.     Review, 

Forestry  Quarterly,  Vol.  VIII,  1910,  p.  377. 

»  Forest  Valuation,  H.  H.  Chapman.     John  Wiley  &  Sons,  N.  Y.,  1915. 


CHAPTER  XXXI 

METHODS    OF    MEASURING    AND    PREDICTING    THE 
CURRENT   OR  PERIODIC  GROWTH  OF  STANDS 

335.  Use  of  Yield  Tables  in  Prediction  of  Current  Growth.  The 
current  growth  of  stands  for  short  periods  can  always  be  predicted 
with  greater  accuracy  than  for  long  periods.  Not  only  can  the  present 
condition  of  the  stand  be  gaged,  as  to  species,  numbers,  crown  density, 
form,  thrift  and  rate  of  growth  in  immediate  past,  and  this  information 
applied  in  predicting  the  rate  at  which  growth  will  continue,  but  the 
inevitable  changes,  some  of  them  unforeseen,  which  will  occur  in  the 
future  to  modify  this  rate  of  growth,  take  place  at  a  rate  which  bears 
a  close  relation  to  the  length  of  the  period  of  prediction. 

Only  when  the  net  results  of  all  the  various  factors  which  produce 
yields  have  been  measured  on  stands  after  they  have  passed  through 
the  period  is  an  approximate  degree  of  accuracy  obtained  for  long  periods, 
hence  the  use  of  yield  tables  based  on  age.  It  follows  that  for  the  pre- 
diction of  current  growth  for  short  periods  on  existing  stands,  the  net 
current  growth  shown  by  the  above  yield  tables,  reduced  on  the  basis 
of  age  and  relative  density  to  apply  to  the  stand  in  question,  is  the 
best  basis  of  growth  prediction  even  for  these  short  periods. 

336.  Method  of  Prediction  Based  on  Growth  of  Trees,  with  Cor- 
rections for  Losses.  In  endeavoring  to  use  these  yield  tables  for 
stands  which  differ  greatly  from  the  normal  in  number  of  trees  per  acre, 
density  of  crown  cover,  form  or  distribution  of  age  classes,  and  com- 
position of  species,  it  is  often  difficult  to  find  or  make  a  table  which  will 
apply  to  the  stand  even  when  corrected  for  density.  In  such  cases, 
a  direct  measurement  of  the  stand  may  be  resorted  to  instead  of  a  com- 
parison with  a  standard  yield.  The  growth  of  any  stand  of  whatever 
character,  for  the  next  decade,  will  be  the  sum  of  the  growth  in  volume 
of  the  trees  which  survive  till  the  end  of  this  period  minus  the  loss  of 
the  total  volume  of  the  trees  which  do  not  survive  (§  252).  The  elements 
which  give  stability  to  this  method  are  a  knowledge  of  the  exact  pres- 
ent number  and  diameter  of  the  trees  in  the  stand,  which  may  be 
supplemented  by  a  classification  of  crowns  to  indicate  those  now  domi- 
nant, intermediate  or  already  suppressed,  and  by  a  tabulation  of  past 
growth  in  diameter,  by  diameter  classes  (§278).     The   elements   of 


PREDICTION  BASED  ON  GROWTH  OF  TREES  437 

uncertainty  are  probable  loss  of  numbers  in  the  next  period,  and  future 
rate  of  diameter,  height  and  volume  growth  of  the  survivors.  At  best, 
owing  to  the  great  difficulty  of  predicting  for  a  given  stand  the  loss  in 
numbers  and  the  rate  at  which  diameter  growth  will  be  maintained, 
for  long  future  periods,  the  method  can  be  used  only  for  periods  of 
ten  to  twenty  years,  except  for  slow-growing  or  long-lived  species  where 
the  factors  of  change  are  slowed  down  correspondingly. 

To  apply  this  method  of  predicting  tree  growth  to  obtain  current 
growth  of  stands,  the  steps  are, 

1.  Prepare  a  stand  table  of  the  forest  or  area  (§  188). 

2.  As  an  aid  in  determining  mortality,  tally  or  estimate  the  number 
or  per  cent  of  each  diameter  class  which  is  suppressed  or  will  probably 
die  within  ten  or  twenty  years. 

3.  Decide  upon  the  method  to  be  applied  in  predicting  diameter 
growth  (§  278  and  §  279)  and  prepare  table  of  growth  by  diameter 
classes  to  conform  to  the  requirements  of  the  method. 

4.  Obtain  data  and  construct  a  curve  of  average  height  growth 
(§  248),  which  will  probably  be  best  expressed  as  current  height  growth 
based  on  height,  for  the  last  decade  or  two. 

5.  Obtain  volume  tables  giving  the  volume  of  trees  of  each  diameter 
and  average  height.  A  standard  volume  table  classified  by  heights  is 
needed  for  best  results. 

6.  From  present  number  of  trees  in  each  diameter  class,  deduct 
the  per  cent  or  number  which  will  probably  die  within  the  period. 

7.  Compute  the  average  diameter  which  surviving  trees  of  each 
diameter  class  will  attain  at  end  of  period. 

8.  Compute  the  increase  in  height  for  each  diameter  class.  (The 
false  method  described  in  §  285  is  frequently  used  as  a  substitute  for 
a  curve  of  height  growth.) 

9.  The  volume  of  the  present  stand  is  calculated  from  the  stand 
table  and  volume  table. 

10.  The  volume  of  the  surviving  stand  at  end  of  period  is  obtained 
from  the  future  diameter  and  height  of  the  surviving  trees  of  each  diam- 
eter class,  and  volumes  taken  from  the  standard  volume  table. 

11.  The  difference  in  volume  thus  found  is  the  net  growth  for 
the  period,  in  stands  which  have  not  been  thinned  and  in  which  no 
salvage  of  dying  or  dead  timber  is  possible.  The  volume- of  the  trees 
which  die  is  thus  deducted  from  the  growth  on  the  survivors,  and 
only  the  net  growth  is  represented  in  increased  volume  of  the  stand. 

In  stands  which  are  thinned,  this  prospective  loss  in  numbers  is 
not  lost  nor  deducted,  but  is  expressed  in  the  form  of  thinnings.  Where 
thinnings  are  marked  and  will  be  made  in  such  stands,  they  will  com- 
monly include  more  trees  than  will  actually  die  during  the  period, 


438  CURRENT  OR  PERIODIC  GROWTH  OF  STANDS 

since  the  suppression  of  diameter  growth  is  to  be  avoided,  and  this  begins 
considerably  in  advance  of  the  death  of  the  tree  and  may  affect  the 
entire  stand  if  too  crowded. 

By  this  method,  neither  a  full  volume  analysis  of  current  growth 
of  trees  is  needed  on  the  one  hand,  nor  a  yield  table  based  on  area  and 
age  on  the  other.  Nor  is  it  necessaiy  to  compute  the  average  tree  of 
the  stand,  and  by  predicting  the  growth  of  this  tree  for  the  next  decade, 
seek  to  determine  that  of  the  stand  (§  275)  since  all  the  trees  in  the  stand 
are  given  their  proper  weight  in  predicting  growth.  Only  for  very 
regular  stands  can  average  trees  be  used  safely,  and  for  such  stands 
yield  tables  are  better. 

337.  Increased  Growth  of  Stands  after  Cutting.  The  method  of 
predicting  diameter  and  volume  growth  of  trees  after  release  by  cutting 
is  shown  in  §  280.  The  problem  of  predicting  growth  of  stands  left 
on  cut-over  lands  is  one  of  properly  combining  the  growth  data  for  the 
different  classes  of  trees  left  on  the  area. 

That  diameter  growth  of  individual  trees  should  increase  when 
their  crowns  and  roots  are  given  increased  growing  space  is  a  natural 
law  of  growth  of  stands.  The  question  is,  "  What  is  the  total  net 
current  growth  per  acre  on  such  lands?  " 

The  first  result  of  cutting  should  be  to  tremendously  increase  the 
growth  per  cent  on  the  remaining  stand,  or  change  its  status,  by  removing 
large,  old  and  slow-growing  trees  with  a  low  growth  per  cent,  and  leaving 
small,  young  and  more  vigorous  trees  with  a  larger  growth  per  cent. 
This  change  would  occur  even  if  no  increased  growth  followed  the  cutting. 

The  total  growth  per  acre  laid  on  after  cutting  is  the  sum  of  the 
current  increments  on  the  residual  trees.  In  spite  of  change  in  growth 
per  cent  or  status,  and  of  possible  increased  growth  on  the  trees  left, 
the  total  net  volume  increase  may  be  less  than  on  the  original  stand. 
If  the  number  of  trees  is  greatly  reduced  this  is  usually  the  case.  But 
if  the  stand  cut  over  is  many-aged,  and  only  the  decadent  and  sup- 
pressed trees  are  taken,  the  combination  of  a  large  number  of  trees 
left  on  the  area,  an  increased  rate  of  growth  on  these  trees,  and  especially 
the  prevention,  by  cutting,  of  a  loss  of  volume  by  death  of  trees  which 
would  otherwise  have  to  be  deducted  from  current  growth,  may  result 
in  a  larger  actual  net  increase  per  acre  from  the  cut-over  stand  than 
before  it  was  cut,  as  well  as  a  greater  growth  per  cent. 

This  expansion  of  diameter  and  volume  growth  of  the  residual 
stand  after  cutting,  is,  for  even-aged  stands,  a  response  to  increased 
light,  soil,  moisture  and  space  in  which  to  expand.  In  many-aged 
stands  it  may  mean,  as  well,  an  expansion  of  the  total  area  of  the  age 
class  (§253). 

The  method  of  determining  the  growth  of  individual  trees  in  the 


REDUCED  GROWTH  OF  STANDS  AFTER  CUTTING  439 

stand  to  obtain  the  growth  of  the  stand  (§  277),  is  favored  in  studies 
of  cut-over  lands,  first,  because  such  studies  are  usually  made  in  many- 
aged  stands  of  mixed  species,  second,  because  the  difficulty  of  sepa- 
rating the  age  classes  by  area  and  age  is  even  greater  than  on  stands 
before  cutting;  hence  the  application  to  these  stands  of  yield  tables 
based  on  age  is  very  difficult. 

The  stimulation  of  growth  on  the  trees  left  after  logging  is  similar 
in  character  to  the  beneficial  effects  of  repeated  thinnings  on  stands 
under  management.  It  undoubtedly  increases  the  rate  of  jdeld  per 
acre  over  that  realized  if  the  natural  processes  of  selection  are  not 
interfered  with. 

Two  factors  must  be  considered  in  analyzing  this  growth;  first, 
to  what  extent  have  the  trees  left  on  the  area  been  liberated  or  given 
increased  growing  space? — second,  to  what  extent  can  they  utilize  or 
monopolize  the  area  released  by  cutting?  The  maximum  of  increased 
growth  would  be  found  in  a  stand,  either  even-  or  many-aged,  in  which 
the  cutting  was  so  evenly  distributed  as  to  affect  all  of  the  remaining 
trees,  and  so  light  that  the  space  released  could  all  be  absorbed  by  these 
trees. 

When  cutting  is  either  too  light  or  too  poorly  distributed  to  affect 
all  trees,  the  trees  showing  increased  growth  will  be  only  a  certain  per 
cent  of  the  total  number.  This  per  cent  of  each  diameter  class  which 
will  be  released,  as  affected  by  the  increased  rate,  will  give  the  net 
actual  increase  over  the  previous  rate  of  growth. 

Table  LXVI  illustrates  the  data  required  in  a  study  of  increased 
growth  after  cutting  (p.  440). 

From  a  table  of  this  character  the  average  increase  in  growth  may 
be  computed  by  weighting  the  rate  of  increase  by  the  per  cent  of  trees 
affected;  e.g.,  since  18  per  cent  of  the  trees  are  affected,  an  average 
increase  of  18  per  cent  of  the  difference  between  the  two  classes  of  trees, 
those  not  affected  and  thus  growing  faster,  can  be  added  to  the  slower 
or  original  rate  to  get  the  new  average  for  the  forest. 

338.  Reduced  Growth  of  Stands  after  Cutting.  In  heavier  cuttings, 
even  on  parts  of  the  same  cut-over  area,  openings  may  easily  occur 
from  cutting  even-aged  or  mature  groups,  which  affect  but  few  of  the 
remaining  trees.  These  clear-cut  spots  will  result  in  a  net  reduction 
of  current  increment  per  acre  for  the  forest,  just  as  would  the  clear 
cutting  of  a  larger  area.  There  is  no  possibility  of  increased  growth 
because  there  is  no  timber  left  on  which  to  lay  this  growth.  In  even- 
aged  stands  cut  clear,  the  growth  for  the  forest  occurs  on  separate  areas 
of  maturing  timber,  not  on  the  areas  cut  over;  the  growth  on  cut-over 
areas  must  result  from  reproduction  of  a  new  crop  and  come  along  in 
time.     Thus  on  heavily  cut-over  areas,  in  mixed  age  classes,  a  heavy 


440 


CURRENT  OR  PERIODIC  GROWTH  OF  STANDS 


reduction  of  growth  per  acre  will  occur  for  the  present  regardless  of  in- 
crease on  the  residual  trees  or  stand. 


TABLE  LXVI 

Adirondack  Spruce 

Average  Rate  of  Gro'ni:h  in  Diameter  on  the  Stump  of  1593  Trees  on  Cut-over  Land 
at  Santa  Clara,  New  York 


Current 

annual 

Diam- 
eter. 

No.  of 
trees 

Current 

annual 

growth  in 

diameter 

just  before 

first 

cutting. 

Current 
annual 
growth  in 
diameter 
since  first 

growth  in 
diameter 
since  first 

cutting. 

Values 
made 

No.  of 

years 

required 

to  grow 

1  inch 

No.  of 

trees 

showing 

increased 

growth 

Current 
annual 
growth  in 
diameter 
since  first 

cutting. 

regular  by 
a  curve. 

diameter 

cutting. 

Inches 

Inches 

Inches 

Inches 

Inches 

5 

8 

0.095 

0.095 

0.09 

11 

1 

0.100 

6 

158 

.080 

100 

.10 

10 

16 

.180 

7 

329 

.090 

110 

.109 

9 

63 

.185 

8 

350 

.105 

125 

.125 

8 

77 

.205 

9 

277 

.120 

140 

.140 

7 

59 

.205 

10 

226 

.135 

150 

.150 

7 

50 

.215 

11 

135 

.130 

145 

.160 

7 

18 

.210 

12 

64 

.165 

175 

.170 

6 

7 

.240 

13 

30 

.165 

170 

.178 

6 

2 

.170 

14 

11 

.150 

150 

.185 

6 

1 

.200 

15 

1 

.080 

080 

.192 

6 

16 

4 

.200 

200 

.200 

5 

0.112 

0.137 



0.20 

No.  years 

3  to  grow 

•    1  inch. 

9 

7 

5 

Total  number  of  trees,  1593. 

Number  of  trees  showing  increased  growth,  294,  or  18  per  cent. 

The  condition  of  such  cut-over  areas  would  be  more  accurately  gaged 
if  it  were  possible  to  separate  the  age  classes  in  the  cut-over  stand  on 
the  basis  of  the  actual  area  which  they  occupy.  Thus,  in  a  stand  on 
which  the  timber  cut  formerly  occupied  90  per  cent  of  the  growing 
space,  it  is  not  reasonable  to  expect  that  the  trees  which  occupy  the 
remaining  10  per  cent  of  space  will  be  able  to  expand  sufficiently  to 
absorb  nine  times  their  former  crown  space,  even  if  properly  distributed 


YIELD  TABLES  BASED  ON  AGE,  TO  CUT-OVER  AREAS        441 

SO  as  to  make  this  possible.  The  increment  on  this  area  for  any  con- 
siderable period  into  the  future  depends  on  securing  reproduction 
to  fill  the  gaps. 

The  method  of  measuring  increment  on  cut-over  lands  solely  by  the 
growth  expected  on  the  trees  left  after  cutting  is  best  adapted  to  typical 
many-aged  or  "selection"^  forests,  and  the  more  closely  the  conditions 
both  as  to  distribution  of  cutting  and  of  the  residual  stand  resemble 
a  many-aged  forest,  the  better  the  results  obtained.  This  method 
gives  best  results  also  on  areas  under  intensive  management,  where  if 
trees  die  or  are  blown  over,  their  volume  is  not  lost,  and  when  the  danger 
of  reduction  or  loss  in  numbers  is  at  a  minimum. 

The  necessity  for  reducing  the  number  of  trees  for  loss  during  the 
period  remains,  and  applies  to  all  stands  on  cut-over  lands  as  well  as 
elsewhere.  Neglect  of  this  factor  means  over-estimation  of  probable 
net  growth. 

339.  Application  of  Yield  Tables  Based  on  Age,  to  Cut-over  Areas. 
Where  stands  in  the  original  forest  can  be  or  have  been  separated 
by  area  and  age  by  any  method,  and  a  yield  table  based  on  age  exists, 
a  more  conservative  method  of  calculating  growth  on  cut-over  lands 
can  be  used,  which  bases  this  growth  not  on  the  theory  of  the  many- 
aged  forest  and  crown  expansion  of  the  age  class,  but  on  that  of  even- 
aged  stands  (§  298).  If  age  classes  are  on  separate  areas  and  cut  clean, 
the  cutting  of  one  stand  has  no  effect  on  the  growth  of  another.  If 
the  forest  is  divided  into  age  classes,  and  part  is  cut  over,  it  can  be 
assumed  that  this  cutting  removes  an  age  class  without  stimulating 
the  growth  on  the  remainder,  and  that  this  area  cut  over  is  to  be  repro- 
duced to  young  timber  rather  than  absorbed  by  existing  age  classes. 

To  determine  the  area  which  is  cut  over,  and  that  which  remains 
stocked,  the  density  or  reduction  per  cent  already  determined  for  the 
original  forest  (§  317)  is  assumed  to  apply  to  the  residual  stand.  The 
area  stocked  to  this  degree  of  density  can  be  found  by  dividing  the 
volume  in  each  age  class  left  on  the  cut-over  area,  by  that  of  the  empirical 
yield  table  for  the  given  age  which  has  been  prepared  for  the  original 
forest  previous  to  cutting  (§  304).  The  sum  of  these  areas,  including 
that  stocked  already  by  young  or  immature  age  classes,  subtracted 
from  the  total  area,  gives  the  area  actually  cut  over.  The  actual  yields 
of  the  age  classes  left  on  the  cutover  area  will  be  in  proportion  to  the 
per  cent  of  the  total  area  which  they  occupy,  plus  the  degree  of  expansion 
or  increased  growth  which  they  put  on.  The  growth  to  be  expected 
in  the  absence  of  any  such  expansion  will  be  predicted  by  the  empirical 
yield  table  from  the  net  area  or  per  cent  of  area  stocked.     This  fixes 

1  Selection — A  term  applied  to  forests  in  which  the  entire  series  of  age  classes  is 
intermingled  over  the  whole  area  and  not  separated  by  areas. 


442 


CURRENT  OR  PERIODIC  GROWTH  OF  STANDS 


the  minimum  expectancy  and  is  safe  for  a  long  future  period  (§  248). 
Studies  of  growth  on  the  individual  trees  and  on  permanent  sample 
plots  as  stimulated  by  release  will  in  time  indicate  the  maximum  growth 
possible  on  the  same  area.  The  actual  growth  will  be  somewhere 
between  these  two  extremes,   dependent  on  the  balance  between  the 

forces  tending  to  expand  the  crown 
area,  and  the  destructive  agencies 
tending  to  reduce  the  numbers  in  the 
stand,  as  shown  in  Fig.  87  by  the  lines; 

A.  Based  on  average  growth  per 
acre  in  original  stand,  with  normal 
)oss  of  numbers. 

B.  Based  on  increased  growth  after 
cutting  and  no  loss  of  numbers. 

C.  Probable  rate  somewhere  between 
A  and  B,  based  on  increased  growth 
of  a  part  of  the  stand  and  a  reduced 
rate  of  loss  in  numbers. 

Probably  the  safest  basis  for  growth 
prediction  for  long  periods  on  cut- 
over  lands  is  not  the  current  growth 
study  based  on  diameters,  but,  where 
possible,  yields  based  on  age,  at  the 
rate  produced  in  the  past  on  virgin 
forests,  and  figured  for  the  net  areas 
stocked,  to  which  a  percentage  of  in- 
crease may  be  added  to  represent  expansion  of  crowns  due  to  release 
and  stimulus  following  cutting. 

An  illustration  of  tliis  principle  of  growth  prediction  is  as  follows : 

The  empirical  yield  table  for  Western  yellow  pine,  Coconino  National  Forest, 
Arizona,  gives  66.2  per  cent  of  the  normal  or  index  yield. 

The  stand  of  timber  left  on  the  cut-over  areas,  separated  into  three  age  classes 
by  the  method  given  in  §  321  is  found. 

By  dividing  the  stand  for  each  age  class  by  the  yield  per  acre  from  the  empirical 
yield  table,  the  area  which  is  stocked  with  timber,  for  each  age  class,  is  determined. 

The  area  reproduced  to  poles  and  saplings  is  estimated.  The  total  area  of  cut- 
over  land  is  known.  The  remaining  area,  not  shown  as  stocked  either  with  mature 
timber  or  young  timber  is  the  area  cut  clean  and  awaiting  restocking.  The  results 
are  given  in  Table  LXVII. 

The  prediction  of  growth  is  now  made  by  applying  the  empirical 
yield  table  to  the  areas  and  ages  represented  in  the  table. 

With  the  area  and  age  of  each  age  class  indicated,  the  future  yields 
on  cut-over  lands  may  be  predicted  by  applying  the  empirical  yield 
table,  increased  by  the  per  cent  of  expansion  agreed  upon. 


Fig. 


87. — Possibilities  of  Growth 
on  Cut-over  Areas. 


PLOTS  FOR  MEASUREMENT  OF  CURRENT  GROWTH 


443 


TABLE  LXVII 
Areas  Remaining  Stocked  on  Cut-over  Lands 


Class 

Age. 
Years 

Yield  per           Stand,  • 

acre.         I     total  M. 

i 

Board  feet    j    Board  feet 

Empirical 

area 
equivalent 

acres 

Per  cent  of 

70,654  acres; 

also  per  cent 

of  1  acre 

Veteran 

Mature 

Blackjack  

Poles 

300 

200 

100 

50 

20 

0 

12,050 

16,750 

7,480 

Totals 

27,900 

9,702 

70,908 

2,315 
579 
9,493 
6,006 
17,663 
34,598 

3.2 

0.8 

13.4 

8.5 

25.0 

Not  restocked. .  . 

49.1 

108,510               70,654 

100.0 

340.  Permanent  Sample  Plots  for  Measurement  of  Current  Growth. 

The  best  method  of  measuring  the  current  growth  of  a  stand  is  by  means 
of  permanent  sample  plots,  established  in  stands  which  are  typical  of 
the  conditions  to  be  studied,  and  re-measured  at  intervals  of  from  five 
to  ten  years.  Methods  of  establishing  and  measuring  such  plots  are 
described  in  §  243.  In  this  way,  just  as  for  yield  tables  the  actual  net 
results  of  all  factors  which  affect  the  current  growth  of  the  stand  as  a 
whole,  such  as  wind,  insects,  disease,  suppression,  or  increased  growth, 
are  measured,  rather  than  either  compared  or  predicted.  The  only 
precautions  to  observe  on  re-measurement  of  plots  are  that  the  diameters 
and  heights  of  the  trees  must  be  taken  in  successive  measurements  in 
such  a  way  as  to  give  exact  comparisons,  whose  difference  indicates 
growth  rather  than  discrepancies  in  re-measurements. 

Krauch  has  pointed  out  that  the  height  of  trees  should  be  measured 
on  such  plots  from  the  same  position  or  point  at  each  measurement, 
to  avoid  discrepancy  due  to  the  departure  of  the  tree  from  the  per- 
pendicular (§  199).  The  diameter  tape  insures  consistency  in  re-measure- 
ment of  diameters  (§  190).  The  same  volume  table  should  be  used  in 
calculating  successive  volumes  for  trees  of  each  size  class.  These  pre- 
cautions insure  the  isolation  of  the  current  growth  in  successive  measure- 
ments. 

341.  Measurement  of  Increment  of  Immature  Stands  as  Part  of 
the  Total  Increment  of  a  Forest  or  Period.  The  increment  of  a  forest 
or  large  area,  just  as  in  the  case  of  a  single  stand,  may  be  expressed  as 
the  total  growth  over  a  definite  period,  or  yield,  the  average  annual 
growth  or  mean  for  this  period,  or  the  actual  volume  laid  on  each  year 


444  CURRENT  OR  PERIODIC  GROWTH  OF  STANDS 

or  current  annual  growth.  A  forest  resembles  more  closely  a  many- 
aged  stand  than  one  composed  of  a  single  age  class.  In  such  a  stand 
or  forest,  it  is  not  possible  to  separate  one  period  which  coincides  with 
the  complete  cycle  of  production  for  a  crop  of  timber,  as  can  be  done 
in  the  even-aged  stand.  The  total  production  of  the  many-aged  area 
or  of  the  forest,  for  a  period  equal  to  that  required  to  grow  one  crop 
from  seed  to  maturity,  may  equal  that  of  the  even-aged  stand,  but  it 
is  laid  on  in  many  stands. 

In  a  regular  many-aged  forest  the  current  growth  for  one  year  is 
the  growth  in  volume  of  each  stand,  including  those  which  are  as  yet 
unmerchantable.  This  is  true  of  the  forest,  whatever  its  form.  The 
current  growth  on  the  mature  timber  is  but  part  of  the  total;  that  which 
represents  the  younger  stands  is  equally  important.  Growth  is  not 
usually  measured,  on  either  trees  or  stands,  until  a  size  is  attained  which 
is  merchantable  for  some  form  of  product.  Another  reason  for  post- 
poning the  measurement  of  young  stands  is  that  a  very  large  per  cent 
of  the  existing  trees  in  such  stands  will  never  reach  maturity,  and  the 
total  volume  at  any  period  previous  to  an  age  at  which  it  can  be  used 
is  misleading  and  serves  no  useful  purpose,  while  by  contrast  the  natural 
selection  of  surviving  trees  in  stands  measured  at  merchantable  age 
has  already  occurred  and  the  results  are  accurately  gaged. 

When  the  volume  is  finally  measured  on  a  young  stand  for  the  first 
time,  it  represents  the  growth  for  the  entire  preceding  period.  Perhaps 
but  10  per  cent  of  the  trees  are  large  enough  to  measure  at  this  time. 
After  another  decade,  the  stand  is  again  measured.  By  this  time 
50  per  cent  of  the  trees  may  be  merchantable.  The  growth  for  this 
decade  now  includes  the  current  growth,  for  ten  years,  on  the  original 
10  per  cent,  plus  the  growth  since  germination  on  the  remaining  40 
per  cent.  At  the  third  measurement,  all  trees  which  survive  may  be 
merchantable  and  are  measured,  but  a  portion  of  them  have  entered 
the  merchantable  class^ after  being  missed  for  the  two  previous  decades. 
What  happens  is  that  although  current  increment  by  decades  is  sought, 
yet  for  trees  which  mature  and  are  measured  for  the  first  time,  total 
growth  is  substituted  for  current  growth  since  there  is  no  other  way 
to  handle  it. 

If  this  example  is  now  applied  to  a  forest  composed  of  a  series  of 
even-aged  stands,  the  same  thing  is  seen  to  occur.  For  the  forest, 
the  current  increment  is  the  increase  in  merchantable  cubic  volume 
of  stands  already  partly  merchantable;  but  to  this  is  added,  in  each 
decade,  stands  measured  for  the  first  time,  whose  volume  though  added 
as  current  increment  is  in  reality  the  total  gi-owth  of  several  periods 
instead  of  one.  It  follows  that  for  a  stand  just  becoming  merchantable, 
the  apparent  current  growth  will  be  very  rapid  during  this  process 


VALUE  OF  CURRENT  GROWTH  VERSUS  YIELD  TABLES     445 

while  its  actual  average  or  mean  annual  growth,  which  takes  in  the  true 
period  required,  is  much  less. 

But  in  a  many-aged  stand,  or  on  a  forest  composed  of  stands  of  all 
ages,  these  elements  counterbalance  each  other.  As  growth  cannot 
be  measured  on  stands  below  merchantable  age  or  size,  it  is  not  meas- 
ured on  the  areas  covered  by  such  young  stands,  or  on  the  portion 
occupied  by  immature  trees  in  mixed-  stands.  But  as  soon  as  these 
stands  or  trees  mature,  the  growth  is  measured  all  at  once  and  greatly 
exceeds  the  actual  current  rate  on  the  areas  measured  or  for  the  trees 
in  these  age  classes.  Wlienever  the  age  classes  are  distributed  evenly, 
the  excess  of  current  growth  so  caused  is  balanced  for  the  area  or  forest 
by  the  neglect  of  the  current  growth  on  the  younger  stands.  It  follows, 
first,  that  in  forests  with  well  distributed  age  classes,  the  total  current 
annual  growth  actually  laid  on  in  stands  of  all  ages  should  be  about 
equal  to  the  current  growth  obtained  by  measuring  only  the  merchant- 
able stands,  provided  the  maturing  volumes  of  young  timber  are  included 
as  current  growth.  For  a  single  even-aged  stand,  or  a  forest  devoid 
of  younger  age  classes,  this  premise  does  not  hold  good,  and  the  current 
growth  for  the  period  of  early  maturity  will  greatly  exceed  the  real 
rate  for  the  area  or  total  period.  On  such  stands  or  forests  this  rate 
will  not  be  maintained,  and  the  true  yield  must  be  found  by  dividing 
by  age,  in  the  form  of  mean  annual  growth. 

342.  Comparative  Value  of  Current  Growth  versus  Yield  Tables 
and  Mean  Annual  Growth.  The  relative  value  and  utility  of  the 
methods  of  studying  the  increment  on  forests  or  large  areas  may  be 
summed  up  as  follows: 

Increment  or  growth  is  always  desired  for  areas  of  land  rather  than 
individual  trees. 

The  rate  of  growth  per  year  on  an  average  acre  is  the  object  sought. 

Where  forestry  is  a  permanent  land  policy,  the  rate  of  growth  desired 
is  that  which  represents  the  average  for  the  life  of  a  crop  of  timber, 
and  which  can  be  maintained,  in  consequence,  indefinitely. 

This  rate  can  be  found  most  accurately  whenever  growth  can  be 
measured  directly  on  the  basis  of  area  and  total  age,  as  in  yield  tables 
for  even-aged  stands,  and  applied  to  the  forest  by  the  necessary  reduc- 
tion per  cents. 

The  current  growth  on  stands  or  forests  is  best  obtained  from  these 
same  yield  tables. 

But  where  it  is  not  possible  or  practicable  to  construct  such  yield 
tables,  current  growth  for  short  periods  only  can  be  measured  directly 
on  merchantable  trees,  and  applied  in  predicting  growth  of  the  stand 
and  forest. 

This  method  gains  in  accuracy  over    yield   tables,  by  measuring 


446  CURRENT  OR  PERIODIC  GROWTH  OF  STANDS 

directly  the  density  of  the  stand,  and  by  predicting  growth  on  basis 
of  actual  volume  and  conditions.  It  loses  in  comparison,  because  it 
measures  only  one  current  section  of  the  growth  curve  for  the  stand  or 
forest,  which  may  be  above  or  below  the  mean,  and  because  the  basis, 
the  individual  tree,  while  accurate  to  start  with,  rapidly  loses  its  reli- 
ability, while  by  contrast,  yield  tables  retain  a  fair  degree  of  reliability 
over  long  future  periods. 

Current  growth,  if  it  is  actually  measured  in  terms  of  volume,  and 
the  errors  of  using  growth  per  cent  are  avoided,  is  well  adapted  to  answer 
questions  regarding  the  immediate  future  growth  of  specific  stands, 
but  is  poorly  adapted  to  growth  predictions  covering  long  periods. 

References 

Growth  Rate  in  Selection  Forest.     Der  Gemischte  Buchen  Plenterwald  auf  Muschel- 

kalk  in  Thiiringen,  Mathes,  Allgemeine  Forst-  u.  Jagdzeitung,  May  1910,  p. 

149.     Review,  Forestry  Quarterly,  Vol.  IX,  1911,  p.  129. 
Increment  in  Selection  Forests.     Zur  Ermittlung  des  laufenden  Zuwachses  speziell 

im  Plenterwalde,    Christen,   Schweizerische  Zeitschrift   flir   Forstwesen,    Feb. 

1909,  p.  37.     Review,  Forestry  Quarterly,  Vol.  VII,  1909,  p.  206. 
A  Method  of  Investigating  Yields  per  Acre  in  Many-aged  Stands,  H.  H.  Chapman, 

Forestry  Quarterly,  Vol.  X,  1912,  p.  458. 
Accelerated  Growth  of  Spruce  after  Cutting,  in  the  Adirondacks,  John  Bentley, 

Jr.,  Journal  of  Forestry,  Vol.  XV,  1917,  p.  896. 
Method  of  Regulating  the  Yield  in  Selection  Forests,  Walter  J.  Morrill,  Forestry 

Quarterly,  Vol.  XI,  1913,  p.  21. 
Determination  of  Stocking  in  Uneven-aged  Stands,  W.  W.  Ashe,  Proc.  Soc.  Am. 

Foresters,  Vol.  IX,  1914,  p.  204. 
The  Relation  of  Crown  Space  to  the  Volume  of  Present  and  Future  Stands  of  Western 

Yellow  Pine,  George  A.  Bright,  Forestry  Quarterly,  Vol.  XII,  1914,  p.  330. 
Remeasurement  of  Permanent  Sample  Plots,  G.  A.  Pearson,  Forestry  Quarterly, 

Vol.  XIII,  1915,  p.  60. 
Observations  in  Connection  with  Annual  Increment  of  Growing  Crops  of  Timber, 

Transactions  of  Royal  Scottish  Arboricultural  Society,  July,  1918,  p.  164. 


CHAPTER  XXXII 

COORDINATION  OF  FOREST  SURVEY  WITH  GROWTH  DETER- 
MINATION FOR  THE  FOREST 

343.  Factors  Determining  Total  Growth  on  a  Large  Area.     The 

solution  of  the  problem  of  determining  the  amount  or  volume  of  wood 
which  will  be  grown  on  a  forest  or  area  of  forest  land  in  a  given  period 
depends  upon  six  factors: 

1.  An  analysis  or  classification  of  the  forest  into  the  areas  included 
in  each  of  the  site  quahties  present. 

2.  The  areas  occupied  by  stands  of  given  type  and  mixture  of  species. 

3.  The  actual  present  density  of  stocking,  volume  and  number  of 
trees  per  acre,  and  size  of  diameters  of  the  present  stand  on  the  forest. 

4.  The  actual  age  classes  present,  and  the  area  which  each  occupies. 

5.  The  length  of  the  period  for  which  growth  is  desired,  whether 
for  a  short  current  period,  or  for  permanent  management  and  a  rotation. 

6.  The  rate  of  growth,  to  be  determined  by  whatever  method  can 
best  be  applied  to  the  forest  as  a  whole  by  obtaining  the  actual  growth 
on  the  stands  which  compose  it. 

344.  Data  Required  from  the  Forest  Survey.  The  first  four  of 
these  elements  require  the  collection  of  data  in  connection  with  the 
forest  survey.  Studies  of  the  rate  of  growth  (6)  for  the  period  deter- 
mined (5)  will  not  solve  this  problem  in  the  absence  of  quantitative 
data  to  tie  this  growth  study  to  the  tract  in  question. 

Unless  a  forest  is  to  be  cleared  for  farms,  the  prediction  of  future 
growth  is  a  basic  consideration  of  its  future  management.  A  forest 
survey  that  is  so  conducted  as  to  fail  to  obtain  the  necessary  data  on 
which  growth  for  the  forest  can  be  determined  must  later  be  repeated 
to  obtain  this  data,  or  supplemented  in  some  way,  while  if  the  need 
were  recognized  at  the  start,  the  information  could  be  obtained  in  final 
form  with  trivial  extra  cost. 

The  character  of  this  data  depends  upon  the  form  of  the  forest  as 
to  its  age  classes.     It  may  be  itemized  as, 

1.  Site  classification. 

2.  Age  of  stands. 

3.  Area  of  stands. 

4.  Volume  of  stands. 

447 


448  COORDINATION  OF  FOREST  SURVEY 

When  these  factors  cannot  be  directly  ascertained,  the  requisite  basis 
must  be  obtained  for  calculating  them.  The  most  fundamental  and 
useful  basis  is, 

5.  Diameter  of  trees  in  stand  b}-  species,  or  a  stand  table. 
Finally,  because  of  its  inadequate  handling,  special  emphasis  must 

be  placed  on  obtaining 

6.  The  area  stocked  by  immature  age  classes. 

345.  Site  Qualities — Separation  in  Field.  Site  qualities  in  the 
forest  should  be  separated  by  area.  Where  several  types  exist,  such 
as  cove,  lower  slope,  upper  slope  and  ridge,  which  correspond  closely 
with  difference  in  site,  the  division  by  types  goes  a  long  way  toward 
separating  the  site  qualities  (§  228). 

Where  site  qualities  must  be  determined  directly,  there  are  but  two 
methods  possible  of  which  the  first  is  direct  judgment  based  on  obser- 
vation of  site  factors,  such  as  soil,  altitude,  slope,  rock,  moisture  (as 
swamps)  and  general  character  of  the  timber  growth.  This  method 
is  subject  to  serious  errors  (§  226).  The  second  method  ^  is  based  on 
the  height  growth  of  dominant  trees  (§  227).  But  to  determine  directly 
the  site  class  indicated  by  trees  of  different  heights,  their  age  must  be 
known.  When  the  forest  is  composed  of  a  few  large  age  classes  of  even 
age,  direct  determination  of  a  few  ages  may  give  this  basis. 

But  where  the  age  classes  are  mixed,  the  age  of  individual  dominant 
trees,  rather  than  age  of  stand,  must  be  relied  on  to  indicate  site  quality. 
If  we  could  assume  that  diameter  growth  did  not  decrease  for  the  average 
tree,  on  poor  sites,  and  that  average  trees  of  a  given  diameter  were 
as  old  on  Quality  I  site  as  on  Quality  III,  diameter  could  be  substituted 
for  age;  but  average  diameter  growth  varies  with  the  site  quality  itself, 
which  prevents  this  substitution. 

To  obtain  the  basis  of  field  classification  of  site,  the  heights  of  dif- 
ferent trees  based  on  age  are  plotted  and  divided  into  site  qualities 
based  on  the  standard  chosen,  as  illustrated  in  Fig.  84  (§  310)  except 
that  in  this  case  the  data  are  obtained  by  plotting  individual  trees, 
and  by  analysis  of  the  height  growth  of  trees,  rather  than  from  plots. 

To  apply  this  table  or  set  of  curves,  in  determining  the  quality  of 
a  given  site,  a  selected  tree  or  two  is  measured  for  height.  If  fully 
matured,  total  height  may  indicate  directly  the  site  quality.  If  the 
stand  is  young,  age  must  always  be  ascertained.  The  average  height 
for  the  given  age  is  then  looked  up  on  the  chart.  The  trees  chosen 
should  preferably  be  dominant  and  must  never  be  suppressed.  The 
position  of  the  height  with  reference  to  the  curves  or  table  indicates 
the  site  quality. 

The  unit  of  area  on  which  sites  are  separated  should  be  that  used 
1  Journal  of  Forestry,  Vol.  XV,  1917,  p.  552. 


RELATION  BETWEEN  VOLUME  AND  AGE  OF  STANDS         449 

in  separating  stands  or  units  of  volume  estimating,  such  as  small  legal 
subdivisions,  e.g.,  10  acres,  except  where,  by  the  aid  of  topography, 
the  site  qualities  can  be  mapped  to  conform  more  closely  with  natural 
boundaries.  Types  are  commonh'  separated  in  the  forest  survey  by 
mapping  the  areas,  and  the  estimate  is  usually  separated  to  coincide 
with  the  divisions  thus  made  (§221)  though  on  forties  this  is  not  always 
done. 

346.  Relation  between  Volume  and  Age  of  Stands.  Density  of 
stocking,  as  shown,  is  not  determined  l)y  the  total  merchantable  volume 
of  a  stand,  but  by  a  comparison  of  the  existing  volume  with  the  index 
volume  which  stands  should  have  at  given  ages.  Density  when  deter- 
mined by  comparison  of  volumes,  is  therefore  a  function  not  solely  of 
area  but  also  of  age.  To  determine  density  for  large  areas,  therefore, 
a  basis  of  separation  of  the  volume  into  age  classes  is  required.  This 
means  either  the  direct  mapping  of  areas  of  separate  age  classes,  or  a 
tally  of  diameters  and  a  stand  table  for  diameter  classes  in  the  stand. 
IMethods  of  forest  survey  which  utilize  diameter  tallies  to  obtain  volumes 
(§  207  and  §  209)  naturally  lend  themselves  to  the  securing  of  such 
a  stand  table.  The  use  of  such  talhes  for  determining  age  groups  and 
average  ages  are  shown  in  §  320  and  §  323.  In  general,  density  of  stock- 
ing for  mature  age  classes  will  be  found  not  in  the  field,  but  after  the 
volumes  have  been  computed  or  stand  tables  prepared,  and  by  means 
of  a  comparison  of  volumes  with  the  yield  table,  on  the  basis  of  similar 
ages. 

Age  classes  and  their  actual  ages  may  be  determined  directly  during 
timber  survey  only  when  the  areas  which  they  occupy  are  separate,  large 
and  easily  distinguished,  and  when  time  permits  of  the  testing  of  trees 
for  age.  In  intensive  management,  this  method  will  be  followed  on  small 
areas;  but  for  large  areas  of  mixed  ages,  the  general  method  of  depending 
upon  diameters  to  indicate  age  should  be  relied  on;  hence  the  stand 
table  is  the  basis  of  this  age  class  division,  both  for  age  and  area  (§318 
to  §  323.) 

347.  Averaging  the  Site  Quality  for  the  Entire  Area.  Site  qualities, 
when  not  con-elated  with  type,  present  difhculties  in  classification, 
so  much  so  that  on  large  extensive  projects  site  qualities  may  for  the 
time  have  to  be  waived  and  an  average  yield  table  obtained  for  all 
sites.  (This  method  was  adopted  in  the  preliminary  working  plan 
for  the  Coconino  Nationa'  Forest,  Arizona.)  A  composite  stand  table, 
including  stands  on  all  sites,  is  best  for  this  purpose.  Its  application 
to  the  average  site  will  depend  on  the  average  density  or  reduction 
per  cent  found  for  the  area.  Only  when  the  divisions  of  the  total  area 
into  site  qualities  can  be  coordinated  with  similar  divisions  of  the  esti- 
mate and  stand  can  these  divisions  be  made  the  basis  of  separate  growth 


450  COORDINATION  OF  FOREST  SURVEY 

predictions  for  the  forest.  Wherever  possible,  this  division  must  be 
made. 

348.  Growth  on  Areas  of  Immature  Timber.  The  growth  on  any- 
large  area,  whether  the  form  of  forest  is  even-aged  in  pure  stands,  or 
many-aged  in  mixed  stands  (§  314)  must  include  that  of  the  young, 
unmerchantable  stands.  This  growth  is  a  prediction  of  future  volume, 
and  as  such,  may  be  obtained,  not  by  measuring  the  present  volume 
of  the  stand,  nor  by  counting  the  number  of  trees  in  very  young  stands, 
but  by  the  method  of  comparison  with  older  stands.  The  yield  table 
based  on  area  and  age  gives  this  comparison.  But  to  utiHze  the  table, 
the  one  thing  necessary  to  determine  is  the  area  which  is  stocked  with 
the  immature  timber.  Its  age  is  more  easily  determined  than  for  old' 
timber,  either  by  cutting  or  by  counting  whorls.  Based  on  area  and 
age,  the  future  yield  is  a  matter  of  density  of  stocking.  The  rate  of 
growth  per  year  may  be  taken  as  the  mean  annual  growth,  shown 
by  the  reduced  or  empirical  yield  table,  for  the  age  at  which  the  stand 
will  be  cut. 

The  density  per  cent  for  young  stands  is  practically  independent 
of  the  density  of  crown  cover,  and  depends  instead  upon  the  number 
of  trees  per  acre  as  compared  with  the  normal  number  required  at 
maturity,  the  distribution  of  these  trees  over  the  area,  and  the  chance 
of  survival  (§316).  Mortality  in  scattered  stands  where  each  tree 
has  room  to  grow  is  much  less  than  in  crowded  stands;  and  if  the 
spacing  of  the  reproduction  is  such  that,  allowing  for  a  reasonable 
rate  of  loss  from  insects  and  causes  other  than  suppression,  the  stand 
will  reach  full  stocking  at  least  a  decade  before  maturity,  it  can  be 
considered  as  fully  stocked  now. 

If  a  large  area  is  being  measured  and  an  average  density  per  cent 
is  found  for  this  area,  resulting  in  an  empirical  yield  table  somewhat 
lower  in  values  than  the  normal  table,  a  conservative  plan  is  to  assume 
that  the  ultimate  yield  of  young  stands  will  not  exceed  this  density, 
and  to  use  the  emphical  yield  table  as  the  basis  for  calculating  their 
future  yields. 

That  area  and  yield  per  acre  is  the  only  possible  basis  of  prediction 
of  yield  for  immature  stands  must  become  evident  by  considering  the 
difficulties  of  the  opposite  plan,  that  of  counting  numbers  of  trees  on 
snail  plots.  In  tallying  or  counting  reproduction  or  immature  sizes, 
it  is  customary  to  lay  off  the  plots  at  fixed  intervals,  comprising  from 
one-tenth  of  the  estimated  strip,  down  to  less  than  1  per  cent  of  the 
strip,  and  to  count  the  seedlings  and  saplings  upon  these  plots.  The 
only  way  in  which  these  data  can  be  used  to  predict  growth  on  such 
small  timber  is  by  predicting  the  percentage  of  this  count  which  will 
survive.     The  method  of  comparison  by  numbers  of  trees  is  useless, 


GROWTH  ON  AREAS  OF  IMMATURE  TIMBER  451 

first,  because  number  of  trees  per  acre  at  these  ages  does  not  in  any  way 
indicate  the  future  yield,  since  this  is  determined  by  the  number  that 
survive;  second,  because  the  area  rather  than  the  number  will  determine 
the  future  yield.  On  a  plot  of  100  square  feet  there  may  be  one  hundred 
seedlings;  yet  if  fully  stocked  at  maturity  not  more  than  one  tree  would 
be  able  to  survive  from  this  number.  Such  counts  on  plots  serve  only 
to  determine  the  extent  to  which  reproduction  is  becoming  established 
and  do  not  give  the  data  needed  for  growth  predictions. 

Age  Classes  Based  on  Size.  Immature  timber  may  be  divided  into 
at  least  three  classes  for  purposes  of  growth  study;  seedlings,  saplings 
and  poles.  Seedlings  are  trees  under  3  feet  high.^  Saplings  include 
trees  from  3  feet  high  to  4  inches  D.B.H.  Poles  are  trees  from  4  to  12 
inches  D.B.H. 

Saplings  may  be  divided  into 
Small — from  3  to  10  feet  high. 
Large — from  10  feet  high  to  4  inches  D.B.H. 

Poles  may  be  divided  into 

Small— from  4  to  8  inches  D.B.H. 
Large — from  8  to  12  inches  D.B.H. 

Methods  for  Seedlings  and  Saplings.  In  determining  the  quantity 
of  reproduction  and  immature  timber  present  on  an  area,  in  order  to 
predict  its  growth  by  comparison  with  a  yield  table,  the  procedure 
will  depend  upon  the  form  of  the  forest.  In  even-aged  stands,  areas 
stocked  with  seedlings  in  sufficient  numbers  can  be  entered  by  mapping 
them  as  fully  stocked.  Danger  of  destruction  is  chiefly  by  fire,  and  for 
this,  correction  can  be  made  when  fires  occur.  But  in  many-aged 
stands,  suppression  must  be  considered.  Depending  upon  the  silvical 
characteristics  of  the  species  and  the  behavior  of  the  seedlings,  the  object 
should  be  to  record  only  the  area  of  mature  forest  which  will  result  from 
the  present  stocking.  Seedlings  which  are  suppressed  wiU  be  ignored. 
Those  which  grow  in  openings  and  are  thrifty  will  be  regarded  as  prob- 
able survivors.  In  rather  open,  group-selection  -  forests  like  yellow 
pine,  the  areas  stocked  in  this  manner  are  easily  distinguished.  With 
species  such  as  spruce,  seedlings  starting  under  shade  and  not  in  open- 
ings should  be  disregarded  altogether,  both  because  of  suppression, 
and  because  their  age  will  be  prolonged  b}^  this  cause  and  they  wiU 
not  become  an  economic  factor  in  the  stand  till  a  later  period  (§  263). 

With  saplings,  the  establishment  of  the  stand  in  many-aged  forests 

^  Standard  definitions,  Society  of  American  Foresters. 

^  Group-selection,  a  forest  composed  of  trees  of  all  ages  intermingled  in  small 
fairly  even-aged  groups. 


452  COORDINATION  OF  FOREST  SURVEY 

is  more  certain,  and  the  area  so  stocked  with  trees  which  will  probably 
survive  can  be  better  determined. 

For  both  these  classes  of  timber,  the  best  method  of  determining  the 
area,  and  consequent  future  growth,  during  the  forest  survey,  is  to  record 
on  each  strip  the  per  cent  of  total  area  on  the  strip  which  is  stocked 
with  young  timber,  on  the  basis  of  probable  survival  to  maturity. 
This  per  cent  is  then  reduced  to  acres  for  the  strip.  The  average  size 
and  age  can  also  be  noted.  Seedlings  and  saplings  can  be  separately 
noted,  or  thrown  together,  depending  on  the  intensiveness  of  the  work 
and  size  of  area. 

A  second  method  of  record  on  the  basis  of  area,  formerly  used  in  the 
Southwest,  was  to  note  the  reproduction  in  general  terms,  based  on 
whether  the  stocking  was  sufficient  to  replace  the  present  stand.  If  so 
it  was  termed  excellent.  Different  per  cents  less  than  this  were  termed 
good,  fair,  poor,  and  none.  This  system  does  not  distinguish  between 
the  areas  of  mature  and  young  timber  or  consider  the  relation  which 
one  bears  to  the  other. 

To  supplement  the  per  cent  method  of  ocular  guessing  at  areas 
restocked,  plots  may  be  laid  out  at  given  intervals,  on  which  the  areas 
stocked  can  be  mapped,  and  computed  in  terms  of  acres.  The  per  cent 
of  the  plot  thus  shown  as  reproduced  serves  to  correct  the  ocular  work 
and  to  check  the  results. 

Methods  for  Poles.  With  poles,  the  area  method  can  still  be  applied 
directly  in  even-aged  stands,  by  mapping.  In  many-aged  stands,  a 
choice  of  two  methods  is  offered.  Either  the  area  per  cent  can  be  used 
as  for  saplings,  but  separately,  and  the  number  of  trees  in  this  class 
ignored  as  before,  in  which  case  merely  the  average  size  and  age  of  the 
poles  on  each  strip  is  recorded  with  the  per  cent  of  area  occupied,  or 
instead,  the  poles  fnay  be  counted. 

The  purpose  of  the  count  is  to  obtain  a  second  basis  of  comparison 
with  the  empirical  yield  table.  The  latter  should  show  the  number 
of  trees  per  acre  required  at  different  ages.  The  yield  table  data  may 
be  made  to  include  pole  sizes,  by  including  plots  of  this  age  in  construct- 
ing the  normal  tables  of  yield.  In  case  this  has  been  done,  the  area 
occupied  by  poles  can  be  verj^  roughly  determined  by  means  of  the 
numerical  comparison  with  the  empirical  table.  For  instance,  if  poles, 
averaging  sixty  years  old  and  7  inches  in  diameter  run  120  per  acre 
in  the  normal  table,  and  the  reduction  per  cent  is  66f ,  the  empirical 
stocking  is  80  poles  per  acre.  A  count  of  8000  poles  on  the  area  indicates 
an  area  of  100  acres  stocked  with  pole  sizes. 

A  definite  plan  for  the  determination  of  the  stocking  with  poles  must 
be  made  preliminary  to  undertaking  the  timber  survey.  Trees  which 
are  part  of  an  even-aged  mature  stand,  but  which  are  not  yet  merchant- 


SEPARATION  OF  AREAS  OF  IMMATURE  TIMBER  453 

able  or  are  suppressed,  are  not  considered,  since  the  yield  table  for  the 
stand  takes  care  of  them.  Only  in  many-aged  stands  must  poles  be 
counted,  or  their  area  determined  by  per  cent  of  the  total,  the  former 
method  to  be  used  if  the  yield  table  permits  of  direct  comparison  of 
numbers,  the  later,  if  only  the  mature  classes  are  shown  in  the  table. 

349.  Effect  of  Separation  of  Areas  of  Immature  Timber  on  the 
Density  Factor  for  Mature  Stands.  The  separation  by  area  of  the 
immature  age  classes  accomplishes  more  than  the  determination  of 
future  3'ield  for  these  age  classes.  In  the  many-aged  forest,  the  mature 
timber  is  not  segregated  as  it  is  in  even-aged  stands,  but  is  intermingled 
with  areas  of  reproduction,  saplings,  and  poles.  In  the  attempt  to 
separate  this  mature  timber  into  two  or  more  age  classes,  either  based 
on  diameter  classes,  or  by  age  groups  (§  320  and  §  323)  it  is  necessary  to 
l)egin  with  a  knowledge  of  the  total  area  occupied  by  all  the  mature 
age  classes.  If  the  area  actually  stocked  with  seedlings,  saplings  and 
poles  to  the  exclusion  of  mature  timber  is  neglected,  then  the  area  appar- 
ently required  by  the  mature  timber  is  greater  than  that  actually 
required,  by  just  the  amount  of  this  error.  In  the  even-aged  forest 
no  such  mistake  is  possible,  and  by  analogy,  its  correction  for  the  many- 
aged  forest  must  be  undertaken. 

The  effect  of  not  separating  the  area  of  immature  stands  is  to  lower 
the  reduction  per  cent  or  apparent  density  factor  for  the  mature  age 
class.  E.g.,  a  reduction  per  cent  of  40  is  found  for  mature  timber  when 
it  is  assumed  to  occupy  the  entire  area.  Segregation  of  young  timber 
shows  that  one-half  or  50  per  cent  of  the  area  is  occupied  by  these  age 
classes.  The  total  area  is  10,000  acres.  The  actual  area  occupied  by 
mature  timber  is  now  5000  acres,  which  doubles  its  density,  and  gives 
a  density  per  cent  of  80  instead  of  40. 

At  first  glance  it  would  appear  that  no  difference  is  made  in  the  cal- 
culation of  yield  of  these  mature  age  classes  by  either  assumption  since 
reduced  area  and  increased  density  are  reciprocal  and  refer  to  the  same 
actual  stocking  and  volume  and  presumably  the  same  future  yield. 
The  benefit  lies  in  the  fact  that  the  corrected  density  factor  more  nearly 
indicates  the  rate  of  growth  per  year  for  the  forest  or  on  the  average  acre, 
which  is  the  information  most  needed  in  permanent  management. 
By  separating  the  yield  and  area  of  the  young  tunber,  it  is  possible 
to  predict  the  total  actual  yield  of  the  forest  over  a  long  period,  instead 
of  for  the  shorter  period  required  to  harvest  timber  now  mature.  Instead 
of  an  extremely  low  per  cent  of  density  for  mature  timber  and  for  the 
forest,  which  would  indicate  the  need  of  considerable  reduction  in  yields 
from  the  standard  table  (§316),  the  true  conditions  are  revealed. 
Finally,  it  gives  the  same  data  as  to  age  classes  for  the  manj'-aged 
forests  as  are  obtained  by  mapping  for  even-aged  stands. 


454  COORDINATION  OF  FOREST  SURVEY 

350.  Stand  Table  by  Diameters  for  Poles  and  Saplings:  When 
Required.  When  diameter  is  definitely  substituted  for  age  and  area, 
the  growth  of  the  forest  for  a  period  of  from  ten  to  twenty  years  into 
the  future  will  include  not  only  the  increase  on  existing  merchantable 
trees,  but  the  volume  of  all  young  trees  which  grow  during  the  period 
to  a  size  which  brings  them  into  the  merchantable  class  (§  277). 

The  number  of  diameter  classes  which  will  become  merchantable 
will  be  determined  by  the  length  of  the  period  and  the  rate  of  growth 
in  diameter.  At  a  rate  of  1  inch  in  five  years,  trees  now  4  inches  below 
the  minimum  diameter  will  reach  the  required  size  in  20  years. 

In  order  to  predict  the  growth  of  the  stand  for  this  period,  the  number 
of  trees  of  each  diameter  class  included  in  the  group  which  will  mature 
within  the  period  must  be  recorded  during  the  forest  survey.  Either 
all  of  the  trees  of  these  sizes  must  be  calipered  or  counted,  and  the 
average  diameter  approximated,  or  these  sizes  may  be  calipered  on  a 
part  of  the  area,  distributed  mechanically  to  obtain  an  average  for  the 
whole.  This  again  indicates  the  need  for  correlation  of  the  method 
to  be  used  in  predicting  growth  with  the  timber  survey,  before  the  latter 
is  undertaken. 

References 

Coordination  of  Growth  Studies,  Reconnaissance  and  Regulation  of  Yield  on  National 
Forests,  H.  H.  Chapman,  Proc.  Soc.  Am.  Foresters,  Vol.  VIII,  1913,  p.  317. 


APPENDIX  A 
A.    LUMBER  GRADES  AND  LOG  GRADES 

351.  Purpose  of  Log  Grades.  The  most  useful  purpose  of  timber  estimating 
and  log  scaling  is  to  determine  the  value  of  the  logs  and  standing  timber.  This 
value  depends  upon  the  amount  or  per  cent  of  lumber  of  different  qualities  which 
can  be  obtained  from  the  logs  or  timber  to  be  valued.  In  §  87  it  was  shown  that  for 
this  purpose  logs  are  separated  into  grades,  usually  three  in  number,  but  that  the 
specifications  for  and  value  of  each  log  grade  depend  upon  the  contents  of  logs  as 
expressed  in  grades  of  lumber,  and  in  residtant  average  value  or  price  per  1000  board 
feet. 

352.  Grades  of  Lumber.  Wood  varies  in  texture  or  closeness  of  grain,  difference 
between  heart-  and  sapwood,  uniformity  of  texture  and  freedom  from  knots,  number, 
size,  placement  and  character  of  knots,  and  presence  of  or  freedom  from  various 
defects  which  lower  the  value  of  the  piece  by  altering  its  appearance,  strength, 
surface  or  suitability  for  the  purposes  for  which  it  may  be  used.  Pieces  which  are 
entirely  free  from  all  defects  are  suitable  for  the  highest  uses  and  possess  the  greatest 
value.  At  the  opposite  extreme  are  found  pieces  with  defects  so  numerous  or  serious 
that  they  are  imfitted  for  any  useful  purpose,  hence  possess  no  market  value  and  are 
disposed  of  as  refuse  to  the  burner  or  as  fuel.  Certain  "  cull  "  grades,  formerly 
refuse,  are  now  generally  handled  as  merchantable,  but  the  practice  of  scaling  has 
not  been  altered  and  such  grades  are  still  excluded  from  the  scale  as  unsound. 

The  output  of  a  mill  in  lumber,  if  separated  according  to  the  quality  and  value 
of  each  board,  would  form  an  unbroken  series  from  the  most  perfect  pieces  descend- 
ing through  an  increasing  per  cent  of  more  and  more  serious  defects  until  the  poorest 
merchantable  boards  are  passed,  and  refuse  only  is  left. 

For  practical  purposes,  this  series  must  be  separated  by  arbitrarj^  standards 
into  groups  termed  lumber  grades,  so  defined  that  any  piece  may  be  assigned  by  its 
appearance  to  its  proper  classification  or  grade.  These  grades  are  then  made  the 
basis  of  lumber  prices  and  lumber  trade. 

The  specifications  for  a  grade  are  intended  to  define  the  poorest  piece  which  will 
be  accepted  in  the  grade,  thus  excluding  all  liunber  whose  quality  and  defects  are 
such  as  to  unfit  it  for  this  grade.  The  average  quality  of  lumber  in  any  grade  will 
therefore  be  better  than  the  minimum  specifications.  Lumber  which  would  qualify 
for  a  given  grade  is  sometimes  included  in  a  lower  grade,  but  this  is  not  in  the  interest 
of  the  seller  and  tends  to  destroy  the  standards  of  grading. 

353.  Basis  of  Lumber  Grades.  The  requirements  of  a  lumber  grade  are,  that  it 
be  generally  adopted  in  a  region  or  for  the  trade  which  handles  the  lumber  from  this 
species  or  region;  that  it  be  consistently  appHed  throughout  this  region;  that  it  be 
capable  of  definition  and  application  in  grading;  and  that  it  conform  to  the  require- 
ments for  certain  definite  uses  of  lumber.  To  use  lumber  for  a  given  purpose,  when 
it  is  better  than  is  necessary  and  is  suitable  for  a  higher  use,  is  wasteful,  but  to  admit 

455 


456  APPENDIX  A 

lumber  to  a  grade  intended  for  a  given  use,  when  it  possesses  defects  which  unfit  it 
for  this  use,  destroys  the  basis  of  sound  business. 

Again,  a  grade,  as  appUed  to  the  lumber  of  a  given  species  or  region,  must  be  so 
defined  as  to  permit  of  securing  a  sufficient  volume  of  output  qualifying  for  the 
grade  to  make  it  a  commercial  or  market  product.  No  purpose  is  served  in  making 
grades  for  clear  lumber,  to  apply  to  second-growth  stands  which  produce  little  if  any 
lumber  of  this  grade. 

Defects  characteristic  of  one  species  but  absent  or  rare  in  others  call  for  modi- 
fications of  grading  rules  to  suit  the  species  in  order  to  prevent  the  rejection  of  too 
large  a  percentage  of  the  output  for  grades  for  which  it  is  othen\dse  suited. 

To  secure  uniformity  in  both  definition  and  application,  gi-ades  of  lumber  are 
established  by  regional  associations  of  lumber  manufacturers  and  dealers,  which 
frequently  employ  a  corps  of  grading  insjiectors  acting  under  a  central  head.  These 
grading  rules  are  modified  from  time  to  time  as  market  conditions  change.  The 
latest  specifications  for  any  region  or  species  should  be  obtained  from  the  local 
associations.  Not  only  do  specifications  change,  but  there  is  considerable  fluctua- 
tion in  their  application  as  a  whole,  and  in  individual  mills,  which  it  is  the  purpose 
of  inspection  and  standardization  to  avoid  as  far  as  possible. 

354.  Grades  for  Remanufactured  and  Finished  versus  Rough  Lumber.  For 
the  purpose  of  valuing  logs  and  standing  timber,  onlj'  those  grades  of  lumber  are 
serviceable  which  can  be  apphed  with  some  degree  of  accuracy  directly  to  the  log. 
Liunber  is  finally  sold  on  the  basis  of  its  grade  when  finished  or  remanufactured. 
But  these  final  grades  are  made  the  basis  of  the  grading  of  the  rough  boards  on  the 
sorting  table,  with  the  modification  that  the  better  grades  of  rough  lumber  may  be 
split  up  into  several  special  grades,  including  lumber  intended  for  specific  uses.  In 
all  such  cases,  the  general  grade  of  the  rough  lumber  is  the  basis  of  log  grading. 

Structural  and  dimension  lumber  calls  for  a  different  basis  of  grading,  as  do 
sawed  cross  ties.  Where  a  considerable  proportion  of  the  output  is  in  these  forms, 
the  basis  of  log  grading  is  affected.  While  a  system  based  on  this  form  of  products 
could  be  worked  out  for  logs,  it  has  not  been  attempted,  but  the  basis  of  log  grades 
has  been  confined  to  1-inch  rough  lumber.  The  average  value  of  each  standard  grade 
of  lumber  may  be  obtained  from  that  of  the  grades  of  remanufactured  lumber  which 
it  produces. 

It  is  always  possible  to  recognize  and  estimate  separately  the  quantity  and  value 
of  trees  containing  unusual  or  special  dimensions,  in  the  nature  of  piece  products. 

355.  General  Factors  which  Serve  to  Distinguish  Lumber  Grades.  Face.  Lum- 
ber is  graded  on  the  appearance  of  the  poorest  face  for  certain  uses  and  in  certain 
regions.  For  other  uses  and  in  other  regions,  the  appearance  of  the  best  face  deter- 
mines the  grade.  The  specific  practice  is  in  each  case  determined  by  the  local  grad- 
ing rules. 

Defects.  With  respect  to  perfect  pieces,  all  departures  from  standard  as  defined 
in  §  352  constitute  defects.  With  regard  to  each  specific  grade,  the  defects  which 
disqualify  the  piece  and  throw  it  into  lower  grade  are  defined.  Defects  which  dis- 
qualify in  one  grade  may  be  accepted  in  the  grade  below. 

The  principal  defects  are  caused  by, 

1.  Knots,  sound  or  unsound,  encased,  firm  or  loose,  and  knot  holes. 

2.  Rot. 

3.  Shake,  season  checks,  seams  and  cracks. 

4.  Pitch. 

5.  Worm  holes. 

6.  Stain,  either  as  blue  sap  or  red  heart. 


LUMBER   GRADES  AND  LOG  GRADES  457 

7.  Mechanical  defects,  as  splits,  torn  grain. 

8.  Wane,  or  round  edges. 

These  defects  or  any  combination  of  them  may  reduce  grade  by  affecting  the 
utihty  and  value  of  the  piece  through  its  appearance,  surface,  texture,  or  strength. 

356.  Grouping  of  Grades  of  Rough  Lumber.  Even  when  standard  grades  of  rough 
lumber  only  are  considered,  it  is  best  not  to  attempt  to  base  log  grades  or  quality  of 
standing  timber  on  the  determination  of  given  per  cents  of  each  of  these  standard 
grades  supposed  to  be  contained  in  the  logs.  Instead,  these  grades  should  be  com- 
bined into  a  few  groups  with  similar  characteristics  conforming  to  the  grading  rules 
for  the  species  and  region.  Three  such  groups  may  be  distinguished  in  softwoods, 
namely,  finishing  grades,  factory  or  shop  grades,  and  common  grades.  Based  on  the 
practice  of  "  sound  "  scaling,  a  fourth  group  may  be  made  to  include  grades  which 
contain  rot  or  other  defects  in  sufficient  quantity  to  cause  their  rejection  in  scaling 
logs. 

Finishing  grades  include  all  of  the  so-called  upper  grades  of  lumber,  characterized 
by  freedom  from  all  but  a  few  small  defects.  These  grades  are  suitable  for  use  with- 
out being  cut  up,  for  purposes  requiring  appearance  as  the  prime  factor,  combined 
with  definite  and  sometimes  considerable  width  and  length. 

These  grades  are  used  for  outside  and  inside  finish  and  for  many  purposes  of 
manufacture.  The  entire  piece  is  graded  as  a  unit,  any  defect  serving  to  reduce  its 
grade  as  a  whole. 

Factory  or  Shop  Grades.  Boards  suitable  for  factory  or  shop  grades  are  such  as 
will  yield  smaller  pieces  of  upper  grade  material  when  ripped  or  cut  up  as  to  exclude 
or  cull  out  disqualifying  defects.  In  these  grades,  therefore,  the  piece  is  not  graded  as 
a  unit  but  on  the  basis  of  the  per  cent  of  its  volume  that  can  be  utilized.  The 
remainder  is  rejected  as  refuse  and  may  therefore  contain  defects  of  any  character 
without  affecting  the  grade  of  the  piece. 

Common  Grades.  As  applied  to  lumber  cut  from  conifers  or  "  softwoods,"  com- 
mon lumber  is  distinguished  from  the  other  two  groups  by  a  general  coarseness  of 
appearance  caused  by  various  defects  or  combinations  of  defects,  such  as  nu- 
merous large  or  small  knots,  which  not  only  render  it  unsuitable  for  the  upper  grades 
but  prevent  cuttings  being  made  from  it  which  would  qualify  it  for  factory  grades. 

Common  lumber  of  this  class  is  graded  for  the  entire  piece  and  finds  its  principal 
use  in  construction.     Owing  to  the  large  volume  of  common  lumber,  in  conifers, 
which  constitutes  from  60  to  95  per  cent  of  the  total  output,  this  grou])  may  be 
subdivided  in  each  given  region.     These  specific  common  grades  are  not  always 
given  identical  names  any  more  than  are  the  grades  in  the  other  two  groups.     The 
most  widely  accepted  nomenclature  is. 
No.  1  Common, 
No.  2  Common, 
No.  3  Common. 

357.  Example  of  Grading  Rules.  Southern  Yellow  Pine. — Finishing,  or  Upper 
Grades.  "  A  "  Finishing,  inch,  Ij,  I5  and  2-inch,  dressed  one  or  two  sides,  up  to 
and  including  12  inches  in  width,  must  show  one  face  practically  clear  of  all  defects, 
except  that  it  may  have  .such  wane  as  would  dress  off  if  surfaced  four  sides. 

13-inch  and  wider  "  A  "  finishing  wiU  admit  two  small  defects  or  their  equivalent. 

"  B  "  Finishing,  inch,  Ij,  1^  and  2-inch,  dr&ssed  one  or  two  sides,  up  to  and 
including  10  inches  in  width,  in  addition  to  the  equivalent  of  one  split  in  end  which 
should  not  exceed  in  length  the  width  of  the  piece,  will  admit  any  two  of  the  following 
or  their  equivalent  of  combined  defects:  slight  torn  grain,  three  pin  knots,  one 
standard  knot,  three  small  pitch  pockets,  one  standard  pitch  pocket,  one  standard 


458  APPENDIX  A 

pitch  streak,  5  per  cent  of  sap  stain,  or  firm  red  heart;  wane  not  to  exceed  1  inch  in 
width,  J-inch  in  depth  and  ^  the  length  of  the  piece;  small  seasoning  checks. 

11-inch  and  wider  "  B  "  Finishing  will  admit  three  of  the  above  defects  or  their 
equivalent,  but  sap  stain  or  firm  red  heart  shall  not  exceed  10  per  cent. 

Select  Common  Finishing,  up  to  and  including  10-inch  in  width  will  admit,  in 
addition  to  the  equivalent  of  one  split  in  end  which  should  not  exceed  in  length  the 
width  of  the  piece,  any  two  of  the  following,  or  their  equivalent  of  combined  defects: 
25  per  cent  of  sap  stain,  25  per  cent  firm  red  heart,  two  standard  pitch  streaks, 
medium  torn  grain  in  three  places,  slight  shake,  seasoning  checks  that  do  not  show 
an  opening  through,  two  standard  pitch  pockets,  six  small  pitch  pockets,  two  stand- 
ard knots,  six  pin  knots,  wane  1  inch  in  width,  ^  inch  in  depth  and  one-third  the 
length  of  the  piece.  Defective  dressing  or  slight  skips  in  dressing  will  also  be  allowed 
that  do  not  prevent  its  use  as  finish  without  waste. 

11  and  12-inch  "  C  "  Finishing  will  admit  one  additional  defector  its  equivalent. 
Pieces  w^der  than  12  inches  \vill  admit  two  additional  defects  to  those  admitted  in 
10-inch  or  their  equivalent,  except  sap  stain,  which  shall  not  be  increased. 

Pieces  othenvise  as  good  as  "  B  "  will  admit  of  twenty  pin-worm  holes. 

Common  Grades.  No.  1  Common  boards,  dressed  one  or  two  sides,  will  admit 
any  number  of  sound  knots.  The  mean  or  average  diameter  of  any  one  knot  should 
not  be  more  than  2  inches  in  stock  8  inches  wide,  nor  more  than  2h  inches  in  stock 
10  and  12  inches  wide;  two  pith  knots;  the  equivalent  of  one  split,  not  to  exceed  in 
length  the  width  of  the  piece;  torn  grain,  pitch,  pitch  pockets,  slight  shake,  sap  stain, 
seasoning  checks,  firm  redheart;  wane  |  inch  deep  on  the  edge  not  exceeding  1  inch 
in  width  and  one-third  the  length  of  the  piece,  or  its  equivalent;  and  a  limited  num- 
ber of  pin-worm  holes  well  scattered;  or  defects  equivalent  to  the  above. 

No.  2  Common  boards,  dressed  one  or  two  sides;  No.  2  Shiplap,  Grooved  Roof- 
ing, D.  &  M.  and  Barn  Siding  will  admit  knots  not  necessarily  sound; .  but  the  mean 
or  average  diameter  of  any  one  knot  shall  not  be  more  than  one-third  of  the  cross 
section  if  located  on  the  edge,  and  shall  not  be  more  than  one-half  of  the  cross  section 
if  located  away  from  the  edge;  if  sound  may  extend  one-half  the  cross  section  if 
located  on  the  edge,  except  that  no  knot,  the  mean  or  average  diameter  of  which 
exceeds  4  inches  should  be  admitted;  worm  holes,  splits  one-fourth  the  length  of 
the  piece,  wane  2  inches  wide  or  through  heart  shakes,  one-half  the  length  of  the 
piece;  through  rotten  streaks  5  inch  mde  one-fourth  the  length  of  the  piece,  or  its 
equivalent  of  unsound  red  heart;  or  defects  equivalent  to  the  above. 

A  knot  hole  2  inches  in  diameter  will  be  admitted,  provided  the  piece  is  otherwise 
as  good  as  No.  1  Common. 

Miscut  1-inch  common  boards  which  do  not  fall  below  f-inch  in  thickness  shall 
be  admitted  in  No.  2  Common,  provided  the  grade  of  such  thin  stock  is  otherwise 
as  good  as  No.  1  Common. 

No.  3  Common  boards.  No.  3  Common  Shiplap,  D.  &  M.  and  Barn  Siding  is  defect- 
ive lumber,  and  will  admit  of  coarse  knots,  knot  holes,  very  wormy  pieces,  red  rot, 
and  other  defects  that  will  not  prevent  its  use  as  a  whole  for  cheap  sheathing,  or 
which  will  cut  75  per  cent  of  lumber  as  good  as  No.  2  Common. 

358.  Relation  between  Grades  of  Lumber  and  Cull  in  Log  Scaling.  From  the 
standpoint  of  the  lumber  trade,  lumber  which  is  merchantable,  no  matter  what  the 
extent  and  character  of  defects  it  contains,  is  placed  in  a  recognized  grade,  while 
cull  lumber  is  lumber  which  is  not  merchantable.  Grades  of  common  lumber  below 
No.  3  are  sawed  from  unsound  or  defective  portions  of  logs,  which  would  be  culled 
in  scaling.  In  mill-scale  studies  and  in  determining  log  grades,  it  is  proper,  there- 
fore to  throw  all  grades  under  No.  3  Common  into  the  group  termed  cull.     In  addi- 


LUMBER  GRADES  AND  LOG  GRADES  459 

tion,  the  grade  designated  as  No.  3  Common  may  in  certain  regions  contain  unsound 
material  which  would  not  be  scaled  on  the  basis  of  sound  scale.  Hence  a  portion  of 
the  No.  3  grade,  if  so  constituted,  plus  all  of  the  cull  grades  of  lumber,  when  utilized, 
go  to  increase  the  amount  of  over-run  secured  in  manufacture. 

From  one  to  three  grades  of  lumber  below  No.  3  Common  may  be  recognized, 
according  to  the  species  and  region. 

Common  Grades  Culled  in  Sound  Scale,  of  Logs.  Southern  Yellow  Pine.  No.  4 
Common  boards  shall  include  all  pieces  that  fall  below  the  grade  of  No.  3  Common, 
excluding  such  pieces  as  will  not  be  held  in  place  by  nailing,  after  wasting  one-fourth 
the  length  of  the  piece  by  cutting  into  two  or  three  pieces;  mill  inspection  to  be 
final. 

359.  Log  Grades.  Determination.  The  purpose  of  defining  log  grades  is  to 
furnish  a  basis  for  separating  the  logs  into  groups  w^iose  average  value  or  price  per 
1000  board  feet  can  be  determined,  instead  of  attempting  to  arrive  at  an  average 
price  for  the  entire  run  of  logs.  Three  such  groups  permit  of  a  sufficient  diflferentia- 
tion  for  this  purpose. 

Where  logs  are  not  bought  or  sold,  but  standing  timber  is  manufactured  by  the 
purchaser,  log  grades  (§  87)  form  the  best  basis  for  appraising  the  value  of  this  timber. 

The  specification  for  determining  the  grade  of  logs  must  apply  to  the  external 
appearance  and  dimensions  of  the  log.  In  application,  logs  on  the  border  line  between 
two  grades  are  usually  thrown  to  the  gi-adc  below,  since  a  part  of  the  surface  is  invis- 
ible.    Log  grades  are  based  on 

L   Minimum  diameters  and  lengths. 

2.  Surface  appearance,  and  presence  of  knots  or  visible  defects. 

3.  Judgment  of  scaler,  based  on  1  and  2  as  to  the  minimum  per  cent  of  upper 

or  better  grades  of  lumber  contained  therein. 

The  specifications  for  log  grades  are  more  elastic  than  for  lumber  grades,  since 
the  presence  of  a  small  per  cent  of  high  grade  lumber  may  serve  to  ofi'set  serious 
defects  and  give  the  log  the  value  of  a  grade  from  which  it  would  be  excluded  if  based 
solely  on  quantity  or  scale.  These  specifications  should  be  drawn  in  such  a  manner 
as  to  furnish  the  most  serviceable  basis  of  subdivision  of  the  existing  range  of  quality 
found  for  the  species  and  region,  which  object  may  be  secured  by  modifying  the 
requirements  as  to  size  and  per  cent  of  upper  grades  required  for  logs  of  first  and 
second  grades. 

Log  grades  should  be  established  only  after  thorough  mill-scale  studies,  and  by 
some  agency  similar  to  that  of  the  United  States  Forest  Service  or  a  Lumber  Manu- 
facturers' Association,  .so  as  to  secure  uniformity  over  as  wide  an  area  as  possible. 

Within  the  limits  of  a  log  grade  a  certain  variation  in  average  quality  will  occur 
in  different  quantities  of  logs,  owing  to  the  preponderance  of  higher  or  lower  grades 
of  lumber  within  the  limits  set.  The  quality  of  the  logs  which  form  the  basLs  of  the 
mill-scale  study  may  be  better  or  poorer  than  the  average,  even  after  classification 
into  grades.  But  as  logs  and  timber  stumpage  are  worth  considerably  less  than 
lumber,  it  is  unnecessary  to  attempt  a  greater  refinement;  nor  could  it  be  practically 
applied. 

Diameter  For  logs  of  the  best  grade,  diameter  is  a  reliable  guide.  Up  to  a 
certain  size,  trees  retain  the  branches,  either  alive  or  dead,  and  the  central  bole  of 
the  tree  is  filled  with  these  knots.  Stunted,  slow-growing,  and  consequently  small 
trees  still  have  these  knots,  and  during  their  growth,  have  made  very  little  clear 
lumber.  Large  trees,  on  the  other  hand,  even  if  no  older,  have  laid  on  niuch  clear 
wood  outside  of  the  knots. 

The  minimum  diameter  for  tbo  highest  grade  can  be  fixed  to  include  jiractically 


460  APPENDIX  A 

all  logs  of  this  class,  not  barred  by  knots  or  defects.  This  diameter  will  vary  with 
the  same  species  in  different  regions,  and  for  different  species. 

Effect  of  Defect  upon  Grades  of  Logs.  The  defect  most  easily  seen,  both  in  logs 
and  standing  timber,  is  a  knot.  In  grading  hardwood  logs,  one  sound,  bright  knot, 
with  a  maximum  diameter  of  4  inches  is  taken  as  a  standard  defect.  Other  defects 
are  compared  with  this  knot,  on  the  basis  of  an  equal  amount  of  damage  to  quality. 
These  may  be  worm  holes,  smaller  or  larger  knots,  shake,  rot,  cat  faces  or  fire  scars. 
The  maximum  number  of  standard  defects,  or  their  equivalent,  is  prescribed  for  each 
grade  of  logs. 

For  conifers,  a  different  system  is  employed,  and  the  specifications  lay  stress  on 
the  possible  percentage  of  yield  of  certain  grades,  with  indication  as  to  the  general 
appearance  and  character  of  defect  in  logs  which  will  yield  this  ratio. 

Defects  are  of  two  classes,  those  which  cause  loss  of  grade,  but  no  discount  in 
total  scale,  i.e.,  sound  defects,  and  those  which  require  elimination  from  the  scale 
of  the  defective  part.  To  the  first  class  belong  sound  knots,  stain,  firm  red  heart 
and  pitch.  In  the  second  class  fall  rot,  shake,  fire  scars,  cat  faces,  and  crook  or 
sweep.     Worm  holes  may  be  in  either  class,  according  to  size  and  frequency. 

In  the  grading  of  hardwood  logs,  no  distinction  is  made,  and  the  presence  of  more 
than  two  "  standard  "  defects  serves  to  throw  the  log  into  the  lowest  class,  or  No. 
2,  except  when  over  24  inches  in  diameter,  when  it  must  cut  at  least  75  per  cent  of 
No.  1  common  and  better  lumber. 

With  conifers,  the  presence  of  either  class  of  defect  will  not  reduce  the  grade  of 
a  log  as  long  as  the  minimum  i)ercentage  of  upper  grades  can  still  be  secured.  But 
in  reaUty,  the  value  of  the  log  is  greatly  lessened  by  such  defects.  With  increasing 
amounts  of  defect,  the  log  is  de-graded  cither  to  second  or  third  grade,  and  finally 
is  rejected  as  cull. 

360.  Examples  of  Log  Grades.  Hardwoods — National  Hardwood  Lumber 
Association,  1916  Oak,  White  and  Red. 

No.  1  logs.  2  inches  of  bright  sap  is  no  defect.  Sap  in  excess  of  2  inches  is  one 
standard  defect. 

No.  1  logs  must  be  24  inches  and  over  in  diameter. 

24  to  29  inches  inclusive  will  admit  of  one  standard  defect  or  its  equivalent. 

30  inch  and  over  will  admit  of  two  standard  defects  or  their  equivalent. 

Select.     Select  logs  must  be  18  inches  and  over  in  diameter. 

2  inches  of  bright  sap  is  no  defect.     Sap  in  excess  of  2  inches  is  one  standard  defect. 

18  to  21  inches  wide  inclusive  must  have  ends  and  surface  clear. 

22  and  23  inches  will  admit  of  one  standard  defect  or  its  equivalent. 

24  inches  and  over  will  admit  of  one  more  standard  defect  than  is  admitted  in  No. 
1  logs  of  same  size. 

No.  2  logs.     No.  2  logs  must  be  IG  inches  and  over  in  diameter. 

Bright  sap  is  not  a  defect  in  this  grade. 

16-  and  17-inch  will  admit  of  one  standard  defect  or  its  equivalent. 

18  to  23  inches  inclusive  will  admit  of  two  standard  defects  or  their  equivalent. 

24  inches  and  over  must  cut  75  per  cent  or  more  into  No.  1  common  and  better 
lumber. 

The  grades  for  other  species  arc  similar. 

Softwoods — Columbia  River  Log  Scaling  and  Grading  Bureau,  Washington 
and  Oregon,  1920. 

No.  1  Logs.  No.  1  logs  shall  be  logs  which,  in  the  judgment  of  the  scaler,  will  be 
suitable  for  the  manufacture  of  lumber  in  the  grades  of  No.  2  clear  or  better  to  an 
amount  of  not  less  than  50  per  cent  of  the  scaled  contents. 


LUMBER  GRADES  AND  LOG  GRADES  461 

No.  1  logs  shall  contain  not  less  than  six  annual  rings  to  the  inch  in  the  outer 
portion  of  the  log  equal  to  one-half  of  the  log  content;  and  No.  1  logs  shall  be  straight 
grained  to  the  extent  of  a  variation  of  not  more  than  2  inches  to  the  lineal  foot  for  a 
space  of  2  lineal  feet  equidistant  from  each  end  of  the  log. 

Rings,  rot,  or  any  defect  that  may  be  eliminated  in  the  scale,  are  permitted  in  a 
No.  1  log,  providing  their  size  and  location  do  not  prevent  the  log  producing  the 
required  amount  of  No.  2  clear  or  better  lumber. 

A  No.  1  log  may  contain  a  few  small  knots  or  well  scattered  pitch  pockets  as  per- 
mitted in  grades  of  No.  2  clear  or  better  lumber;  or  may  contain  a  very  few  grade 
defects  so  located  that  they  do  not  prevent  the  production  of  the  required  amount  of 
clear  lumber. 

No.  2  Logs.  No.  2  logs  shall  be  not  less  than  12  feet  in  length,  having  defects 
which  prevent  their  grading  No.  1,  but  which,  in  the  judgment  of  the  scaler,  will 
be  suitable  for  the  manufacture  of  lumber,  principally  in  the  grades  of  No.  1  common 
or  better. 

No  3  Logs.  No.  3  logs  shall  be  not  less  than  12  feet  in  length,  having  defects 
which  prevent  their  grading  No.  2  but  which,  in  the  judgment  of  the  scaler,  will  be 
suitable  for  the  manufacture  of  inferior  grades  of  lumber. 

Cull  Logs.  Cull  logs  shall  be  any  logs  which  do  not  contain  335  per  cent  of  sound 
lumber. 

Logs  which  contain  considerable  clear  lumber  but  not  sufficient  to  grade  No.  1, 
and  contain  also  large  coarse  knots  or  other  grade  defects  of  No.  3  quality,  will  be 
classed  as  No.  2  if  the  average  value  of  the  lumber  falls  in  this  class,  regardless  of  its 
actual  grade.  Logs  which  are  on  the  border  Hne  between  two  grades  should  be  graded 
alternately  or  in  equal  amount  in  the  upper  and  the  lower  grade. 

361.  Mill-Grade  or  Mill-scale  Studies.  In  §81  and  §82  it  was  shown  that  the 
log  scale  should  make  no  attempt  to  measure  the  actual  sawed  contents,  which  is 
the  sum  of  the  scale,  plus  this  over-run.  It  is  equally  impossible  for  the  scaler  to 
separate  his  scale  into  grades,  for  in  doing  so  he  would  be  compelled  to  substitute 
judgment  for  facts;  yet  the  actual  value  of  logs  can  be  determined  only  by  a  knowl- 
edge of  both  of  these  factors. 

When  the  sawed  output  of  a  run  of  logs  has  been  tallied  and  totaled  separately 
by  grades,  its  comparison  with  the  log  scale  shows  for  the  entire  quantity  scaled,  the 
average  over-run  per  thousand  board  feet  of  scale,  and  the  per  cent  represented  by 
each  grade  produced.  The  value  of  the  product  of  an  average  thousand  feet  B  M. 
log  scale  in  terms  of  sawed  lumber  is  determined  by  first  multiplying  the  price  of 
each  grade  of  lumber  sawed  by  the  per  cent  of  the  grade  in  one  thousand  board  feet, 
adding  the  bj- -products,  and  multiplying  b}-  the  total  per  cent  of  over-run. 

This  general  check,  applied  to  an  average  run  of  logs,  and  termed  the  mill  run, 
will  serve  to  determine  the  value  of  similar  average  sizes  and  quality.  But  for 
timber  averaging  larger  or  better,  or  smaller,  knottier  and  poorer,  the  true  value  can 
be  obtained,  by  this  method,  only  after  sawing. 

But  individual  logs  of  similar  sizes  possessing  certain  distinctive  features,  as 
shown  by  surface  indications  such  as  clearness,  knots  and  other  defects,  will  cut  out 
about  the  same  per  cent  of  grades  and  values  wherever  found. 

By  using  the  log  as  the  standard,  it  is  possible  to  apply  the  results  of  mill-scale 
studies  of  separate  logs  to  stands  whose  average  quality  may  be  entirely  different 
from  that  which  is  being  sawed,  provided  only  that  some  logs  of  all  qualities  are 
analyzed.  For  this  reason,  mill-scale  studies  should  be  based  on  the  separate  analy- 
sis of  the  product  of  individual  logs,  by  grades  of  lumber.  Such  studies  determine, 
for  logs  of  each  diameter,  length  and  grade,  first,  the  over-run  in  sound  lumber,  and 


462  APPENDIX  A 

in  all  merchantable  grades;  second,  the  amount  of  each  standard  grade  of  rough 
boards,  expressed  in  per  cent  of  the  total  scale  of  the  log,  net  and  gross. 

362.  Method  of  Conducting  Mill-scale  Studies.  A  tabulation,  classification 
and  summary  of  the  logs  so  anah'zed  permits,  first,  a  correlation  between  logs  of  given 
sizes,  appearance  and  defects,  and  the  actual  sawed  contents  in  grades  which  these 
logs  will  produce,  hence  their  actual  value;  second,  the  adoption  of  arbitrary 
specifications  for  separating  the  logs  themselves  into  log  classes  or  grades;  third,  a 
comparison  of  the  value  of  logs  of  each  size  and  grade  with  the  cost  of  logging  them, 
enabling  both  owner  of  stumpage  and  operator  to  determine  both  the  lower  limits  of 
merchantability  as  to  minimum  size  and  per  cent  of  sound  lumber  in  a  log  which 
warrants  its  removal  and  manufacture,  and  in  case  only  a  portion  of  the  merchant- 
able stand  is  removed,  to  know  the  relative  value  and  profit  of  removing  certain 
definite  classes  and  sizes  of  material  and  leaving  others  (§  96). 

The  steps  in  a  mill-scale  study  are: 

1 .  Decision  as  to  the  exact  number  and  designation  of  the  grades  of  rough  lumber 
to  be  tallied. 

2.  Scale  and  record  of  each  log,  on  the  deck.  If  log  grades  have  already  been 
adopted,  the  scaler  assigns  each  log  to  its  apparent  grade.  A  full  record  would 
embrace  the  following  items:  number  of  log  (serial);  length,  in  feet  and  inches; 
position  in  tree,  as  butt,  middle,  top;  species;  average  diameter  inside  bark  at  small 
end ;  at  large  end ;  width  of  sapwood ;  thickness  of  bark ;  scale,  by  standard  log  rule, 
full  and  net  after  deductions  for  cull  defects;  estimated  log  grade;  description  of 
defects,  preferably  graphic,  on  a  diagram  showing  large  and  small  ends,  and  both 
sides  of  logs.  This  record  requires  one  man,  an  experienced  log  scaler,  who  will 
place  a  number  on  each  log  to  coincide  with  his  record.  Logs  scaled  sound  are  given 
a  special  mark,  and  separated  in  the  final  tables. 

3.  Identification  of  this  product  of  separate  logs.  A  marker  standing  behind  the 
head  saw  marks  with  crayon  each  piece  sawed  from  a  log.  The  number  of  the  log  is 
placed  on  the  first  few  pieces.  Different-colored  crayons  are  used  for  alternate  logs. 
A  count  may  be  made  of  the  total  number  of  pieces  from  a  log,  as  a  check  on  the  tally. 
This  work  is  made  quite  difficult  by  a  resaw,  which  tends  to  mix  the  products  of  con- 
secutive logs  on  the  chains  and  requires  the  marking  of  both  sides  of  the  piece.  Gang 
saws  further  complicate  the  study.  The  marker  can  also  check  logs  scaled  as  sound 
for  unseen  defects  appearing  in  sawing,  and  make  final  record  of  the  logs  which  saw 
up  sound. 

4.  Record  of  grades  and  sizes.  An  expert  grader,  familiar  with  the  standard  for 
the  species  and  locality,  will  grade  each  piece.  The  record,  kept  on  a  separate  sheet 
for  each  log,  and  given  the  log  number,  will  show  length,  width,  and  grade,  by  pieces, 
and  a  recapitulation  or  summary  for  the  log,  giving  in  addition  to  the  data  copied 
from  the  scales,  the  total  board-foot  contents  in  each  grade,  and  the  per  cent  of  the 
sound  scale  which  this  equals.  This  tally  requires  the  services  of  a  tallyman,  mak- 
ing a  crew  of  four  men. 

5.  Additional  data  needed,  (a)  Data  on  per  cent  of  total  contents  utilized 
embrace  the  measurement  of  the  cubic  contents  of  a  log,  and  the  analysis  of  the 
volume  which  goes  into  slabs,  edgings,  and  sawdust. 

(b)  Data  on  sawing  practice  include  gage  of  saws,  actual  widths  and  lengths  of 
lumber  sawed,  efficiency  of  sawyers,  methods  of  sawing,  and  the  output  or  per- 
formance of  mill. 

(r^  Data  on  the  character  of  the  timber  and  logs  measured,  to  indicate  the 
comparison  with  other  tracts,  whether  of  higher  or  lower  quality. 

6.  Tables  or  compilation  of  results.     The  logs  can  be  classified,  first,  into  sound 


LUMBER  GRADES  AND  LOG  GRADES  463 

and  defective.  Where  log  grades  are  used,  these  grades  are  also  separated. 
Next,  the  logs  in  each  separate  class  are  sorted  into  diameter  classes,  1-inch  or  2- 
inch  (volume  based  on  differences  of  100  board  feet  was  used  in  the  studies  conducted 
in  District  1,  Missoula,  Montana).  As  a  result  of  this  tabulation,  the  logs  when  orig- 
inally classed  by  the  scaler  into  grades  by  judgment,  can  be  re-graded  in  accordance 
with  actual  specifications  for  the  grades.  A  sample  form  of  tabulation  would  be, 
by  columns: 

Diameter  class. 
Number  of  logs  as  a  basis. 
Average  lengths  of  logs. 

Per  cent  and  value  per  1000  board  feet  of  each  grade,  represented  in  the  prod- 
uct obtained. 
Total  lumber  tally,  excluding  cull  lumber  sawed. 
Over-run,  excluding  cull  lumber  sawed. 
Tally  of  cull  lumber  sawed. 
Over-run,  including  cull  lumber  sawed. 
Net  scale. 

Per  cent  of  total  net  scale  in  each  class  of  logs. 
Value  per  1000  board  feet,  based  on  net  tally. 
Value  per  1000  board  feet,  based  on  net  scale. 
Gross  scale. 
Per  cent  deducted  for  defect. 

These  data,  shown  thus  for  each  class  of  logs,  can  be  totaled  for  all  logs,  and 
averaged. 

7.  Deductions  or  summaries.  Irregularities  are  sure  to  occur  in  the  final  sum- 
maries. These  can  frequently  be  evened  off  by  means  of  curves.  The  final  curves 
and  tables  should  show,  for  each  separate  log  grade,  the  per  cent  of  each  grade  of 
lumber  obtained  for  logs  of  each  diameter  class,  and  the  value  of  the  average  log  for 
the  class. 

Effect  of  Waste  or  Cull.  Such  studies  indicate  the  effect  of  increasing  amounts 
of  waste  or  cull  upon  the  value  of  the  gross  scale  or  log.  Cull  lumber  may  not 
reduce  the  sale  value  of  the  residual  lumber  cut  from  the  log,  but  the  cost  of  log- 
ging is  based  upon  the  actual  size  of  the  log,  which  is  best  measured  by  its  gross 
scale.  The  value  of  the  ])roduct  divided  by  this  total  scale  gives  a  more  correct 
gage  of  the  value  of  the  whole  log  in  terms  of  price  per  1000  board  feet,  for  the 
purpose  of  determining  whether  the  log  is  merchantable 

A  crew  of  five  men  can  usually  tally  two  hundred  logs  per  day  of  average 
sizes.  A  single  mill-scale  study  requires  from  one  thousand  to  two  thousand  logs 
for  best  results 

Instructions  for  Recording  Data,  U.  S.  Forest  Sernce.  Logs  should  be  lettered 
A,  B,  C,  etc.,  A  being  the  butt  log.  The  species  may  be  written  out  or  the  atlas 
number  may  be  used,  thus:  "  Loblolly  pine"  or  "  P76."  The  log  length  should 
be  measured  to  the  nearest  tenth  of  a  foot.  The  crook  may  be  measured  by  noting 
the  distance  in  inches  between  a  straight  line  connecting  the  ends  of  the  log  on  the 
concave  side  and  the  log  itself.  If  relative  terms  such  as  ""  V  "  (vcr>'  crooked), 
"  M  "  (moderately  crooked),  and  "  S  "  (slightly  crooked)  are  used,  they  should  be 
carefully  defined.  Thus,  if  the  crook  is  more  than  one-half  the  diameter  of  the  log 
the  term  "  V  "  might  be  applied;  if  one-quarter  to  one-half  the  diameter  it  would 
be  '  M  ' ';  while  less  than  one-quarter  it  would  be  "  S."  If  practically  straight 
indicate  this  by  ''  O  "  after  heading  •'  Crook." 


464  APPENDIX  A 

Form  of  Record  for  Mill-scale  Studies,  U.S.  Forest  Service 


Form  234 
Revised  July  1,  1912 

Large 

END. 

Small 

END. 

Tree Log 

(Number.)                                  (Letter.) 

D.  i.  b„ 

Species                                                             .      ... 

Width  of  bark. 

Log  length Crook Knots 

D.  o.  b.. 

1 

2 

3 

Width  of  sap, 

HiiiKS, 

Cubic  )  Peeled. 

I  With  bark. 

Full  scale, 

Net  scale. 

Sawod  out. 

4 

!r. 

7 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

8 

9 

10 

M 

12 

Remarks: 


Date. 


191 


LUMBER  GRADES  AND  LOG  GR.\DES  465 

Knottiness  may  not  always  be  of  importance,  but  if  it  is  recorded  letters  may 
be  used,  as  for  crook.  Two  diameters  inside  bark  at  right  angles  should  be  measured 
and  the  average  recorded  to  the  nearest  tenth  inch.  The  average  width  of  bark, 
measured  on  a  radius,  should  be  recorded,  care  being  taken  to  make  the  measurements 
where  bark  is  not  partly  worn  oflf.  The  width  of  sap,  in  case  desired,  should  be 
measured  along  an  average  radius.  In  case  the  age  at  either  end  of  the  log  is  found 
it  can  be  inserted  opposite  "  Rings."  If  the  cubic  content  of  a  log  is  found  in  the 
office  it  may  be  entered  opposite  "  Cubic  feet."  "  Full  scale  "  means  the  number  of 
board  feet  that  would  be  tallied  by  the  log  scaler  if  the  log  were  straight  and  sound. 
"  Net  scale  "  is  the  nxmiber  of  board  feet  taUied  by  the  scaler  after  deducting  for 
defects  of  any  kind.  "  Sawed  out  "  is  the  number  of  board  feet  of  lumber  actually 
sawed  out. 

The  large  spaces  are  for  the  dimensions  of  boards  sawed  out,  each  space  being 
for  a  separate  grade.  The  name  of  the  grade  may  be  written  or  stamped  in  at  the 
head  of  the  column.  The  total  niunber  of  board  feet  of  each  grade  sawed  out  should 
be  entered  opposite  the  proper  grade  number  in  the  small  spaces  under  "  Sawed  out," 
which  is  the  grand  total  of  these  grade  totals.  The  boards  may  be  tallied  thus: 
"  1X3X16,"  meaning  a  board  1  inch  thick,  3  inches  wide,  and  16  feet  long.  Frac- 
tions may  be  indicated  thus:  31X3^X12  (3|"X3i"Xl2').  As  a  rule  the  thickness 
should  be  recorded  to  the  nearest  even  quarter  inch  below,  the  width  to  the  nearest 
inch  below,  and  the  length  to  the  nea/ast  foot  below  the  actual  measurement.  In 
some  cases  it  may  be  preferable  to  tally  the  number  of  board  feet  direct.  This 
means  that  the  number  of  board  feet  in  a  board  is  read  from  a  rule  and  entered  at 
once.     Thus  for  a  board  1"  X3"  X 12',  the  figure  3  would  be  tallied. 


APPENDIX  B 
THE  MEASUREMENT  OF  PIECE  PRODUCTS 

363.  Basis  of  Measurement.  Any  finished  products  of  uniform  or  standard  dimen- 
sions, manufactured  or  cut  from  trees  or  logs  may  be  measured  by  tallying  or  count- 
ing the  pieces.  The  size  or  contents  of  the  standard  piece  determines  its  value, 
either  directly  or  by  conversion  to  cubic  or  board-foot  contents.  The  relative 
value  of  pieces  of  different  sizes  is  seldom  directly  proportional  to  their  cubic  volume, 
though  for  such  products  as  mining  timbers  this  may  be  true.  But  for  piling  and 
poles,  value  per  cubic  foot  increases  with  increased  length.  The  contents  of  sawed 
or  hewn  pieces  of  rectangular  shape  is  easily  computed  in  board  feet.  Finished  pieces 
may  be  classed  as  round,  hewn,  or  manufactured  products.  Squares  and  bolts 
intended  for  further  manufacture  may  be  sold  by  count  (§9). 

364.  Round  Products.  RoiukI  products  include  poles,  piling,  posts,  mine 
timber,  and  certain  lesser  products  such  as  hop  poles  and  converter  poles.  Prac- 
tically all  round  pieces  are  intended  for  uses  requiring  durability  against  atmospheric 
and  soil  moisture,  and  strength  to  support  weight  or  strains.  Peeling  reduces 
weight  for  transportation. 

Durability  differs  markedly  with  different  species;  hence  whenever  two  or  more 
species  are  available,  at  least  two  classes  of  product  are  recognized,  the  first  con- 
taining the  more  durable  or  resistant  species,  the  second,  those  which  decay  more 
rapidly  or  require  preservative  treatment. 

Round  products  are  classed  by  length  and  diameter.  Both  minimum  and  maxi- 
mum specifications  are  quoted  for  length.  For  diameter,  the  minimum  is  given 
for  each  grade,  since  an  excess  adds  to  strength  of  piece.     Prices  are  fixed  by  grades. 

Straightness  is  a  quality  necessary  to  strength,  in  poles  and  especially  in  piling. 
The  degree  of  crook  or  sweep  permitted  in  such  products  is  always  specified. 

A  minimum  taper  is  desired  in  poles  and  piles,  especially  when  long,  in  order  to 
diminish  weight  in  handling.  The  diameter  or  circumference  at  both  ends  of  poles 
and  piling  is  specified,  and  both  minimum  and  maximum  limits  given,  corresponding 
to  specified  top  diameters.  Such  limitations  must  coi respond  to  the  average  shape 
of  the  material  available,  both  to  insure  strength  and  prevent  rejection  of  too  large 
a  percentage  of  pieces. 

Defects  which  will  weaken  the  piece  or  decrease  its  durability  serve  to  reject 
products  of  this  character.  The  specifications  are  remarkably  similar  whether  for 
poles,  piles,  mining  timbers  or  cross  ties.  Such  defects  are  shake,  checks,  splits, 
large  coarse  or  rotten  knots  which  weaken  the  piece,  and  rot.  When  the  qualities 
of  the  piece  for  the  use  for  which  it  is  intended  permit  of  knots,  or  of  a  certain  amount 
of  center  or  pipe  rot,  these  defects  may  be  permitted,  especially  if  their  exclusion 
would  cause  the  rejection  of  a  large  percentage  of  the  output.  For  poles,  the  presence 
of  center  rot  requires  an  increased  diameter  at  the  butt,  for  acceptance  of  piece. 

Round  products  as  a  class  give  almost  complete  utilization  of  the  bolt  or  log,  and 
of  the  tree.  The  ends  of  piling,  cross  ties,  and  butts  of  poles  are  cut  square  with  a 
saw,  and  the  only  waste  is  the  bark.     Where  there  is  a  market  for  posts  or  small 

46(3 


THE  MEASUREMENT  OF  PIECE  PRODUCTS 


467 


mine  props,  the  tops  are  also  utilized  down  to  3  or  4  inches.  These  small  round  prod- 
ucts also  permit  the  utilization  of  suppressed  trees  and  small  timber,  thus  reducing 
total  per  cent  of  waste  in  a  stand  to  a  minimum. 

365.  Poles.  Standard  poles  are  20  feet  or  more  in  length,  and  are  used  prin- 
cipally for  telegraph  or  telephone  lines.  Specifications  are  based  usually  on 
circumference  rat'  er  than  diameter.  Since  the  ratio  between  the  two  measure- 
ments for  a  circle  is  3.1416  to  1,  and  this  is  exceeded  for  eccentric  cress  sections, 
specifications,  especially  for  large  sizes,  call  for  Ho  1  inch  greater  circumference  than 
the  proportion  of  3  to  1  for  dry  poles  and  an  extra  5  to  f  inch  for  green  or  water- 
soaked  poles. 

Whit';  cedar,  which  furnishes  the  larger  part  of  the  poles  utilized,  is  measured 
either  by  circumference  or  diameter.  The  specified  relation  of  these  measurements 
for  peeled  poles  is, 

TABLE  LXVni 

Relation  between  Circumference  and  Dia.meter  for  White  Cedar  Poles 


Sea.soned  poles. 

Top  diameter. 

Inches 

Sea.soned  poles. 

Circumference  at  top. 

Inches 

Green  or  water-.soaked  poles, 

Circumference  at  top. 

Inches 

4 
5 
6 

7 

12 
15 
18^ 
22 

12» 
16 
191 
22f 

An  excess  of  6  inches  in  length  is  permitted,  or  1  half-inch  scant  for  every  5  feet 
in  length.' 

The  standard  specifications  for  Eastern  white  cedar  poles,  (American  Telephone 
and  Telegraph  Company),  are  given  below: 

All  poles  shall  be  reasonably  straight,  well  proportioned  from  butt  to  top,  shall 
have  both  ends  squared,  the  bark  peeled,  and  all  knots  and  limbs  closely  trimmed. 

The  dimensions  of  tlie  poles  shall  be  in  accordance  with  the  following  table,  the 
"  top  "  measurement  being  the  circumference  at  the  top  of  the  pole  and  the  "  butt  " 
m3asurement  the  circumference,  six  (6)  feet  from  the  butt.  The  dimensions  given 
are  the  minimum  allowable  circumferences  at  the  points  specified  for  measurement 
and  are  not  intended  to  preclude  the  acceptance  of  poles  of  larger  dimensions. 

When  the  dimension  at  the  butt  is  not  given,  the  poles  shall  be  reasonably  well 
proportioned  throughout  their  entire  length.  No  pole  shall  be  over  six  (6j  inches 
longer  or  three  (3)  inches  shorter  than  the  length  for  which  it  is  accepted.  If  any 
pole  is  more  than  six  (6)  inches  longer  than  is  required,  it  shall  be  cut  back. 

Quality  and  Defectx  of  Timber.  The  wood  of  a  dead  pole  is  grayish  in  color.  The 
presence  of  a  black  line  en  the  edge  of  the  sapwood  (as  seen  on  the  butt)  also  shows 
that  a  pole  is  dead.  No  dead  poles,  and  no  poles  having  dead  streaks  covering  more 
than  one-quarter  of  their  surface,  shall  be  accepted  under  these  specifications.  Poles 
having  dead  streaks  covering  less  than  one-quarter  of  their  surface  shall  have  a  cir- 
cumference greater  than  otherwise  required.  The  increase  in  the  circumference 
shall  be  sufficient  to  afTord  a  cross-sectional  area  of  sound  wood  equivalent  to  that  of 
.sound  pieces  of  the  same  class. 

1  Northwestern  Cedarmen's  Association. 


468 


APPENDIX  B 


TABLE  LXIX 
Minimum  Dimensions  of  White  Cedar  Poles  in  Inches 

CLASSES 


A 

B 

c 

D 

E 

F 

G 

Length 

6  feet 

6  feet 

ie  feet 

6  feet 

of 

Top 

from 

Top 

from 

Top  j  from 

Top 

from 

Top 

Top 

Top 

poles 

butt 

butt 

1  butt 

butt 

(Feet) 

1 

Circumference,  Inches 

20 

23i 

33 

2U 

30 

181 

281 

18i 

26 

15^ 

12i 

22 

23^ 

34 

2U 

31 

18f 

291 

18i 

27 

15^ 

121 

25 

23§ 

36 

2U 

33 

ISi 

3U 

m 

28^ 

15^ 

12i 

30 

231 

40 

21§ 

36 

ISf 

34i 

m 

3U 

15i 

m 

35 

23^ 

43 

2U 

40 

ISf 

37^ 

m 

34i 

151 

40 

23i 

47 

2U 

43 

18f 

40 

m 

37i 

15^ 

45 

23  i 

50 

2U 

46 

18^ 

43 

m 

40 

50 

23^ 

53 

2U 

49 

18f 

46 

m 

43 

55 

23^ 

56 

21i 

52 

60 

23  J 

59 

21i 

54 

No  dark  red  or  copper-colored  poles,  which  when  scraped  do  not  show  good 
live  timber,  shall  be  accepted  under  these  specifications. 

No  poles  having  more  than  one  complete  twist  for  every  twenty  (20)  feet  in  length, 
no  cracked  poles  and  no  poles  containing  large  season  checks  shall  be  accepted  under 
these  specifications. 

No  poles  having  "  cat  faces,"  unless  they  are  small  and  perfectly  sound  and  the 
poles  have  an  increased  diameter  at  the  "  cat  face,"  and  no  poles  having  "  cat  faces  " 
near  the  six  (6)  foot  mark  or  within  ten  (10)  feet  of  their  tops,  shall  be  accepted  under 
these  specifications. 

No  shaved  poles  shall  be  accepted  under  these  specifications. 

No  poles  containing  sap  rot,  evidence  of  internal  rot  as  disclosed  by  a  careful 
examination  of  all  black  knots,  hollow  knots,  woodpeckers'  holes,  or  plugged  holes; 
and  no  poles  showing  evidences  of  having  been  eaten  by  ants,  worms  or  grubs  shall 
be  accepted  under  these  specifications  except  that  poles  containing  worm  or  grub 
marks  below  the  six  (6)  foot  mark  will  be  accepted. 

No  poles  having  a  short  crook  or  bend,  a  crook  or  bend  in  two  planes  or  a  reversed 
curve  shall  be  accepted  under  these  specifications.  The  amount  of  sweep,  measured 
between  the  (6)  foot  mark  and  the  top  of  the  pole,  that  may  be  present  in  poles  accept- 
able under  these  specifications,  is  shown  in  the  following  tables : 

35-foot  poles  shall  not  have  a  sweep  of  over  10^  inches. 
40-foot  poles  shall  not  have  a  sweep  of  over  12  inches. 
45-foot  poles  shall  not  have  a  sweep  of  over  9  inches. 
50-foot  poles  shall  not  have  a  sweep  of  over  10  inches. 
55-foot  poles  shall  not  have  a  sweep  of  over  11  inches. 
60-foot  poles  shall  not  have  a  sweep  of  over  12    inches. 


THE  MEASUREMENT  OF  PIECE  PRODUCTS 


469 


Poles  having  tops  of  the  required  dimensions  must  have  sound  tops.  Poles 
having  tops  one  (1)  inch  or  more  above  the  requirements  in  circumference  may  have 
one  (1)  pipe  rot  not  more  than  one-half  (5)  inch  in  diameter.  Poles  with  double 
tops  or  double  hearts  shall  be  free  from  rot  where  the  two  parts  or  hearts  join. 

No  poles  containing  ring  rot  (rot  in  the  form  of  a  complete  or  partial  ringj  shall 
be  accepted  under  these  specifications.  Poles  having  hollow  hearts  may  be  accepted 
under  the  conditions  shown  in  the  following  table : 


Average  diameter 

Add 

TO  Butt  Requirements 

or  rot 

of  25  and  30-foot 

of  35-,  40-  and  45- 

of  50-,  55-,  60-  and 

poles 

foot  poles 

65-foot  poles 

2  inches 

Nothing 

Nothing 

Nothing 

3  inches 

1  inch 

Nothing 

Nothing 

4  inches 

2  inches 

Nothing 

Nothing 

5  inches 

3  inches 

1  inch 

Nothing 

6  inches 

4  inches 

2  inches 

1  inch 

7  inches 

Reject 

4  inches 

2  inches 

8  inches 

Reject 

6  inches 

3  inches 

9  inches 

Reject 

Reject 

4  inches 

10  inches 

Reject 

Reject 

5  inches 

11  inches 

Reject 

Reject 

7  inches 

12  inches 

Reject 

Reject 

9  inches 

13  inches 

Reject 

Reject 

Reject 

Scattered  rot,  unless  it  is  near  the  outside  of  the  pole,  may  be  estimated  as  being 
the  same  as  heart  rot  of  equal  area. 

Poles  with  cup  shakes  (checks  in  the  form  of  rings)  which  also  have  heart  or  star 
checks  may  be  considered  as  equal  to  poles  having  hollow  hearts  of  the  average 
diameter  of  the  cup  shakes. 

Western  Red  Cedar  forms  the  main  source  of  supply  of  poles  in  the  West.  The 
specifications  for  these  poles  permit  a  much  smaller  taper  than  for  Eastern  timber 
since  the  tree   form  is  more  cylindrical. 

The  specifications  (American  Telephone  and  Telegraph  Companj')  are  given 
in  Table  LXX,  p.  470. 

For  Southern  Yellow  Pine  poles  for  creosoting,  the  required  dimensions  are 
given  in  Table  LXXI,  p.  471. 

Chestnut  has  been  a  standard  pole  timber  but  is  rapidly  disappearing  in  Eastern 
states  because  of  the  ravages  of  the  chestnut  blight.  The  specifications  differ  only 
slightly  from  those  for  white  cedar,  and  are  as  follows: 

Dimensions.  Length.  Poles  shall  not  be  over  six  (6)  inches  shorter  or  twenty- 
four  (24)  inches  longer  than  the  length  specified  in  the  order. 

Circumference.  Poles  shall  be  classified  with  respect  to  their  circumferences  at 
six  (6)  feet  above  the  butt  and  at  their  top  in  accordance  with  Table  LXXII,  p. 
472.  This  table  gives  the  minimum  allowable  circumference  at  six  (6)  feet  above 
the  butt  and  at  the  top  for  poles  of  each  class  and  length  hsted  and  shall  not  preclude 
the  acceptance  of  poles  having  greater  circumferences  at  those  points  of  measure- 
ment than  those  given  in  the  table. 


470 


APPENDIX  B 


TABLE  LXX 

(Minimum  Dimensions  of  Western  Red  Cedar  Poles  in  Inches) 

CLASSES 


A 

B 

C 

D 

E 

F 

(Minimum 

(Minimum 

(Minimum 

(Minimum 

Length 

of 
poles 
(Feet) 

top  circum- 
ference 

28). 
Circumfer- 

top circum- 
ference 

25). 
Circumfer- 

top circum- 
ference 

22). 
Circumfer- 

top circum- 
ference 

18^). 
Circumfer- 

(Minimum 
top  circum- 
ference 
15) 

(Minimum 
top  circum- 
ference 
12) 

ence  6  feet 

ence  6  feet 

ence  6  feet 

ence  6  feet 

from  butt 

from  butt 

from  butt 

from  butt 

Inches 

20 

30 

28 

26 

24 

No     butt 

No    butt 

22 
25 

32 
34 

30 
31 

27 

28 

25 
26 

require- 
ment 

require- 
ment 

30 

37 

34 

30 

28 

35 

40 

36 

32 

30 

40 

43 

38 

34 

32 

45 

45 

40 

36 

34 

50 

47 

42 

38 

36 

55 

49 

44 

40 

38 

60 

52 

46 

41 

39 

65 

54 

48 

43 

(Chestnut  poles,  continued)  Shape.     No  poles  shall  contain  short  crooks. 

With  respect  to  other  deviations  from  straightness,  poles  required  in  the  order  to  be 
of  the  "  town  "  class  shall  be  free  from  all  deviations  from  straightness  excei)t  sweep 
in  one  plane  only.  The  amount  of  sweep  between  the  top  and  the  butt  of  these  poles 
shall  not  be  greater  than  that  specified  for  their  length  in  the  Table  LXXIII,  p.  472. 

Poles  required  by  the  order  to  be  of  "  country  "  class  may  have  sweep  in  two 
planes  or  sweep  in  two  directions  in  one  plane  provided  that  a  straight  line  con- 
necting the  center  of  the  butt  with  the  center  of  the  top  does  not,  at  any  intermediate 
point,  pass  through  the  external  surfaces  of  the  pole.  Where  sweep  is  in  one  plane 
and  one  direction  onty,  the  amount  between  the  top  and  the  butt  shall  not  be  greater 
than  that  specified  for  the  length  of  the  pole  in  Table  LXXIV,  p.  473. 

366.  Piling.  All  piles  are  peeled  before  measuring.  Piling  should  show  close 
grain  or  slow  growth,  and  be  straight,  with  a  minimum  taper.  If  a  straight  line 
drawn  between  the  centers  of  the  butt  and  top  falls  outside  the  peeled  pile  at  any 
point  the  piece  is  usually  rejected.  Hence  long  piling  brings  a  proportionally  higher 
price.  Specifications  for  piling  prescribe  minimum  and  maximum  diameters  for 
the  butt,  and  a  minimum  top  diameter.  Examples  of  such  specifications  are  shown 
in  Table  LXXV,  p.  473. 

Piling  is  sold  by  the  linear  foot,  but  the  price  per  foot  increases  with  length  of 
stick.  In  Southern  pine,  piling  is  frequently  measured  by  log  scale,  by  taking  the 
diameter  at  the  middle  of  the  log. 


THE  MEASUREMENT  OF  PIECE  PRODUCTS 


471 


TABLE  LXXI 

Minimum  Dimensions  of  Southern  Yellow  Pine  Poles  in  Inches — 

Classes 


A 

B 

C 

D 

E 

Length 

of 

6  feet 

6  feet 

6  feet 

6  feet 

6  feet 

poles 

Top 

from 

Top 

from 

Top 

from 

Top 

from 

Top 

from 

(Feet) 

butt 

butt 

butt 

butt 

butt 

Circumference,  Inches 

20 

22 

29§ 

20 

27 

18 

26 

16 

24 

21 

22 

22 

30i 

20 

28 

18 

27 

16 

25 

22 

25 

22 

32i 

20 

291 

18 

28  i 

16 

26 

23 

30 

22 

35 

20 

32 

18 

30i 

16 

281 

24J 

35 

22 

38 

20 

34 

18 

32  i 

16 

30 

14 

26 

40 

22 

40 

20 

36 

18 

34^ 

16 

32 

27i 

45 

24 

42^ 

22 

38 

20 

36 

18 

331 

.   50 

24 

44§ 

22 

40 

20 

38 

18 

35 

55 

24 

47 

22 

42i 

20 

40 

60 

24 

49 

22 

44i 

20 

42 

65 

24 

51 

22 

47 

70 

24 

53 

22 

49 

75 

24 

55 

22 

51 

80 

24 

57 

85 

24 

59 

90 

24 

61 

Defects.  Defects  in  piling  are  rot,  loose  or  rotten  knots,  wind  shake,  twisted 
grain,  checks  or  other  defects  which  interfere  with  driving  or  durability. 

367.  Posts,  Large  Posts  and  Small  Poles.  Standard  fence  posts  are  cut,  7,  7^ 
or  8  feet  long.  Dimensions  up  to  10  feet  are  termed  large  posts,  while  lengths  of 
12  to  18  feet  inclusive  are  small  poles;  the  distinction  being  based  partly  on  the 
uses  to  which  they  are  put.  Standard  cedar  posts  may  be  2  inches  short,  and  \ 
inch  scant  in  diameter  when  seasoned,  but  must  be  full  if  green  or  water-soaked. 

Posts  are  graded  by  inch  classes  measured  at  top  or  small  end.  They  will  permit 
knots  and  other  defects  which  will  not  weaken  the  piece  for  the  purpose  of  a  post. 
Cedar  may  contain  a  certain  amount  of  center  or  pipe  rot.  White  cedar  posts  may 
have  a  sweep  of  4  inches.  Western  juniper  and  red  cedar  posts  may  have  much 
greater  sweep,  provided  it  lies  in  one  plane  or  "  crooks  one  way." 

Post  material  in  round  bolts  whose  diameter  exceeds  6  to  7  inches,  when  not 
needed  for  corner  or  gate  posts,  is  usually  split  into  two  or  more  fence  posts  whose 
cross-sectional  area  will  equal  or  exceed  that  of  round  posts  of  the  standard  dimen- 
sions. 

Posts  must  be  cut  from  live  timber  and,  in  white  cedar,  rot  or  other  defects  are 
permitted  which  do  not  impair  the  strength  of  the  post  for  uses  of  a  fence  post. 


472 


APPENDIX  B 


TABLE  LXXII 

Minimum  Circumfersxcss  of  Chestnut  Poles  in  Inches 
Classes 


A 

B 

C 

D 

E 

K        lo 

Length 

(Feet) 

6  feet 

6  feet 

6  feet 

6  feet 

6  feet 

6  feet 

Top 

from 

Top 

from 

Top 

from 

Top 

from 

Topi  from 

Top 

from  j  Top 

butt 

butt 

butt 

butt 

butt 

butt 

1 

I 

NCHES 

20 

24 

34 

22 

31 

20 

29 

18 

27 

16 

24 

15 

! 
22    I  15 

25 

24 

37 

22 

34 

20 

32 

18 

29 

16 

27 

15 

24       15 

30 

24 

40 

22 

37 

20 

35 

18 

32 

16 

29 

15 

27    !  15 

35 

24 

43 

22 

40 

20 

37 

18 

35 

16 

32 

15 

29 

15 

40 

24 

46 

22 

43 

20 

40 

18 

37 

16 

35 

15 

32 

15 

45 

24 

49 

22 

46 

20 

43 

18 

40 

16 

37 

50 

24 

52 

22 

49 

20 

46 

18 

43 

55 

24 

55 

22 

52 

20 

49 

60 

24 

58 

22 

55 

65 

26 

60 

22 

58 

70 

26 

62 

22 

60 

75 

26 

64 

22 

62 

80 

26 

66 

22 

64 

85 

26 

68 

22 

66 

90 

26 

70 

22 

68 

f 

TABLE  LXXIII 

Maximum  Sweep,  Poles,  Standard 


Length 

Maximum 

Length 

Maximum 

Length 

Maximum 

of  pole. 

sweep. 

of  pole. 

sweep. 

of  pole. 

sweep. 

Feet 

Inches 

Feet 

Inches 

Feet 

Inches 

20 

4 

45 

9 

70 

14 

25 

5 

50 

.     10 

75 

15 

30 

6 

55 

11 

80 

16 

35 

7 

60 

12 

85 

17 

40 

8 

65 

13 

90 

18 

SmaU  cedar  poles  up  to  and  including  18  feet  in  length  may  have  a  sweep  of 
4  inches,  which  for  lengths  of  16  to  18  feet  is  measured  from  a  point  4  feet  from  the 
butt,  in  the  manner  prescribed  for  long  poles. 

Fire-killed  lodgepole  pine  is  accepted  for  poles  and  posts  in  the  Rocky  Mountains. 


THE  MEASUREMENT  OF  PIECE  PRODUCTS 


473 


TABLE  LXXIV 
Maximum  Sweep,  Poles,  Country 


Length 

Maximum 

Length 

Maximum 

Length 

Maximum 

of  pole. 

sweep. 

of  pole. 

sweep. 

of  pole. 

sweep. 

Feet 

Inches 

Feet 

Inches 

Feet 

Inches 

20 

6 

45 

13.| 

70 

21 

25 

71 

50 

15 

75 

22i 

30 

9 

55 

m 

80 

24 

35 

lOi 

60 

18 

85 

25^ 

40 

12 

65 

19§ 

90 

27 

TABLE  LXXV 

Dimensions  for  Piling 


Species,  region  or 
purchaser 

Length. 
Feet 

Minimum  top 

diameter — Inches 

Not  less  than 

Diameter  limits, 
butt- 
Inches 

Hardwoods — Eastern 

Panama  Canal 

California 

Southern  Pacific  R.R 

20-35 

40-50 
Under  30 

30-50 
Under  60 
Over    60 
Under  30 

30-40 

40-69 
70  and  over 

6 
6 
6 
6 
9 
9 
9 
9 
8 
8 

12  and  over 

14  and  over 

12  to  16 

12  to  18 

13  to  17 
13  to  20 

A.,  T.  &  S.  F.  R.R 

13  to  18 

14  to  18 
14  to  18 
16  to  18 

All  classes  of  poles  and  posts  are  usually  seasoned  to  decrease  weight  for  trans- 
portation. 

Fence  stays  are  round  or  split  pieces  about  2  inches  in  diameter  and  5  to  6  feet 
long.  They  are  used  between  posts  for  wire  fences  as  upright  pieces  not  set  in  the 
ground,  to  which  the  wires  are  stapled  to  prevent  their  being  spread  apart  by  stock, 
and  to  reduce  the  number  of  posts  required. 

Converter  poles,  called  also  furnace  poles  and  brands,  are  consumed  in  the  process 
of  refining  copper.  The  Montana  specifications  call  for  poles  with  a  top  diameter  of 
3  to  4  inches  and  length  of  24  feet.  They  should  have  as  little  taper  as  possible. 
Eastern  bra.ss  mills  use  poles  25  to  40  feet  long,  2  inches  and  over  at  top,  and  5  inches 
and  over  at  butt.     The  bark  is  not  removed  and  poles  must  be  green. 

Standard  California  hop  poles  are  made  from  split  pieces  2  by  2  inches  by  8  feet. 
In  the  East  hop  poles  are  usually  made  from  round  pieces  of  approximately  the  same 
dimensions. 

368.  Mine  Timbers.  Mine  timber  can  be  classed  as  stulls  and  props,  lagging, 
shaft  timbers  and  lumber,  and  mine  ties.  Stulls  include  round  props  used  as  posts, 
caps  to  connect  pairs  of  opposite  posts,  and  girts  to  connect  posts  lengthwise  of  the 


474  APPENDIX  B 

gallery.  Their  dimensions  depend  on  size  of  galleries.  Diameters  vary  from  5| 
to  24  inches.  Square  props  are  used  for  similar  purposes.  Small  round  props  used 
principally  in  coal  mines  are  termed  mine  props  and  rim  from  4  inches  up  in  diam- 
eter and  from  4  to  10  feet  in  length.  These  timbers  are  used  to  support  the  ground 
and  must  be  straight,  sound  and  free  from  knots  that  will  impair  the  strength  of 
the  piece,  or  from  defects  affecting  strength  or  durability. 

Mine  timber  is  bought  by  the  linear  foot,  by  classes  based  on  top  diameter. 
Spht  props  mast  have  a  cross-sectional  area  in  square  inches  equal  to  that  of  a  round 
post  of  minimum  .specified  diameter. 

Pole  lagging  varies  from  H  to  5  inches  in  diameter  at  small  end  and  averages  16 
feet  in  length.  Four-  to  five-inch  poles  may  be  split.  Lodgepole  pine  is  the 
principal  .species  used.     Lagging  is  bought  by  the  piece. 

Mine  Ties.  Cross  ties  for  mine  tramways  are  usually  5  to  5^  feet  long  but  may 
be  from  3  feet  to  6  feet  in  length,  and  var>'  for  individual  mines,  from  3  by  4  inches 
to  5  by  6  inches  in  diameter.  Their  small  size  makes  a  market  for  very  small  timber, 
which  can  be  grown  in  20  to  30  years.  Ties  are  bought  by  count,  and  on  basis  of 
specifications. 

Round  mine  timber  of  these  classes  and  mine  ties  not  only  utilize  the  entire  stick, 
but  permit  the  almost  complete  utilization  of  the  felled  tree  and  of  the  stand.  In 
fact,  the  tendency  is  to  exploit  young  second-growth  stands  while  still  too  small  to 
bear  seed,  and  under  private  management  forests  in  mining  regions  are  rapidly 
destroyed.  The  same  conditions  permit  of  thinnings  in  dense  stands,  the  removal 
of  small  diseased  trees  and  a  short  rotation,  and  under  forest  management  offer 
verj-  favorable  conditions  for  profitable  j^roduction  of  timber. 

369.  Cross  Ties.  Standard  railroad  cross  ties  are  either  hewn,  with  two  jiarallel 
faces,  or  sawed  to  specified  dimensions.  Switch  ties  are  sawed  in  sets  of  graduated 
lengths.  Hewn  ties,  termed  also  pole  ties,  are  made  from  round  bolts  hewn  on  two 
sides  to  produce  parallel  faces.  Bolts  14  inches  and  over  in  diameter  are  usually 
split  into  two  or  more  ties,  hewn  on  four  sides.  Hewn  ties  are  preferred  to  sawed 
ties  as  they  are  said  to  be  more  durable. 

The  standard  specifications  for  cross  ties  of  the  U.  S.  Railroad  Administration 
have  since  March,  1920,  been  adopted  with  slight  changes  by  over  two-thirds  of  the 
railroad  mileage  of  the  country.  These  specifications  are  shown  graphically  in  Fig. 
88.  The  specifications  of  the  Penn.sylvania  Railroad  System,  based  on  the  above, 
are  as  follows: 

All  ties  shall  be  free  from  any  defects  that  may  impair  tKeir  strength  or  thiraljiUty 
as  cross  ties,  such  as  decay,'  splits,  shakes,  large  or  numerous  holes  -  or  knots,'  or 
oblique  fiber  with  slope  greater  than  one  in  fifteen. 

Ties  from  needle-leaved  trees  shall  be  of  compact  wood  with  not  less  than  one- 

'  Ties  must  be  rejected  when  decayed  in  the  slightest  degree,  except  that  the 
following  may  be  allowed:  in  cedar,  "  pipe  or  stump  rot  "  up  to  1§  inches  diameter 
and  15  inches  deep;  in  cypress,  "  peck  "  up  to  the  limitations  as  to  holes;  and,  in 
pine,  "  blue  sap  stain." 

2  A  large  hole  in  woods  other  than  cedar  is  one  more  than  ^  inch  in  diameter  and 
3  inches  deep  within,  or  one  more  than  1  inch  in  diameter  and  3  inches  deep  outside 
the  sections  of  the  tie  between  20  and  40  inches  from  its  middle.  Numerous  holes 
are  any  number  equaling  a  large  hole  in  damaging  effect. 

'  A  large  knot  is  one  exceeding  in  width  more  than  \  of  the  width  of  the  surface 
on  which  it  appears;  but  such  a  knot  may  be  allowed  if  it  occurs  outside  the  .sections 
of  the  tie  between  20  and  40  inches  from  its  middle.  Numerous  knots  are  any 
number  equaling  a  large  knot  in  damaging  effect. 


THE  MEASUREMENT  OF  PIECE  PRODUCTS 


475 


third  summerwood  when  averaging  five  or  more  rings  of  annual  growth  per  inch,  or 
with  not  less  than  one-half  summerwood  in  fewer  rings,  measured  along  any  radius 
from  the  pith  to  the  top  of  the  tie.  Ties  of  coarse  wood,  with  fewer  rings  or  less 
summerwood,  will  be  accepted  when  specially  ordered. 


S                              |.                             Ue-gW        .^          ?>,           ^  .     ^ 

^          < 

.     ^J-i^         Kl-^           \&^ 

< 

1 

C^ 

& 

Pi-   tt 

D  *l 

c_ 

^_4o^             r^^ 

1        ^°° 

jfQ 

iL__ 

i. 

\ 

I 

I 

'   1 

00       ^  o> 


kr\i 


J' 

Ties  for  use  without  preservative  treatment  shall  not  have  sapwood  wider  than 
one-fourth  the  width  of  the  top  of  the  tie  between  20  and  40  inches  from  the  middle, 
and  will  be  designated  as  "  heart  "  ties.  Those  with  more  sapwood  will  be  desig- 
nated as  "  sap  "  ties. 

Manufacture.  Ties  should  be  made  from  trees  which  have  been  felled  not  longer 
than  one  month. 


476 


APPENDIX  B 


All  ties  shall  be  straight,  well  manufactured,  ^  cut  square  at  the  ends,  have  bottom 
and  top  parallel,  and  have  bark  entirely  removed. 

Dimensions.  Before  manufacturing  ties,  producers  should  ascertain  which  of 
the  following  grades  will  be  accepted. 

All  ties  shall  be  eight  (8)  feet  six  (6)  inches  long. 

All  ties  shall  measure  as  follows  throughout  both  sections  between  20  and  40 
inches  from  the  middle  of  the  tie. 


Grade 

Sawed  or  hewn  top, 
bottom  and  sides 

Sawed  or  hewn  top 
and  bottom 

1 

2 

3 

4 
5 

None  accepted 

6"  thick  X  7"  wide  on  top 

6"  thick  XS"  wide  on  top 

7"  thick  X8"  wide  on  top 
7"  thick  X9"  wide  on  top 

6"  thick  X  6"  wide  on  top 
6"  thick X7"  wide  on  top 
7"  thick  X6"  wide  on  top 
7"  thick  X7"  wide  on  top 
6"  thick  X8"  wide  on  top 
7"  thick  X8"  wide  on  top 
7"  thick  X9"  wide  on  top 

The  above  are  minimum  dimensions.  Ties  over  one  (1)  inch  more  in  thickness, 
over  three  (3)  inches  more  in  width,  or  over  two  (2)  inches  more  in  length  will  be 
degraded  or  rejected. 

The  top  of  the  tie  is  the  plane  farthest  from  the  pith  of  the  tree,  whether  or  not 
the  pith  is  present  in  the  tie. 

Class  U — Ties  which  May  Be  Used  Untreated 


Group  Ua 


Group  Vb 


Group  Uc 


Group  Vd 


'Heart"  Black  Locust 
'Heart"  White  Oaks 
'Heart"  Black  Walnut 


Heart"  Douglas  Fir 
Heart"  Pines 


Heart"  Cedars 
■  Heart"  Cypress 
'Heart"  Redwood 


'Heart"  Catalpa 
'  Heart"  Chestnut 
'Heart"  Red  Mulberry 
'Heart"  Sassafras 


Class  T — Ties  which  Should  Be  Treated 


Group  Ta 

Group  T6 

Group  Tc 

Group  Td 

Ashes 

"Sap"  Cedars 

Beech 

"Sap"  Catalpa 

Hickories 

"Sap"  Cypress 

Birches 

"Sap"  Chestnut 

"Sap"  Black  Locust 

"Sap"  Douglas  Fir 

Cherries 

Elms 

Honey  Locust 

Hemlock 

Gums 

Hackberry 

Red  Oaks 

Larches 

Hard  Maples 

Soft  Maples 

"Sap"  White  Oaks 

"Sap"  Pines 

"Sap"  Mulberries 

"Sap"  Black  Walnut 

"Sap"  Redwood 

"Sap"  Sassafras 
Spruces 
Sycamore 
White  Walnut 

'  A  tie  is  not  well  manufactured  when  its  surfaces  are  cut  into  with  score-marks 
more  than  I  inch  deep  or  when  its  surfaces  are  not  even. 


THE  MEASUREMENT  OF  PIECE  PRODUCTS  477 

370.  Inspection  and  Measurement  of  Piece  Products.  Piece  products,  while 
graded  on  basis  of  dimensions,  maj'  be  rejected  either  because  of  scant  length,  thick- 
ness or  width,  below  requirements  for  lowest  grade,  or  because  of  disqualifying 
defects.  As  these  products  are  usually  hauled  to  track  or  landing  before  being 
graded,  considerable  losses  are  occasioned  by  failure  to  conform  to  these  specifi- 
cations. 

Although  the  character  and  amount  of  defect  disqualif  j'ing  a  piece  is  usually  pre- 
scribed as  exactly  as  possible  in  the  specifications,  yet  there  is  always  considerable 
latitude  exercised  by  the  inspector,  and  the  closeness  or  laxity  of  inspection  may 
vary  under  instructions  according  to  the  demand  for  the  product.  This  method  of 
regulating  supply  supplements  price  adjustments  and  is  open  to  serious  objec- 
tions. Good  inspectors  are  thoroughly  familiar  with  the  qualities  required  of 
product  and  display  a  certain  leniency  in  judging  pieces  which  almost  conform  to 
specifications,  provided  the  general  run  of  the  product  is  of  good  quality  and  work- 
manship. An  inspector  must  command  respect  for  his  integrity  and  reputation  for 
giving  both  parties  a  square  deal. 

The  contents  of  various  classes  of  piece  products  may  be  desired  in  terms  of  either 
cubic  feet  or  board  feet,  in  order  to  reduce  different  kinds  of  products  to  terms  of  a 
common  standard  or  to  simplify  terms  of  payment  or  of  record.  Since  most  of  these 
products  are  exposed  to  decay,  and  their  value  is  measured  by  their  resistance  to 
fungus  attacks,  wood  preservation  is  becoming  more  prevalent.  Creosoting  plants 
base  their  charges  upon  the  cubic  contents  of  such  pieces  as  are  treated  as  a  whole. 

The  volume  in  cubic  feet  of  poles  of  different  dimensions  is  obtained  by  the  for- 
mula? given  in  §  27  by  applying  the  values  for  cubic  volumes  of  cylinders  shown  in 
Table  LXXVII,  Appendix  C.  The  middle  diameter  measurement  is  the  most 
accurate  method  for  long  poles,  owing  to  the  errors  resulting  from  large  butts. 

For  short  poles,  piling  or  mining  stulls,  the  middle  diameter  measurement  is 
probably  the  most  satisfactory,  and  the  table  of  cylindrical  contents,  or  Humphrey 
caliper  cordwood  rule  will  suffice  as  a  standard.  Prices  for  mining  stulls  of  different 
lengths  and  diameters  sold  by  the  U.  S.  Forest  Service  in  Montana,  are  based 
upon  the  cubic  contents  of  pieces  of  each  standard  size. 

Smaller  material  such  as  fence  posts  or  other  round  pieces  may  be  converted  to 
cubic  feet  by  the  same  means. 

Cross  ties,  on  account  of  uniformity  of  size,  are  converted  into  their  equivalent 
in  board  feet,  and  expressed  either  by  average  contents  per  tie,  or  by  the  number  of 
ties  per  1000  feet  B.  M.  The  average  contents  of  hewn  ties  may  be  obtained  by 
scaling  a  large  number  as  logs  8  feet  long.  Or  their  cubic  contents  may  be  cal- 
culated from  the  thickness  and  face  and  reduced  to  board  feet.  The  first  method 
deducts  for  sawdust,  and  the  second  for  squaring  the  tie.  By  either  method  a  6-  by 
8-  inch  tie  scales  about  32  board  feet,  or  30  ties  per  1000  feet  B.M.  Ties  85  feet  long, 
7  inches  thick  by  9-  inch  face  may  average  40  to  44  board  feet,  or  25  to  23  per  1000 
board  feet. 

Ratios  are  easily  worked  out  on  the  basis  of  specifications  and  actual  scale,  and, 
once  determined,  may  be  substituted  for  measurement  and  applied  to  the  count  of 
ties,  separately  for  each  size  class  or  grade  of  tie. 

To  reduce  piling  to  board  feet,  pieces  are  sometimes  scaled  directly  by  a  log  rule. 
For  small  poles,  posts  or  mining  timbers  the  best  method  of  conversion  is  to  apply 
a  converting  factor  to  the  cubic  contents  of  pieces  of  given  dimensions.  Where 
total  or  actual  cubic  contents  is  measured,  the  best  ratio  is  probably  5. .5  board  feet 
per  cubic  foot.  If  cubic  contents  includes  only  the  cylinder  measured  at  small  end, 
a  larger  ratio  is  required. 


478 


APPENDIX  B 


The  following  table  gives  converting  factors  adopted  by  the  U.  S.  Forest  Service 
for  products  of  various  classes  and  dimensions: 


TABLE  LXXVI 

Converting  Factors,  Piece  Products  to   Board   Feet 


Product 

Assumed 
dimensions 

Equiv- 
alent in 
board 
feet 

Product 

Assumed 
dimensions 

Equiv- 
alent in 
board 
feet 

Long  cord  (acid  wood, 
pulpwood,    and    dis- 
tillation wood) 

Cord      (spruce      pulp- 
wood) 

4'  X5'  X8' 

4'  X4'  X8' 
4'  X4'  X8' 
4'  X4'  X8' 

4'  X4'  X8' 

4'  X4'  X8' 
1  cord 
7"X30' 
9"X30' 
7"X30' 
10"X16' 
6"  X  8"  X  8' 
6"X7"X8' 
6"X7"X6' 

625 

560 
600 
333i 

500 

333i 
60 

100 
60 
60 
30 
20 
15 
25 
15 
30 
35 
60 

480 

Trestle  timber 

Trestle  timber 

10"X20' 

7"X12' 

8"X16' 

7"  XI 6' 

7"X10' 

6"X10' 

6"X10' 

4"X20' 
16' 

4"X20' 

3"X6' 

i  pole 

6"X7' 

6"X7' 

2"X6"X16' 

6"X7' 

5.7"X7' 
5"X7' 
10"  XI' 
4"X6' 
2"  X  6' 
4"X6' 
|"X6"X2' 
^"X5"X32" 
3"X5' 
3"X5' 

70 
20 
30 

30 

House  log 

15 

Cord  (shingle  bolts) . .  . 

Cord      (fuel      material 
averaging  5  inches  or 
less  in  middle  diame- 

Mining  timber 

10 
10 

Converter  pole 

10 

8 

Pole  (fence) 

10 

Cord      (fuel      n:aterial 
averaging  6  inches  or 

Lagging  (6  pieces)  .  .  . 
Cubic  foot  (round) .  .  . 
Rail  (split) 

10 
6 
5 

eter) 

Piece 

7 

Load  (in  the  rough)*.  . 

Pole  (telephone) 

Pole  (telephone) 

Pile                         .    ... 

Stick 

7 

Slab 

2 

Post 

Post      (circumference, 
18  inches) 

7 

6 

Tie  (standard) 

Tie  (2d  class) 

Tie  (narrow  gauge)  .  .  . 

Post      

5 

3 

2 

i 

Stay 

2 

Tie             

7"X8"X8' 
7"X9"X8' 
7"X30' 

Shake  (roof) 

Shake  (fruit  tray) .... 
Picket 

i 

Tie                

I 

1 

Derrick  set  (11  pieces) 

1   Stake  (fence) 

1 

*  This  refers  to  small  irregular  pieces  of  wood  and  not  to  material  that  can  be  ricked  for 
measurement. 


APPENDIX  C 
TABLES  USED  m  FOREST  MENSURATION 

TABLE  LXXVII 

Cubic  Contents  of  Cylinders  and  Multiple  Table  of 
Basal  Area 

This  table  serves  a  double  purpose.  It  shows,  in  the  first  place, 
the  contents  of  cylinders  of  different  diameters  and  lengths.  It  may  be 
used  to  determine  the  contents  of  logs  whose  diameters  are  measured 
at  the  middle.  The  table  shows  also  the  sums  of  the  basal  areas  of 
different  numbers  of  trees.  Thus  the  total  basal  area  of  fifty-one 
trees  9  inches  in  diameter  is  22.53  square  feet.  This  table  will  be  found 
ver>^  useful  in  computing  the  total  basal  area  of  different  diameter 
classes  in  forest  surveys. 

The  values  given  in  this  table  are  practically  identical  with  those 
of  the  Humphrey  Caliper  Cordwood  Rule  (§  121)  for  which  it  may  be 
substituted.  By  multiplying  the  values  in  the  table  by  1.28  the 
contents  of  logs  will  be  found  in  terms  of  stacked  cubic  feet  of  cord- 
wood,  p.  480. 

TABLE  LXXX 

The  International  Log  Rule  for  Saws  Cutting  a  j  inch 
Kerf 

This  log  rule  is  derived  from  the  values  of  the  International  log 
rule  for  saws  cutting  a  |-inch  kerf,  by  applying  the  factor  .904762  to 
the  values  in  the  former  rule,  computing  to  the  third  decimal  place, 
and  then  rounding  off  the  resultant  values  to  the  nearest  5  board  feet. 
The  values  were  computed  and  checked  by  Judson  F.  Clark  in  1917, 
p.  493. 

TABLE  LXXXIi 

Values  in  square  feet  for  .16  and  for  .66  of  the  area  of  circles  of  dif- 
ferent diameters,  for  computing  the  cubic  volume  of  trees  by  the  Schiffel 
formula,  F=(.16  ^+.666)  h,  p.  494. 

1  Computed  by  the  U.  S.  Purest  Service. 
479 


480 


APPENDIX  C 


TABLE  LXXVII 
Cubic  Contents  OF  C"iT.iNDERS  AND  Multiple  Table  of  Basal  Areas 


Diameter  in  Inches. 

Length, 
Feet .  or 
Number 
of  Trees. 

■4 

3 

4 

5 

6 

7 

« 

ContL 

nts  of  Cylinders  in  Cubic  Feet,  or 

Basal  Areas  in  Square 

Feet. 

I 

0.02 

0.05 

0 ,  09 

0.  14 

0,  20 

0.  27 

0.35 

2 

0.04 

0.  10 

0.17 

0.  27 

0.39 

0.53 

0.70 

3 

0.07 

0.15 

0.26 

0.41 

0-59 

0 .  80 

1.05 

4 

0.09 

0.20 

0-35 

0.55 

0.79 

1.07 

1.40 

5 

0.  II 

0.25 

0.44 

0.68 

0    98 

1-34 

1-75 

6 

0.13 

0.29 

0.52 

0.82 

I  .  18 

I  .60 

2.09 

7 

o.i5> 

0.34 

0.61 

0.95 

I  -37 

1.87 

2.44 

8 

0.17 

0-39 

0.70 

1.09 

I  -57 

2.14 

2.79 

9 

0.20 

0.44 

0.79 

I  .2-, 

I  -77 

2.41 

3    14 

lO 

0.22 

0.49 

0.87 

1.36 

1.96 

2.67 

3-49 

II 

0.24 

0.54 

0.96 

1.50 

2.16 

2.94 

3.84 

12 

0.26 

0.59 

I   05 

1.64 

2., ^6 

3-21 

4.  19 

13 

0.28 

0.64 

113 

I  .77 

2-55 

3-47 

4-54 

U 

0.31 

0.69 

1 .22 

I. 91 

2-75 

3-74 

4.89 

15 

0.33 

0.74 

1.31 

2.05 

2-95 

4.01 

5   24 

i6 

0 .  35 

0.79 

1.40 

2.18 

3-14 

4.28 

5-59 

17 

0.37 

0.83 

1.48 

2     32 

3-34 

4.. 54 

5.93 

18 

0.39 

0.8S 

1-57 

2.45 

3  •  53 

4.8. 

6.28 

19 

0.41 

0.93 

1.66 

2.59 

3-73 

5.08 

6.63 

20 

0.44 

0 .  98 

1-75 

2-73 

3-93 

5-35 

6.98 

21 

0.46 

I  .03 

1 .  83 

2.86 

4. 12 

5.61 

7-33 

22 

0.4S 

I  .08 

1.92 

3.00 

4-32 

5.88 

7.68 

23 

0.50 

113 

2.01 

3.14 

4-52 

6.15 

8.03 

24 

0.52 

1. 18 

2.09 

3.27 

4-71 

6.4 

8.38 

25 

0.55 

1.23 

2.18 

3-4' 

4,91 

6.68 

8.73 

26 

0.57 

1.28 

2.27 

3-55 

5" 

6-95 

9.08 

27 

0.59 

I  •  33 

2.36 

^.68 

5  •  30 

7  •  22 

9.42 

28 

0.61 

1-37 

2.44 

3.82 

5  50 

7.48 

9-77 

29 

0.63 

I  .42 

2.53 

3-95 

5.69 

7.75 

10. 12 

30 

0.65 

1-47 

2.62 

4.09 

5-89 

8.02 

10.47 

31 

0 .  68 

I  .52 

2.71 

4-23 

6.09 

8.28 

10.82 

32 

0.70 

1.57 

2.79 

4 -,^6 

6.28 

8..SS 

II  .17 

33 

0.72 

1.62 

2 .  88 

4  50 

6.48 

8.  82 

11.52 

34 

0.74 

1.67 

2.97 

4.64 

6.68 

9.09 

II  .87 

35 

0.76 

I  .  72 

3  05 

4  77 

6.87 

9  ■  35 

12.22 

36 

0.79 

I  .  77 

3-14 

4-91 

7.07 

9.62 

12   57 

37 

o.Si 

I  .82 

3-23 

5  05 

7.26 

9.89 

12.92 

TABLES  USED  IN   FOREST  MENSURATION 


481 


TABLE  LXXYll—Continued 


Diameter  in  Inches. 

Length. 

Feet,  or 

2 

3 

4 

5 

6 

7 

8 

Number 
of  Trees. 

Contents  of  Cylinders  in  Cubic  Feet,  or 

Basal  Areas  in  Square 

Fell. 

38 

0.83 

1.87 

3-32 

5.18 

7.46 

10.  16 

'3.26 

39 

0.85 

I  .91 

3-40 

5-32 

7.66 

10.42 

13.61 

40 

0.87 

1.96 

3-49 

5.45 

7.85 

10.69 

13-96 

41 

0.89 

2  .01 

3.58 

5  ■  59 

8.05 

10.96 

14-31 

42 

0.9J 

2.06 

3.67 

5.73 

8.2s 

II  .22 

14.66 

43 

0.94 

2.11 

3-  75 

5 .  86 

8.44 

II  .49 

15.01 

44 

0.96 

2.16 

3  •  84 

6.  ex. 

8 .  64 

II  .76 

'5-36 

45 

0.98 

2.21 

3-93 

.    6.14 

8 .  84 

12.03 

15-71 

46 

I  .00 

2.26 

4.01 

9  03 

12.29 

16.06 

47 

I  .03 

2.31 

4.  10 

6;4i 

9   23 

12.56 

16.41 

48 

1.05 

2  .  36 

4.  19 

6..S4 

9.42 

t  2  .  83 

16.76 

49 

I  .07 

2.41 

4.28 

6  . 6,S 

9.62 

13.  10 

17.10 

50 

I  .  09 

2.45 

4.36 

6.82 

9.82 

13-36 

17-45 

51 

I  .  I  I 

2.50 

4.45 

6-95 

10.01 

13-63 

17.80 

52 

113 

2 .  55 

4-5  t 

7.09 

10.21 

13-90 

IS. 15 

53 

I. 16 

2 .  60 

4-63 

7-23 

10.41 

14-16 

'8.50 

54 

I  .  18 

2.6,s 

4-7' 

7.36 

10.60 

'4-43 

18.85 

55 

I  .  20 

2.70 

4.80 

7 -50 

10.  80 

14.70 

19.20 

56 

1.22 

2.75 

4.89 

7.64 

1 1  .00 

'4-97 

'9-55 

57 

1.24 

2 .  80 

4-97 

7-77 

1 1 .  1 9 

15-23 

19.90 

5« 

I  .27 

2.85 

5.06 

7-91 

1 1  •  39 

1 5  -  50 

20.25 

59 

I  .29 

2 .  90 

5- 15 

8.04 

11.58 

'5-77 

20 .  60 

60 

I -31 

2.95 

5-24 

8.i8 

11.78 

16.04 

20.94 

61 

^■3^ 

2.99 

5-32 

8.32 

II . 98 

16.^,0 

21.29 

62 

I    35 

3  04 

5  41 

8.45 

12.17 

'6.57 

2.. 64 

63 

1.37 

309 

5  ■  50 

8., 59 

12.37 

16.84 

21.99 

64 

I  .40 

3-14 

5-59 

8.73 

12.57 

17.  10 

2    .^4 

65 

I  .4^ 

3-  '9 

5-67 

8 .  86 

12.76 

'7-37 

2    .69 

66 

1.44 

3  •  24 

5-76 

9.00 

12.96 

17.64 

23-04 

67 

1.46 

3  •  29 

5.85 

914 

13.16 

17.91 

23  ■  39 

6<S 

1.48 

3  •  ,U 

5   93 

9   27 

13-35 

18.17 

23-74 

69 

i.5t 

3  ■  39 

6.02 

9.41 

13-55 

18,44 

24.09 

70 

'53 

3-44 

6.  II 

9-54 

13-74 

18.71 

24-43 

7' 

'    55 

3 .  49 

6.20 

9 .  68 

13-94 

18.97 

24.78 

72 

'•57 

3-54 

6.28 

9.82 

14.  14 

19.24 

25-13 

73 

1  -59 

3-58 

6.37 

9-95 

14-33 

19-51 

25-48 

74 

1. 61 

3.63 

6.46 

10.09 

14-53 

19-78 

25   83 

75 

1.64 

3.68 

6.54 

10.23 

14-73 

20.04 

26.18 

482 


APPENDIX  C 


TABLE  LXXVII— Continued 


Diameter  in  Inches. 

Length, 

Feet,  or 

9 

10 

jj 

13 

13 

14 

15 

Number 
of  Trees. 

Contents  of  Cylinders  in  Cubic  Feet,  or 

Basal  Area 

in  Square  Feet. 

I 

0.44 

055 

0.66 

0.79 

0.92 

I  .07 

1  -25 

2 

0.88 

1.09 

1-32 

1-57 

1.84 

2.14 

2-45 

3 

1-33 

1.64 

1.98 

2.36 

2-77 

3-21 

3-68 

4 

I  •  77 

2.18 

2.64 

3-14 

3-69 

4.28 

4-91 

5 

2.21 

2.73 

3-30 

3-93 

4.61 

5-35 

6.14 

6 

2.65 

3-27 

3-96 

4-71 

5-53 

6.41 

7-36 

7 

3  09 

3-82 

4.62 

5-50 

6.45 

7-48 

8-59 

8 

3-53 

4.36 

5.28 

6.28 

7-37 

8-55 

9.82 

9 

3-98 

4.91 

5-94 

7.07 

8.30 

9.62 

11.04 

lO 

4.42 

5-45 

6.60 

7-85 

9.22 

10.69 

12.27 

II 

4.86 

6.00 

7.26 

8.64 

10.  14 

11.76 

1350 

12 

5.30 

6.55 

7-92 

9-42 

II  .06 

12.83 

14.73 

13 

5 -'74 

7.09 

8.58 

10.21 

11.98 

13-90 

15-95 

14 

6.19 

7.64 

9.24 

1 1  .00 

12.90 

14-97 

17.18 

15 

6.63 

8.18 

9.90 

11.78 

13-83 

16.04 

18.41 

i6 

7  07 

8.73 

10.56 

12.57 

14-75 

17.  10 

19-63 

17 

7-51 

9.27 

II  .22 

13-35 

15-67 

18.  17 

20.86 

i8 

7-95 

9.82 

11.88 

14.14 

16.59 

19-24 

22  .09 

19 

8-39 

10.36 

12.54 

14.92 

17-51 

20.31 

23-32 

20 

8.84 

10,91 

13-20 

15-71 

18.44 

21-38 

24-54 

21 

9.28 

11-45 

13-86 

16.49 

19-36 

22.45 

25-77 

22 

9-72 

12.00 

14-52 

17.28 

20.28 

23.52 

27.00 

23 

10. 16 

12,54 

15.18 

18.06 

21 .20 

24-59 

28.23 

24 

10.60 

1 3 .  09 

15-84 

18.85 

22.  12 

25,66 

29-45 

25 

11.04 

1 3  ■  64 

16.50 

19.64 

23.04 

26.73 

30  68 

26 

II  .49 

14.18 

17.16 

20.42 

23.97 

27.79 

31-91 

27 

"•93 

14-73 

17.82 

21  .21 

24.89 

28.86 

33.13 

28 

12.37 

15-27 

18.48 

21.99 

25-81 

29-93 

34.36 

29 

12.81 

15.82 

19.14 

22.78 

26.73 

31.00 

35.59 

30 

1325 

16.36 

19.80 

23-56 

27.65 

32.07 

36.82 

31 

1370 

16.91 

20.46 

24-35 

28.57 

33- 14 

38.04 

32 

14.14 

17-45 

21.12 

25-13 

29.50 

34-21 

39-27 

33 

14.58 

18.00 

21.78 

25.92 

30.42 

35-28 

40.50 

34 

1502 

18.54 

22.44 

26.70 

31.34 

36  -  35 

41.72 

35 

15-46 

19.09 

23.10 

27-49 

32.26 

37  -  42 

42-95 

36 

'  5  90 

19.64 

23.76 

28.27 

33  -  I  8 

38.48 

44-18 

37 

16.35 

20.  18 

24,42 

29.06 

34.10 

39  ■  55 

45  41 

TABLES  USED  IN   FOREST  MENSURATION 


483 


TABLE   LXXYU— Continued 


Length, 
Feet,  or 
Number 
of  Trees. 


Diameter  in  Inches. 


Contents  of  Cylinders  in  Cubic  Feet,  or  Basal  Areas  in  Square  Feet. 


38 
39 
40 

41 
42 
43 

44 
45 

46 
47 
48 
49 
50 

51 
52 
53 
54 
55 

56 
57 
58 
59 
60 

61 
62 
63 
64 
65 

66 

67 
68 
69 
70 

71 

72 
73 
74 
75 


16.79 
17-23 
17.67 


18.56 
19.00 
19 -44 
19.88 


20 

.32 

20 

.76 

21 

.21 

21 

•65 

22 

.09 

22 

■53 

22 

•97 

23 

■41 

23 

.86 

24 

30 

24 

74 

25 

18 

2S 

62 

26 

07 

26 

51 

26 

95 

27 

39 

27 

83 

28 

27 

28 

72 

29 

16 

29 

60 

30 

04 

30 

48 

30 

93 

31 

37 

31 

81 

32 

25 

32 

69 

33 

13 

20.73 


22.36 

22.91 

23-45 
24.00 

24-54 

25.09 
25-63 
26.18 
26.73 

27-27 

27.82 
28.36 
28.91 

29-45 
30.00 

30  -  54 
31.08 
31-63 
32.18 
32.73 

33-27 
33.82 
34  36 
34-91 
35-45 

36.00 
36.54 
37-09 
37-63 
38.18 

38.72 
39-27 
39-82 
40 .  36 
40.91 


25.08 

25-74 
26.40 

27.06 

27.72 
28.38 
29.04 
29.70 

30 .  36 
31.02 
31.68 
32-34 
33- 00 

33-66 
34-32 
34-98 
35-64 
36  -  30 

36 .  96 
37-62 
38.28 

38-94 
39-60 

40.26 
40.92 

41.58 
42.24 
42.90 

43.56 
44.22 
44.88 
45.54 
46.  20 

46.86 
47-52 
48.18 
48.84 
49.50 


29.85 

35.03 

40.62 

30.63 

35.95 

41.69 

31.42 

36.87 

42 .  76 

32 .  20 

37.79 

43.83 

32.99 

38.71 

44.90 

33.77 

39.64 

45-97 

34  56 

40.56 

47-04 

35.34 

41.48 

48.  1 1 

36.13 

42.40 

49-17 

36.91 

43 .  32 

50.24 

37.70 

44.24 

51-31 

38.48 

45.17 

52-38 

39.27 

46.09 

53-45 

40.06 

47.01 

54-52 

40.84 

47.93 

55.59 

41.63 

48.85 

56.66 

42.41 

49.77 

57.73 

43.20 

50.70 

58.80 

43.98 

51.62 

59.86 

44.77 

52.54 

60.93 

45-55 

53.46 

62.00 

46.34 

54.38 

63.07 

47-12 

55.31 

64.14 

47-91 

56.23 

65.21 

48.69 

57.15 

66.28 

49-48 

58.07 

67.35 

50-27 

58.99 

68.42 

51-05 

59.91 

69.49 

51-84 

60.84 

70.55 

52.62 

61.76  ■ 

71.62 

53-41 

62.68 

72.69 

.^4-^9 

63.60 

73.76 

54-98 

64.52 

74.  S3 

55-76 

65.44 

75.90 

56.55 

66.37 

76,97 

57.33 

67.29 

78.04 

58.12 

68.21 

79.  II 

58.91 

69.13 

80.18 

46.63 

47. 86 
49.09 

50.31 
51.54 
52.77 
54.00 

55.22 

56.45 
57.68 
58.90 
60.13 
61.36 

62.59 
63.81 
65.04 
66.27 
67-49 

68.72 
69  •  95 
71.18 
72.40 
73-63 

74-86 
76.09 
77.31 
78.54 
79-77 


80.99 
82.22 


87-13 
88 .  7,6 
89-58 
90.81 
92.04 


484 


APPENDIX  C 


TABLE  LXXYIl—Continued 


Diameter  in  Inches. 

Length. 

Feet,  or 
Number 

16 

17 

18 

19 

20 

21 

22 

of  Trees. 

Contents  of  Cylinders  in  Cubic  Feet,  or 

Basal  Areas  in  Square 

Feet. 

I 

1.40 

1-58 

1.77 

I  .97 

2.18 

2.41 

2.64 

2 

2.79 

3.15 

3  -  53 

3.94 

4.36 

4.81 

5-28 

3 

4.19 

4-73 

5-30 

5.91 

6.54 

7 .  22 

7.92 

4 

5-59 

6.31 

7.07 

7.88 

8.73 

9.62 

10.56 

5 

6.98 

7  .  88 

8.  84 

9-84 

10.91 

1 2 .  03 

1 3 .  20 

6 

8 .  38 

9.46 

10,60 

1 1  .  8 1 

1 3  -  09 

14.43 

15.84 

7 

9-77 

I  I  .o:; 

12.37 

13.  78 

15-27 

16.84 

1 8 .  48 

8 

II .  17 

12.61 

14.14 

15-75 

17-45 

19-24 

21  .  12 

9 

12.57 

14. 19 

1 5  -  90 

19-63 

2 1  .  65 

23.76 

lO 

13.96 

15.76 

17-67 

19 '69 

21.82 

24-05 

26.40 

II 

15.36 

17.34 

19-44 

21.66 

24.00 

26.46 

29.04 

12 

16.76 

18.92 

21  .21 

23.63 

26.18 

28.86 

31.68 

13 

18.15 

20.49 

22.97 

25.60 

28.36 

31  -27 

34  •  32 

14 

19.55 

22.07 

24-74 

27.57 

30.54 

33.67 

36 .  96 

15 

20.94 

23.64 

26.51 

29.53 

32.72 

36.  oS 

39 .  60 

16 

22.34 

25.22 

28.27 

31.50 

34.91 

38.  48 

42.24 

17 

23.74 

26.80 

30.04 

^V47 

37.09 

40.89 

44.88 

18 

25.13 

28.37 

31-81 

•■  S  .  44 

.39.27 

4  3 -.30 

47-52 

19 

26 .  53 

29.95 

33-58 

,v-4i 

41.45 

45  70 

50 . 1 6 

20 

27-93 

31.53 

35 -.34 

.39-38 

43-63 

4S.11 

52.80 

21 

29.32 

33.10 

37-11 

41 -,35 

45-82 

50 . 5 1 

55-44 

22 

30.72 

34.68 

38 .  88 

43-32 

48 .  00 

52  ■92 

5S.08 

23 

32.  II 

36.25 

40.64 

45  -  29 

50.  18 

55-32 

60.72 

24 

33.51 

37 .  83 

42.41 

47-25 

52 -,36 

57-73 

63-36 

25 

34.91 

39.41 

44-18 

49.22 

54-54 

60 .  1 3 

66.00 

26 

36 .  30 

40.98 

45-95 

51  .19 

56.72 

62.54 

68 .  64 

27 

37  ■  70 

42.56 

47-71 

53-  16 

58 .  90 

64 .  94 

71-27 

28 

39.  10 

44.14 

49  -  48 

55.13 

61  .09 

67  ■  35 

73-91 

29 

40.49 

4571 

51-25 

57-  10 

63-27 

69-75 

76.55 

30 

41.89. 

47.29 

53-01 

59-07 

65-45 

72.1  ( ) 

79-19 

31 

43.28 

48.86 

54-78 

61.04 

67.63 

74.56 

Si, 83 

32 

44.68 

50 -44 

56-55 

63.01 

69.81 

76.97 

^4.47 

33 

46.08 

52.02 

58.32 

64.98 

71.99 

79-37 

87.  II 

34 

47.47 

53 .  59 

60.08 

66.94 

74.18 

81  .78 

89.75 

35 

48.87 

5517 

61.85 

68.91 

76.36 

84 .  1 8 

92 .  39 

36 

50.27 

56.75 

63.62 

70.88 

78.54 

86 .  59 

95  03 

37 

51.66 

58-32 

65.38 

72.85 

80.72 

89.00 

97.67 

TABLES  USED  IN  FOREST  MENSURATION 


485 


TABLE  LXXYII— Continued 


Diameter  in  Inches. 

Length, 

Feet,  or 
Number 

16 

17 

18 

19 

20 

21 

22 

of  Trees. 

Contents  of  Cylinders  m  Cubic  Feet,  or 

Basal  Areas  in  Square 

Feet. 

38 

53.06 

59  90 

67.15 

74.82 

82.90 

91  .40 

100.31 

39 

54-45 

61.47 

68.92 

76.79 

85.08 

93.81 

102.95 

40 

55-85 

63.05 

70 .  69 

78.76 

87.27 

96.21 

105 . 59 

41 

57  -  25 

64 . 6  -, 

72.45 

80.73 

89. 45 

98.62 

108.23 

42 

58.64 

66 .  20 

74.22 

82.70 

91.63 

101 .02 

110.87 

43 

60.04 

67  .  78 

75.99 

84.66 

93.81 

103.43 

113-51 

44 

61.44 

69 .  36 

77.75 

86.63 

95.99 

105.83 

116.15 

45 

62.  8;, 

70.93 

79- 52 

88.60 

98.17 

108.24 

118.79 

46 

64-23 

72.51 

81  .29 

90.57 

100.36 

110.64 

121.43 

47 

65-62 

74.08 

83.06 

92.54 

102.54 

113.05 

124.07 

48 

67.02 

75.66 

84.82 

94.51 

104.72 

115.45 

126.71 

49 

68.42 

77-24 

86.59 

96.48 

106.90 

117.86 

129.35 

50 

69.81 

78.81 

88 .  36 

98 .  45 

1 09 . 08 

120. 26 

131.90 

51 

71.21 

80 .  39 

90.12 

100.42 

111.26 

122.67 

134-63 

52 

72.61 

81  .97 

91.89 

102.39 

113.45 

125.07 

137.27 

53 

74- 00 

83-54 

93 .  66 

104.35 

"5.63 

127.48 

I. 39. 91 

54 

75  40 

85.12 

95.43 

106.32 

117.81 

129.89 

142.55 

55 

76.79 

86 ,  69 

97.19 

108.29 

119.99 

132.29 

145-19 

56 

78.19 

88.27 

98.96 

110.26 

122.  17 

I  ,M .  70 

I4/-83 

57 

79-59 

89 .  85 

100.73 

112.23 

' 24 . 35 

137.10 

150.47 

58 

80.98 

91.42 

102.49 

114.20 

126.54 

139.51 

153.11 

59 

82 .  38 

93 .  00 

104.26 

116.17 

128.72 

141. 91 

155.75 

60 

83.78 

94 .  58 

1 06 . 03 

118. 14 

1 3q . 90 

144-32 

158.39 

61 

85.17 

96.15 

107.80 

120. 1 1 

133  08 

146.72 

161.03 

62 

86.57 

97.73 

109.56 

122 .07 

135.26 

149.13 

163.67 

63 

87.96 

99 .  30 

III.  3.^ 

124.04 

137.44 

'51.53 

166.31 

64 

89-36 

100.88 

113.10 

126.01 

'39.63 

'53.94 

168.95 

65 

90.76 

102.46 

114.86 

127.98 

141.81 

156.34 

171.59 

66 

92.15 

104.03 

116,63 

I  29 . 95 

1 43. 99 

158.75 

'74-23 

67 

93  •  55 

105.61 

118. 40 

131 .92 

146.17 

161.15 

176.87 

68 

94-95 

107.19 

120. 17 

1 33 . 89 

'48.35 

163.56 

179-51 

69 

96 .  34 

108.76 

121 .93 

135. 86 

150.53 

165.96 

182. 15 

70 

97.74 

110.34 

123.70 

137.83 

152.72 

168.37 

184-79 

71 

99 .  1 3 

III .91 

125.47 

1 39 . 80 

154.90 

170.77 

'87-43 

72 

100.53 

1 1 3 • 49 

127.23 

141.76 

157.08 

173.18 

190.07 

73 

101.93 

115.07 

129.00 

143.73 

159.26 

175.59 

192.71 

74 

103.32 

116.64 

1,^0.77 

M5.70 

161.44 

177.99 

'95-35 

75 

104.72 

118.22 

132.54 

147-67 

163.62 

1 80 . 40 

197  99 

486 


APPENDIX  C 


TABLE  LXXYU— Continued 


Length, 

Diameter  in  Inches. 

Feet,  or 
Number 

83 

24 

85 

36 

27 

28 

29 

of  Trees. 

Contents  ofiCylinders  in  Cubic  Feet,  or 

Basal  Areas  in  Square 

Feet. 

I 

2.89 

3-14 

3.41 

3-69 

3.98 

4.28 

4-59 

2 

5-77 

6.28 

6.82 

7-37 

7-95 

8.55 

9.  17 

3 

8.66 

9.42 

10.23 

II  . 06 

1 1  -  93 

12.83 

13.76 

4 

11-54 

12.57 

13-64 

14-75 

15-90 

17.  10 

18.35 

5 

14 -43 

15-71 

17.04 

18.44 

19. 88 

21.38 

22.93 

6 

17-31 

18.85 

20.45 

22. 12 

23.86 

25.66 

27.52 

7 

20.  20 

21.99 

23.86 

25.81 

27.83 

29.93 

32.11 

8 

23.08 

25-13 

27.27 

29.50 

31.8. 

34.21 

36.70 

9 

25-97 

28.27 

30 .  68 

33.18 

35.78 

38.48 

41.28 

lO 

28.85 

31-42 

34.09 

36.87 

39.76 

42.76 

45.87 

II 

31-74 

34-56 

37.50 

40.56 

43-74 

47.04 

50.46 

12 

34-62 

37.70 

40.91 

44.24 

47.71 

51.31 

55.04 

13 

37-51 

40.84 

44-31 

47.93 

51.69 

55.59 

59.63 

14 

40-39 

43  -  98 

47.72 

51.62 

55.67 

59.86 

64.22 

15 

43-28 

47-12 

51.13 

55.31 

59.64 

64.14 

68.80 

i6 

46.16 

50.27 

54-54 

58.99 

63.62 

68.42 

73-39 

17 

49-05 

53-41 

57-95 

62.68 

67.59 

72.69 

77-98 

i8 

51-93 

56.55 

61.36 

66.37 

71.57 

76.97 

82.56 

19 

54-82 

59-69 

64-77 

70.05 

75-55 

81.24 

87-15 

20 

57-71 

62.83 

68.18 

73.74 

79-52 

85.52 

91-74 

21 

60.59 

65-97 

71.59 

77-43 

83.50 

89.80 

96.33 

22 

63.48 

69.  II 

74-99 

81.11 

87.47 

94.07 

100.91 

23 

66 .  36 

72.26 

78.40 

84.80 

91.45 

98  -  35 

105.50 

24 

69.25 

75-40 

81.81 

88.49 

95  -  43 

102 .63 

110.09 

25 

72.13 

78 .  54 

85.22 

92.18 

99.40 

106.90 

114-67 

26 

75-02 

81.68 

88.63 

95.86 

103.38 

III.  18 

1 19.26 

27 

77.90 

84.82 

92.04 

99-55 

107.35 

115-45 

123-85 

28 

80.79 

87-96 

95-45 

103.24 

111-33 

119.73 

128.43 

29 

83.67 

91  .11 

98.86 

106.92 

115. 31 

124.01 

133.02 

30 

86.56 

94.25 

102 . 27 

no. 61 

119.28 

128.28 

137.61 

31 

89.44 

97.39 

105.67 

114.30 

123.26 

132-56 

142.20 

32 

92 .  33 

100.53 

109.08 

117.98 

127.23 

136.83 

146.78 

33 

95-21 

103.67 

112.49 

121 .67 

131.21 

141. 11 

151.37 

34 

98.10 

106.81 

115-90 

125.36 

135-  19 

145-39 

155.96 

35 

100.98 

109.96 

119. 31 

129.05 

139-16 

149.66 

160.54 

36 

103.87 

113.10 

122.72 

132.73 

143.14 

153-94 

165.13 

37 

106.75 

116.24 

126.13 

136.42 

147.11 

158.21 

169.72 

TABLES  USED  IN  FOREST  MENSURATION 
TABLE  LXXYII—Continued 


487 


Length, 

Diameter  in  Inches. 

Feet,  or 
Number 

33 

34 

35                36 

37 

38 

39 

of  Trees. 

Contents  of  CyJir 

iders  in  Cubic  Feet,  or 

Basal  Areas  in  Square 

Feet. 

38 

109.64 

119-38 

129-54 

140.11 

151-09 

162.49 

174.30 

39 

112.52 

122.52 

132.94 

143-79 

15507 

166.77 

I  78. 89 

40 

115-41 

125.66 

136.35 

147-48 

159-04 

171.04 

183.48 

41 

1 1 8 . 30 

128.81 

139-76 

151-17 

163.02 

175.32 

188.06 

42 

121. 18 

131-95 

143-17 

154-85 

167.00 

179-59 

192.65 

43 

124.07 

135-09 

146.58 

158.54 

170.97 

183.87 

197.24 

44 

126.95 

138-23 

149-99 

162    23 

174-95 

188.15 

201.83 

45 

129.84 

141-37 

153-40 

165.92 

178.92 

192.42 

206.41 

46 

132.72 

144-51 

156.8- 

169.60 

182.90 

196.70 

211.00 

47 

135-61 

147-65 

160.22 

173-29 

186.88 

200 .97 

215 -59 

48 

138.49 

150.80 

163.62 

176.98 

190.85 

205.25 

220.17 

49 

141.38 

153.94 

167.03 

180.66 

194-83 

209.53 

224.76 

50 

144.26 

157-08 

170.44 

184-35 

198.80 

2  I  3 . 80 

229.35 

51 

147-15 

160.22 

173-85 

188.04 

202.78 

218.08 

233.93 

52 

150.03 

163.36 

177-26 

191.72 

206.76 

222.35 

238.52 

53 

152.92 

166.50 

180.67 

195-41 

210.73 

226.63 

243. 11 

54 

155.80 

169.65 

184.08 

199-10 

214.71 

230.91 

247.69 

55 

158.69 

172.79 

187.49 

202.79 

216.68 

235.18 

252.28 

56 

161.57 

175-93 

190.90 

206.47 

222.66 

239.46 

256.87 

57 

164.46 

1 79  07 

194-30 

210. 16 

226.64 

243.73 

261.46 

58 

167.34 

182.21 

197.71 

213-85 

230.61 

248.01 

266.04 

59 

170.23 

185.35 

201.12 

217-53 

234-59 

252.29 

270.63 

60 

173.12 

188.50 

204.53 

221 .22 

238.56 

256.56 

275.22 

61 

176.00 

191.64 

207 . 94 

224.91 

242-54 

260.84 

279.80 

62 

178.89 

194.78 

211-35 

228.59 

246.52 

265.12 

284.39 

63 

181.77 

197.92 

214.76 

232.28 

250.49 

269.39 

288.98 

64 

184.66 

201 .06 

218.17 

235.97 

254-47 

273.67 

293.56 

65 

187.54 

204.20 

221.57 

239.66 

258.45 

277.94 

298.15 

66 

190.43 

207-34 

224.98 

243  -  34 

262.42 

282.22 

302 . 74 

67 

193-31 

210.49 

228.39 

247-03 

266.40 

286.50 

307-32 

68 

196.20 

213-63 

231.80 

250.72 

270.37 

290.77 

311. 91 

69 

199-08 

216.77 

235-21 

254-40 

274-35 

295.05 

316.50 

70 

201.97 

219.91 

238.62 

258.09 

278.33 

299.32 

321.09 

71 

204.85 

223.05 

242.03 

261 .78 

282.30 

303 . 60 

325.67 

72 

207.74 

226. 19 

245-44 

265 . 46 

286.28 

307 . 88 

330.26 

73 

210.62 

229.34 

248.85 

269.15 

290.25 

312.15 

334.85 

74 

213-51 

232.48 

252-25 

272.84 

294.23 

316.42 

339 . 43 

75 

216.39 

235  62 

255-66 

276.53 

298.21 

320.70 

344 . 02 

488 


APPENDIX  C 


TABLE  LXXYIl— Continued 


Length. 
Feet,  or 
Number 
of  Trees. 


Diameter  in  Inches. 


Contents  of  Cylinders  in  Cuuic  Fe^t,  or  Basal  Areas  in  Square  Feet. 


4-91 

5-24 

5-59 

9.82 

10.48 

1 1 .  17 

14-73 

15-72 

16.76 

19-63 

20.97 

22.34 

24-54 

26.21 

27-93 

29-45 

31 -45 

33-51 

34  -  36 

36.69 

39-10 

39-27 

41-93 

44.68 

44.18 

47-17 

50.27 

49.09 

52.41 

55-85 

54.00 

57-66 

61.44 

58.90 

62  .90 

67.02 

63.81 

68.14 

72.61 

68.72 

73-38 

78.19 

73.63 

73.62 

83.78 

78.54 

83.86 

89.36 

83-45 

89. 10 

94-95 

88.36 

94-35 

100.53 

9327 

99-59 

1 06 . 12 

98.17 

104.83 

111 .70 

103. OS 

110.07 

117.29 

107.99 

115-31 

122.87 

1 1 2 . 90 

120.55 

128.46 

117. 81 

125-79 

1 34  -  04 

122.72 

1 3 1 . 04 

139.63 

127.63 

136.28 

145-21 

132.54 

141-52 

150.80 

137-44 

146.76 

156.38 

142.35 

152.00 

161.97 

147-26 

157-24 

167-55 

152.17 

1 62. 48 

173.14 

157-08 

167-73 

178.72 

161.99 

172.97 

184.31 

166.90 

178.21 

189.89 

171. 81 

183.45 

195.48 

176.71 

188.69 

201 .06 

181.62 

193-93 

206.65 

5-94 
11.88 
17.82 
23-76 
29.70 

35  -  64 
41  -58 
47-52 
53-46 
59-40 

65-34 


83-15 
89.09 

95-03 
100.97 
106.91 

112.85 
118.79 

124-73 
130.67 
136.61 

142.55 
148.49 

154.43 
160.37 
166.31 
172.25 
178.19 

184.13 
190.07 
196.01 
201.95 
207 . 88 

213.82 
219. 76 


6.30 

6.68 

12.61 

13.56 

18.92 

20.44 

25-22 

26.73 

31-53 

33.41 

37-83 

40.09 

44-14 

46.77 

50.44 

53-45 

56-75 

60.13 

63-05 

66.81 

69.36 

73.49 

75-66 

80.18 

81.97 

86.86 

88.27 

93.54 

94-58 

100.22 

100.88 

106.9c 

107.18 

113-58 

113.49 

120.26 

119.80 

126.95 

126. 10 

133.63 

132.41 

140.31 

138.71 

146.99 

145.02 

153-67 

151-32 

1 60 . 35 

157.63 

167.03 

163.93 

173-71 

170.24 

180.4c 

176.54 

187.08 

182.85 

193-76 

189.15 

TOO. 44 

195.45 

207.12 

201.76 

213.80 

208.06 

220.48 

214.37 

227.17 

220.68 

233-85 

226.98 

240.53 

233.28 

247.21 

7.07 
14.14 

21  .21 

28.27 

35-34 

42.41 
49.48 
56-55 
63.62 
70.69 

77-75 
84.82 
91.89 
98.96 
1C6.03 

113.10 
120. 17 

'27-23 

134-30 
141-37 

148.44 
155-51 
162.58 
169.65 
176.71 

183.78 

190.85 
197.92 
104.99 

2 1 2 . 06 

219.13 
226. 19 
233.26 
240.33 
247.40 

254.47 
261.54 


TABLES  USED  IN  FOREST  MENSURATION 


489 


TABLE  LXXYll— Continued 


Diameter  in  Inches. 

Length. 

Feet,  or 
Number 

30 

31 

32 

33 

34 

35 

36 

of  Trees. 

Contents  of  Cylinders  in  Cubic  Feet,  or 

Basa!  Areas  m  Square 

Feet. 

38 

i86.5;> 

199.17 

212.23 

225.70 

239-59 

253-89 

268.61 

39 

191 -44 

204.42 

217.82 

231.64 

245.89 

260.57 

275-67 

40 

196.35 

209 . 66 

223.40 

237.58 

252.20 

267.25 

282.74 

41 

201.36 

214.90 

228.99 

243.52 

258.50 

273-93 

289.81 

42 

206 . I  7 

220.14 

234-57 

249.46 

264.81 

280.62 

296.88 

43 

211. OS 

225.38 

240 . 1 6 

255-40 

271.11 

287.30 

303.95 

44 

2I5-9S 

2^,0.62 

245-74 

261.34 

277.42 

293.98 

311.02 

45 

220.89 

235-86 

251.33 

267.28 

283.7.2 

300 . 66 

318.09 

46 

2 25. So 

241. 1 1 

256. -I 

273-22 

290.03 

307 . 34 

325.15 

47 

2^,0.71 

246.35 

262.50 

279.16 

296.33 

314.02 

332.22 

48 

-^35.62 

251-59 

268.08 

285. 10 

302.64 

320.70 

339  -  29 

49 

2^o.5^ 

256.83 

273.67 

291.04 

308 . 94 

327.39 

346 . 36 

50 

245.44 

262.07 

279-25 

296. 98 

315.25 

334-07 

353-43 

51 

250-35 

267.31 

284.84 

302.92 

321.55 

340.75 

360.50 

52 

255-25 

272.55 

290.42 

308 . 86 

327.86 

347.43 

367.57 

53 

260.16 

277.80 

296.01 

314-80 

334-16 

354-11 

374.63 

54 

265.07 

283.04 

301.59 

320.74 

340.47 

360.79 

381.70 

55 

269 . 98 

288.28 

307. 1 8 

326.68 

346.77 

367.47 

388.77 

56 

274.89 

293-52 

312.76 

332-62 

353-08 

374-15 

395 • 84 

57 

279.80 

298.76 

318.35 

338.56 

359-38 

380.84 

402.91 

58 

284.71 

304.00 

323.93 

344-50 

365  -  69 

387.52 

409.98 

59 

2S9.62 

309 . 24 

329.52 

350.43 

371.99 

,394-20 

417.05 

60 

294. 52 

314-49 

335.10 

356.37 

378.30 

400.88 

424.11 

61 

299-43 

319.73 

340.69 

362.34 

384-61 

407.54 

431.21 

62 

304-31 

324.97 

346.27 

368.28 

390.91 

414.22 

438.28 

63 

.309.25 

330 . 2 1 

351.86 

374-22 

397 . 22 

420.80 

445.35 

64 

314-16 

335.45 

357.44 

380.16 

403-52 

427.58 

452.42 

65 

319-07 

340.69 

363-03 

386.07 

409.82 

434.29 

459-46 

66 

323.98 

345.93 

368.61 

392.04 

416. 13 

440 . 95 

466.55 

67 

328.89 

351.18 

374.20 

397 . 98 

422.44 

447-63 

473.62 

68 

333.79 

356.42 

379.78 

403.92 

428.74 

454-31 

480.69 

69 

338.70 

361.66 

385.37 

409 . 86 

435-05 

460.99 

487.76 

70 

343.61 

366 . 90 

390.95 

415.77 

441-35 

467.69 

494.80 

71 

348.52 

372.14 

396.54 

421.74' 

447-66 

474.35 

501.90 

72 

353-43 

377.38 

402.12 

427.68 

453-96 

481.03 

508.97 

73 

,358.34 

382.62 

470.71 

433-62 

460.27 

487.61 

516.04 

74 

36,^.25 

387.87 

413.29 

439-56 

466.57 

494.39 

523. II 

75 

^6S.  16 

393 ■ 1 1 

418.88 

445 ■ 47 

472.87 

501.10 

530.14 

"490 


APPENDIX  C 


TABLE    LXXVIII 


Areas  of  Circles  or  Table  of  Basal  Areas  for   Diameters  to  Nearest 


/^ 


Inch 


it 

1 
< 

3- 

2.0 
.  I 

•3 
•4 

2-5 

.6 

•7 
.8 
•9 

1 

# 

.022 
.024 
.026 
.029 
.031 

•034 
•037 
.040 
•043 
.046 

11 

3-0 
.  1 

■3 
•4 

3-5 
.6 
■  7 
.8 
-9 

1 

< 

II 

1 
< 

< 

11 

5"" 

1 

< 

1 .0 
.  I 

.  2 

•3 

•4 

1-5 

.6 

.7 
.8 

•9 

.006 
.007 
.008 
.009 
.011 

.012 
.014 
.016 
.018 
.020 

.267 
•275 
.  283 
.291 
.299 

■307 
•315 
•323 

■  332 

■  340 

.922 

■  936 
•  950 
.965 
•979 

•994 
1 .009 
1.024 
^•039 
1-054 

.049 
.052 
.056 
-059 
.063 

.067 
.071 

.075 
.079 
.083 

4.0 
.  I 

•3 
•4 

45 
.6 

•  7 
.8 
•9 

.087 
.092 
.096 

.  lOI 

.  106 

no 

•115 
120 

.126 
-131 

50 

.  2 
•3 
•4 

55 

.6 

^8 
-9 

.136 

.142 
-147 

•  153 

.165 
- 171 

•  177 
-183 
.190 

6.0 
.  I 

•3 
■4 

65 
.6 

^8 
•9 

.  196 
.203 
.210 
.216 
.223 

.230 
-238 
•  245 
.252 
.260 

7.0 
.  I 
.2 
•3 

•  4 

7.5 
.6 

.7 
.8 
•9 

8.0 
.  I 

•3 
■4 

^•5 
.6 
■7 
.8 
•9 

■349 
.35S 
-367 
.376 
•385 

•394 
.403 
•413 

.422 
•  432 

9.0 

■3 
•4 

9-5 
.6 

-7 
.8 
-9 

-442 
-452 
.462 
■  472 
.482 

.492 
.503 
-513 

-524 

•535 

10. 0 

.2 
.3 

-4 

10.5 
.6 

-7 
.8 
-9 

•545 
-556 
567 
-579 
•  590 

.601 
-613 
.624 

.636 
.648 

II  .0 

-3 
•4 

11-5 
.6 

•  7 
.8 
•9 

.660 
.672 
.684 
.696 
.709 

.721 
•734 
•  747 
.759 

.772 

12.0 

•  3 
•4 

12.5 
.6 

•7 
.8 
•9 

•  785 

•  799 
.812 
.825 
-839 

.852 

.866 
.880 
.894 
.908 

13.0 

.2 
■3 
•4 

■  7 
.8 
•9 

14.0 

.3 
•  4 

i4^5 
.6 

.7 
.8 
•9 

1.069 
1.084 
1 .  100 
1. 115 
1-131 

I.  147 
I.  163 
I.  179 
I -195 
1 .  211 

15-0 

.3 
■4 

15-5 
.6 

-7 
.8 

-9 

1 .  227 
I  .244 
1 .  260 
1.277 
1.294 

I. 310 

1.327 
1-344 
1-362 
1-379 

,6.0 

.  I 
.2 
.3 
-4 

16.5 
.6 
.7 
.8 
-9 

1.396 
1. 414 
I -431 
1.449 
1.467 

1^485 
1-503 
1. 521 
1-539 

1-558 

17.0 

.2 
-3 
-4 

175 
.6 
-7 
.8 
-9 

1-576 
1-595 
1.6.4 
1-632 
1-651 

1 .670 
1.689 
1.709 

1.728 
1.748 

18.0 

-3 
•  4 

18.=; 
.6 

."? 
-9 

1,767 
1-787 
1 .807 
1.827 
1.847 

1.867 
1.887 
1.907 
1.928 
1.948 

TABLES  USED  IN  FOREST  MENSURATION 
TABLE  LXXVni—Continued 


491 


ti 

, 

^ 

^ 

^ 

*; 

&H 

fe 

ClH 

d. 

(^ 

ft) 

a  2 

2i 

S?i 

£ 

iif, 

2 

2  0 

£J 

^  Y' 

a 

0  oi 

2 

«'cf 

.2J5 

?:l 

rt  C 

.2^ 

# 

ri 

11 

?l 

P 

<q 

< 

Q 

0 

0 

<i 

Q 

< 

19.0 

1.969 

20.0 

2.182 

21.0 

2.405 

22.0 

2 .  640 

23.0 

2.885 

24.0 

3.142 

.  I 

1.990 

.  I 

2.204 

.  I 

2.428 

.  I 

2.664 

2.910 

.  I 

3-168 

.2 

2. on 

.2 

2.226 

.2 

2.451 

.2 

2.688 

.  2 

2.936 

.2 

3.194 

.3 

2.032 

•3 

2.248 

•3 

2.474 

.3 

2.712 

■3 

2.961 

•3 

3. 221 

•4 

2.053 

.4 

2.270 

•4 

2.498 

•4 

2.737 

•4 

2.986 

•4 

3.247 

19  5 

2.074 

20.5 

2.292 

21.5 

2.521 

22.5 

2.761 

23.5 

3.012 

24 -5 

3-275 

.6 

2.095 

.6 

2.315 

.6 

2.545 

.6 

2.786 

.6 

3.038 

.6 

3.301 

.7 

2. 117 

.7 

2 .  337 

•7 

2.568 

.7 

2.810 

.7 

3.064 

.7 

3.328 

.8 

2.138 

.8 

2.360 

.8 

2.592 

.8 

2.835 

.8 

3.089 

.8 

3-355 

.9 

2.160 

•9 

2.382 

.9 

2.616 

.9 

2.S60 

•9 

3-115 

•9 

3-382 

V, 

u 

fe 

i 

i 

i 

1 

^?^ 

^^ 

£ 

5S 

a 

ss 

2 

2& 

r 
3-409 

--3 

1" 

27.0 

|i 

ii 
p" 

.5 

< 

eI 

P" 

< 

25.0 

26.0 

3.687 

3-976 

28.0 

4.276 

29.0 

4-587 

.  I 

3-436 

.  I 

3-715 

.  I 

4.006 

.  1 

4-307 

.  1 

4.619 

.2 

3.464 

.2 

3-744 

.2 

4.035 

.  2 

4-337 

.2 

4.650 

•3 

3-491 

•3 

3-773 

•3 

4.065 

•3 

4-368 

•3 

4.682 

•4 

3.519 

.4 

3.801 

-4 

4-095 

-4 

4-399 

-4 

4-714 

25.5 

3-547 

26.5 

3-830 

27-5 

4.125 

28.5 

4  -  430 

29-5 

4.746 

.6 

3-574 

.6 

3-859 

.6 

4.155 

.6 

4.461 

6 

4-779 

•7 

3.602 

•7 

3.888 

-7 

4-185 

-7 

4-493 

.7 

4.8n 

.8 

3-631 

.8 

3-917 

.8 

4-215 

.8 

4-524 

.8 

4.844 

-9 

3.659 
4.909 

.9 

3-947 

-9 

4-246 

•9 
33-0 

4-555 
5  940 

■9 

4.876 

30.0 

31.0 

5-241 

32  .0 

5-585 

34  0 

6.305 

35.0 

6.681 

36.0 

7.069 

37  .0 

7-467 

38.0 

7  -  876 

39  -  0 

8.296 

40.0 

8.727 

41.0 

9.168 

42  .0 

9.621 

43-0 

10.085 

44.0 

10.559 

450 

11 .045 

46.0 

II -541 

47  -O 

1 2 . 048 

48.0 

12.566 

49-0 

13.095 

50.0 

13-635 

51-0 

14.186 

52.0 

14.748 

53-0 

15-321 

54-0 

15.904 

55  0 

16.499 

56.0 

17.T04 

570 

17.721 

58.0 

IS. 348 

59  0 

18.986 

60.0 

19-635 

492 


APPENDIX  C 


TABLE  LXXIX 

Tables  for  the  Conversion  of  the  Metric  to  the  English  System  and 
Vice  Versa. 


Hectares 
to  Acres. 

1  = 

2.47109 

2  = 

494213 

3= 

7.41327 

4= 

9 • 88436 

5  = 

12.35545 

6= 

14-82654 

7  = 

17.29763 

8  = 

19.76872 

9= 

22.23981 

Kilos- 

to  Pounds. 

1  = 

2 . 20462 

2  = 

4.40924 

3  = 

6.61386 

4  = 

8.81848 

5  = 

1 1 .02310 

6= 

13.22772 

7  = 

15-43234 

8  = 

17.63696 

9= 

19.84158 

Centimeters  to 
Inches. 

1  = 

.39370423 

2  = 

.78740846 

3=1 

.  1 8 II  I  269 

4=1 

.57481692 

5=  I 

.96852115 

6=2 

.36222538 

7=2 

.75592961 

8=3 

.14963384 

9  =  3-54333807 

Meters  to  Feet, 

•  1  = 

3 . 280869 

2  = 

6.561738 

3  = 

9. 84 2607 

4  = 

13. 123476 

5  = 

16.404345 

6  = 

19.685214 

7  = 

22.966083 

8= 

26.246952 

9= 

29.527821 

Acres  to 
Hectares. 

1=     .40467 

2=     .80934 

3=1.21401 

4=1.61868 

5=2.02335 

6  =  2.42802 

7  =  2.83269 

8  =  3-23736 
9=3.64203 

Cubic  Meters 
per  Hectare 
to  Cubic  Feet 
per  Acre. 

1=  14.291 
2=  28.582 
3=  42.873 
4=  57.164 
5=  71.455 
6=  85.746 

7=100.037 

8=114.328 

.   9=128.619 

Kilometers  to 
Miles. 


1  = 

2=1 

3  =  1 

4=2 

5  =  3 

6  =  3 

7  =  4 


62137676 

24275352 
86413028 
48550704 
10688380 
72826056 
34963732 

8  =  4.97101408 

9  =  5.59239084 

Cubic  Meters 
to  Cubic  Feet. 

1=  35-315617 
2=  70.631234 
3=105.946851 

4=  141 .262468 
5=176.578085 

6  =  211 .893702 

7  =  247.209319 

8  =  282.524936 
9=317.840553 


TABLES  USED  IN  FOREST  MENSURATION 


493 


TABLE  LXXX 
The  International  Log  Rule  for  Saws  Cutting  a  i-mcH  Kerf. 

Standard  scale  for  seasoned  lumber  with  i^-inch  shiinkage  per  1-inch  board,  and  saws  cutting 




Length  of  Log  in  Feet 

Diam. 

8  1 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

Diam. 

4 
5 

5 
5 

5 

5 

5 

5 

5 

5 

10 

10 

4 

"5 

5 

5 

10 

10 

10 

10 

10 

15 

15 

15 

15 

5 

6 

7 
8 
9 
10 

10 
10 
15 
20 
30 

10 
15 
20 
25 
35 

10 
15 

10 
15 

15 
20 

15 
20 

15 
25 

20 
25 

20 
30 

20 
30 

25 
35 

25 
35 

25 
40 

6 
7 

20 
30 
35 

25 
30 
40 

25 
35 
45 

30 
40 
50 

35 
45 
55 

35 
45 
60 

40 
50 
65 

40 
55 
70 

45 
60 
75 

60 
65 
80 

70 

85 

9 
10 

11 
12 
13 
14 
15 

35 
45 
55 
65 
75 

40 
50 
60 

70 

85 

45 
55 

70 
80 
95 

50 
65 
75 
90 
105 

55 
70 

85 
100 
115 

65 
75 
90 
105 
125 

70 
85 
100 
115 
135 

75 
90 
105 
125 
145 

80 
95 
115 
135 
160 

85 
105 
125 
145  1 
170 

95 
110 
135 
155 
180 

100 
120 
140 
165 
195 

105 
125 
150 
175 
205 

11 
12 
13 
14 
15 

16 
17 
18 
19 
20 

85 
95 
110 
125 
135 

95 
110 
125 
140 
155 

110 

120 
135 

130 
150 

145 
165 

155 
180 

170 
190 

180 
205 

195 
220 

205 
235 

220 
250 

235 
265 

16 
17 
18 
19 
20 

140 
155 
175 

155 
175 
195 

170 
190 
210 

185 
205 
230 

200 
225 
250 

215 
245 
270 

230 
260 
290 

250 
280 
310 

265 
300 
330 

280 
315 
350 

335 
370 

21 
22 
23 
24 
25 

155 
170 
185 
205 
220 

175 
190 
210 
230 
250 

195 
215 
235 
255 
280 

215 
235 
260 
285 
310 

235 
260 
285 
310 
340 

255 
285 
310 
340 
370 

280 
305 
335 
370 
400 

300 
330 
360 
395 
430 

320 
355 
590 
425 
460 

345 
380 
415 
455 
495 

365 
405 
445 
485 
525 

390 
430 
470 
515 
560 

410 
455 
495 
545 
590 

21 
22 
23 
24 
25 

26 
27 
28 
29 
30 

240 
260 
280 
305 
325 

275 
295 
320 
345 
370 

305 
330 
355 
385 
410 

335 
365 
395 
425 
455 

370 
400 
430 
465 
495 

400 
435 
470 
505 
540 

435 
470 
510 
545 
585 

470 
505 
545 
590 
630 

500 
540 
585 
630 
675 

535 
580 
625 
670 
720 

570 
615 
665 
715 
765 

605 
655 
705 
755 
810 

640 
690 
745 
800 
860 

26 

27 
28 
29 
30 

31 
32 
33 
34 
35 

350 
375 
400 
425 
450 

395 

420 
450 
480 
510 

440 
470 
500 
535 
565 

485 
520 
555 
590 
625 

530 
570 
605 
645 
685 

580 
620 
660 
700 
745 

625 
670 
715 
760 
805 

675 
720 
765 
815 
865 

720 
770 
820 

875 
925 

770 
825 
875 
930 
990 

820 
875 
930 
990 
1050 

870 
925 
985 
1050 
115 

915 
980 
1045 
1110 
1175 

31 
32 
33 
34 
35 

36 
37 
38 
39 
40 

475 
505 
535 
565 
595 

540 
570 
605 
635 
670 

600 
635 
670 
710 
750 

665 
700 
740 
785 
825 

725 
770 
810 
855 
900 

790 
835 
885 
930 
980 

855 
905 
955 
1005 
1060 

920 
970 
1025 
1080 
1140 

980 
1040 
1095 
1155 
1220 

1045 
1110 
1170 
1235 
1300 

1115 
1175 
1245 
1310 
1380 

1180 
1245 
1315 
1390 
1460 

1245 
1315 
1390 
1465 
1  40 

36 
37 
38 
39 
40 

41 
42 
43 
44 
45 

625 
655 
■  690 
725 
755 

705 
740 
780 
815 
855 

785 
825 
870 
910 
955 

870 
910 
955 
1005 
1050 

950 
995 
1045 
1095 
1150 

1030 
1085 
1140 
1195 
1250 

1115 
1170 
1230 
1290 
1350 

1200 
1260 
1320 
1385 
1450 

1280 
1345 
1410 
1 1480 
1550 

1365 
1435 
1505 
1580 
1650 

1450 
1525 
1600 
1675 
1755 

1535 
1615 
1695 
1775 
1855 

1620 
1705 
1785 
1870 
1960 

41 
42 
43 
44 
45 

46 
47 
48 
49 
50 

795 
830 
865 
905 
940 

895 
935 
975 
1020 
1060 

995 
1040 
1090 
1135 
1185 

1100 
1150 
1200 
1250 
1305 

1200 
1255 
1310 
1370 
1425 

1305 
1365 
1425 
1485 
1550 

1410 
1475 
1540 
1605 
1675 

1515 
1585 
1655 
1725 
1795 

1620 
1695 
1770 
1845 
1920 

1730 
1805 
1885 
1965 
2045 

1835 
1915 
2000 
2085 
2175 

1940 
2030 
2115 
2205 
2300 

2050 
2140 
2235 
2330 
2425 

46 
47 
48 
49 
50 

51 
52 
53 
54 
55 

980 
1020 
1060 
1100 
1145 

1105 
1150 
1195 
1245 
1290 

1235 
1285 
1335 
1385 
1440 

1360 
1415 
1470 
1530 
1585 

1485 
1545 
1605 
1670 
1735 

1615 
1680 
1745 
1815 

1885 

1745 
1815 
1885 
1960 
2035 

1870 
1945 
2025 
2100 
2185 

2000 
2080 
2165 
2245 
2330 

2130 
2215 
2305 
2395 

2485 

2265 
2355 
2445 
2540 
2640 

2395 
2490 
2590 
2690 
2790 

2525 
2625 
2730 
2835 
2945 

51 
52 
53 
54 
55 

56 
57 
58 
59 
60 

1190 
1230 
1275 
1320 
1370 

1340 
1300 
1440 
1490 

1545 

1495 
1550 
1605 
1660 
1720 

1645 
1705 
1770 
1830 
1895 

1800 
1865 
1930 
2000 

12070 

1 

1955 
2025 
2100 
i2170 
;2250 
1 

2110 
2185 
2265 
2345 
2425 

2265 
2345 

|2430 
12515 
J2605 

2420 
2510 
2600 
2690 

2785 

1 

2575 
2670 
12770 
2865 
^2965 

2735 
2835 
2935 
3040 
j3145 

2895 
3000 
3105 
3215 
3325 

3050 
3165 
3275 
3390 
3510 

56 
57 
58 
59 
60 

Formula:   1(0^X0.22) -0.71D!  X  0.904762  for  4-foot  sections. 
Taper  allowance:  i  inch  per  4  feet  lineal. 


494 


APPENDIX  C 


TABLE  LXXXI 


Tables  for  Values  in  Schtffel's  Formula  for  Cubic  Volumes  of  EhrrniE  Stems. 

)ntents  of  trees  by  a  short  method  (Sphiffel's 
+0.66fa). 


This  tabic  is  for  use  in  calculating  the  cub: 
formula): 

r  =  H(0. 


The  field  measurements  necessary  for  this  calculation  are  the  diameter  breast-high  and  the 
diameter  at  the  middle  height  of  the  tree.  To  find  the  volume  look  up  0.16  of  the  area  corre- 
sponding to  the  D.B.H.  of  the  tree.  Add  to  this  0.66  of  the  area  corresponding  to  the  diameter 
at  the  middle  height.  The  sum  of  the  two  multiplied  by  the  height  of  the  tree  equals  the  total 
volume  of  the  tree  in  cubic  feet.  Thus,  if  the  total  height  of  the  tree  is  62.5  feet,  the  diameter 
breast-high  10.4  inches,  and  the  diameter  at  the  middle  8.1  inches,  from  tables  0.16B  and  0.666 
it  is  found  that  the  areas  corresponding  ot  these  diameters  are  0.094  and  0.236,  respectively. 
Their  sum,  0.330,   multiplied  by  the  height,  62.5,  equals  the  volume,  20.6   cubic  feet. 


0. 16    OF    THE    A 

REA    OF 

A  Circle  .^.t  Breast  Height   (0 

.165) 

0.0     1 

'^r 

0.2 

0.3 

0.4 

0.5 

0.6 

0.7 

0.8 

0.9 

Sq.  ft. 

Sq.  ft. 

Sq.  ft. 

Sq.  ft. 

Sq.  ft. 

Sq.  ft. 

Sq.  ft. 

Sq.  ft. 

Sq.  ft. 

Sq.  ft. 

O.OOI 

0.001 

0.001 

0.001 

0.002 

0.002 

0.002 

0.003 

0.003 

0.003 

.003 

.004 

.004 

.005 

.005 

.005 

.006 

.006 

.007 

.007 

.008 

.008 

.009 

.010 

.010 

.011 

Oil 

.012 

.013 

.013 

.014 

.015 

.015 

.016 

.017 

.018 

.018 

.019 

.020 

.021 

.022 

.023 

.024 

.025 

.025 

.026 

.027 

.028 

.029 

.030 

.031 

.032 

.034 

.035 

.036 

.037 

.038 

.039 

.040 

.042 

.043 

.044 

.045 

.047 

.048 

.049 

.050 

.052 

.053 

.054 

.056 

.057 

.059 

.060 

.062 

.063 

.065 

.066 

.068 

.069 

.071 

.072 

.074 

.075 

.077 

.079 

.080 

.082 

.084 

.086 

.087 

.089 

.091 

.093 

.094 

.096 

.098 

.100 

.102 

.104 

.106 

.108 

.109 

111 

.113 

.115 

.117 

.119 

.122 

.124 

.126 

.128 

.130 

.132 

.134 

.136 

.139 

.141 

.143 

.145 

.147 

.150 

.152 

.154 

.157 

.159 

.161 

.164 

.166 

.169 

.171 

.173 

.176 

.178 

.181 

.183 

.186 

.189 

.191 

.194 

.196 

.199 

.202 

.204 

.207 

.210 

.212 

.215 

.218 

.221 

.223 

.226 

.229 

.232 

.235 

.238 

.240 

.243 

.246 

.249 

.252 

.255 

.258 

.261 

.264 

.267 

.270 

.273 

.276 

.280 

.283 

.286 

.289 

.292 

.295 

.299 

.302 

.305 

.308 

.312 

.315 

.318 

.322 

.325 

.328 

.3.32 

.335 

.339 

.342 

.346 

.349 

.353 

.356 

.360 

.363 

.367 

.370 

.374 

.378 

.381 

.385 

.389 

.392 

.396 

.400 

.403 

.407 

.411 

.415 

.419 

.422 

.426 

.430 

.434 

.438 

.442 

.446 

.450 

.454 

.458 

.462 

.466 

.470 

.474 

.478 

.482 

.486 

.490 

.494 

.498 

.503 

.507 

.511 

.515 

.520 

.524 

.528 

.532 

.537 

.541 

.545 

.550 

.554 

.559 

.563 

.567 

.572 

.576 

.581 

.585 

.590 

.594 

.599 

.604 

.608 

.613 

.617 

.622 

.627 

.631 

.636 

.641 

.646 

.650 

.655 

.660 

.665 

.670 

.674 

.679 

.684 

.689 

.694 

.699 

.704 

.709 

.714 

.719 

.724 

.729 

.734 

.739 

.744 

.749 

.754 

.759 

.765 

.770 

.775 

.780 

.785 

.791 

.796 

.801 

.806 

.812 

.817 

.822 

.828 

.833 

.839 

.844 

.849 

.855 

.860 

.866 

.871 

.877 

.882 

.888 

.894 

.899 

.905 

.910 

.916 

.922 

.927 

.933 

.939 

.945 

.950 

.956 

.962 

.968 

.974 

.979 

.985 

.991 

.997 

1.003 

1.009 

1.015 

1.021 

1.027 

1.033 

1.039 

1.045 

1.051 

1.057 

1.063 

1.069 

1.075 

1.081 

1.087 

1.094 

1.100 

1.106 

1.112 

1.118 

1 

1.125 

TABLES  USED  IN   FOREST  MENSURATION 
TABLE  LXXXl—Continued 


495 


0.16 

OF    THE 

Area  of 

A  Circle  at  Breast  H 

EIGHT    (0,165) 

Diameter. 



0.0 

0.1 

0.2 

0.3 

0.4 

0,5 

0.6 

0.7 

0.8 

0.9 

Inches 

Sq.  ft. 

Sq.  ft. 

Sq.  ft. 

Sq.  ft. 

Sq.  ft. 

Sq,  ft. 

Sq.  ft. 

Sq.  ft. 

Sq.  ft. 

Sq.  ft. 

36 

1.131 

1.137 

1.144 

1.150 

1.156 

1.163 

1.169 

1.175 

1.182 

1.188 

37 

1.195 

1.201 

1.208 

1.214 

1.221 

1 .  227 

1.234 

1.240 

1.247 

1.254 

38 

1.260 

1.267 

1.273 

1.280 

1.287 

1.294 

1.300 

1.307 

1.314 

1.321 

39 

1.327 

1.334 

1.341 

1.348 

1.355 

1 .  362 

1.368 

1.375 

1.382 

1.389 

40 

1.396 

1.403 

1.410 

1.417 

1.424 

1.431 

1,438 

1 .  446 

1.453 

1.460 

41 

1.467 

1.474 

1.481 

1.488 

1.496 

1.503 

1.510 

1.517 

1.525 

1.532 

42 

1.539 

1.547 

1.554 

1.561 

1.569 

1.576 

1.584 

1.591 

1.599 

1.606 

43 

1.614 

1.621 

1.629 

1.636 

1.644 

1.651 

1.659 

1.667 

1.674 

1.682 

44 

1.689 

1.697 

1,705 

1.713 

1.720 

1.728 

1 .  73G 

1.744 

1.751 

1.759 

45 

1.767 

1.775 

1.783 

1.791 

1.799 

1.807 

1.815 

1.823 

1.831 

1.839 

46 

1.847 

1.855 

1.863 

1.871 

1,879 

1.887 

1.895 

1.903 

1.911 

1.920 

47 

1.928 

1.936 

1.944 

1.952 

1,961 

1.969 

1 ,  977 

1.986 

1.994 

2.002 

48 

2.011 

2.019 

2.027 

2.037 

2,044 

2.053 

2,061 

2.070 

2.078 

2.087 

49 

2.095 

2.104 

2.112 

2.121 

2.130 

2 ,  138 

2,147 

2.156 

2.164 

2.173 

50 

2,182 

2.190 

2 ,  199 

2.208 

2.217 

2,226 

2,234 

2.243 

2.252 

2.261 

51 

2.270 

2.279 

2.288 

2.297 

2.306 

2.315 

2.324 

2.333 

2.342 

2.351 

52 

2.360 

2.369 

2.378 

2.387 

2 .  .396 

2,405 

2.414 

2.424 

2.433 

2.442 

53 

2.451 

2.461 

2,470 

2.479 

2,488 

2.498 

2.507 

2.516 

2,526 

2.535 

54 

2 .  545 

2,554 

2 ,  564 

2.573 

2,583 

2.592 

2.602 

2.611 

2,621 

2.630 

55 

2 .  640 

2.649 

2 ,  659 

2.669 

2,678 

2.688 

2.698 

2,707 

2.717 

2.727 

56 

2.737 

2.746 

2.756 

2.766 

2.776 

2,786 

2.796 

2.806 

2.815 

2.825 

57 

2.835 

2.845 

2.855 

2.865 

2.875 

2,885 

2.895 

2.905 

2.915 

2.926 

58 

2.936 

2.946 

2,956 

2.966 

2.976 

2,986 

2,997 

3.007 

3.017 

3.027 

59 

3.038 

3.048 

3.058 

3.069 

3.079 

3,089 

3.100 

3.110 

3.121 

3.131 

60 

3.142 

3.152 

3.163 

3.173 

3.184 

3.194 

3.205 

3.215 

3,226 

3.237 

61 

3.247 

3.258 

3.269 

3.279 

3.290 

3.. 301 

3.311 

3.322 

3,333 

3.344 

62 

3.355 

3.365 

3 .  376 

3.387 

3.398 

3.409 

3,420 

3.431 

3,442 

3.453 

63 

3.464 

3.475 

3 ,  486 

3.497 

3 ,  508 

3.519 

3 ,  530 

3.541 

3.552 

3.563 

64 

3 .  574 

3.. 586 

3 ,  597 

3.608 

3.019 

3.630 

3.642 

3 .  653 

3.664 

3.676 

65 

3.687 

3.698 

3.710 

3.721 

3 ,  733 

3.744 

3.755 

3.767 

3.778 

3.790 

60 

3 .  801 

3.813 

3.824 

3.836 

3 .  848 

3.859 

3.871 

3.882 

3.894 

3.906 

67 

3.917 

3.929 

3.941 

3,953 

3.964 

3.976 

3.988 

4,000 

4,012 

4.023 

68 

4.035 

4.047 

4.059 

4.071 

4.083 

4.095 

4.107 

4.119 

4,131 

4.143 

69 

4.155 

4.167 

4.179 

4.191 

4.203 

4.215 

4.227 

4 .  239 

4.252 

4.264 

70 

4.276 

4.288 

4.301 

4.313 

4.325 

4.337 

4.350 

4.362 

4.374 

4.387 

71 

4 .  399 

4,412 

4.424 

4 .  436 

4 .  449 

4.401 

4.474 

4 .  486 

4.499 

4.511 

72 

4.524 

4.530 

4.549 

4.502 

4.574 

4., 587 

4.600 

4.612 

4.625 

4.638 

73 

4.650 

4.663 

4.676 

4.689 

4.702 

4.714 

4.727 

4.740 

4.753 

4.766 

74 

4.779 

4.792 

4.805 

4.818 

4.831 

4.844 

4.857 

4.870 

4.883 

4.896 

75 

4.909 

4.922 

4 .  935 

4.948 

4.961 

4.975 

4.988 

5.001 

5.014 

5.027 

76 

5.041 

5 .  054 

5 .  067 

5.080 

5.094 

5.107 

5.120 

5.134 

5.147 

5.161 

77 

5.174 

5.187 

5.201 

5.214 

5.228 

5.241 

5 .  255 

5.269 

5.282 

5.296 

78 

5.309 

5.323 

5.337 

5.350 

5.. 364 

5.378 

5.391 

5.405 

5.419 

5.433 

79 

5.440 

5.460 

5.474 

5.488 

5.502 

5.515 

5.529 

5.543 

5.557 

5.571 

80 

5 .  585 

5.599 

5.613 

5.627 

5.641 

5.655 

5.6G9 

5.683 

5.697 

5.711 

496 


APPENDIX  C 


TABLE  JjXXXI— Continued 


Diameter. 

0.6G  OF  THE  Area  of  a  Circle  at  the  Middle  Height 

OF  THE  Tbee    (0.66B) 

Inches 

0.0 

Sq.  ft. 

0.1 
Sq.  ft. 

0.2 
Sq.  ft. 

0.3 
Sq.  ft. 

0.4 

Sq.  ft. 

0.5 

Sq.  ft. 

0.0 
Sq.  ft. 

0.7 
Sq.  ft. 

0.8 
Sq.  ft. 

0.9 

Sq.  ft. 

1 

0.004 

0.004 

0.005 

0.006 

0.007 

0.008 

0.009 

0.010 

0.012 

0.013 

2 

.014 

.016 

.017 

.019 

.021 

.023 

.024 

.020 

.028 

.030 

3 

.032 

.035 

.037 

.039 

.042 

.044 

.047 

.049 

.052 

.055 

4 

.058 

.061 

.064 

.  067 

.070 

.073 

.076 

.080 

.083 

.086 

5 

.090 

.094 

.097 

.101 

.105 

.109 

.113 

.117 

.121 

.125 

6 

.130 

.134 

.138 

.143 

.147 

.152 

.157 

.162 

.100 

.171 

7 

.176 

.182 

.187 

.192 

.197 

.202 

.208 

.213 

.219 

.225 

8 

.230 

.236 

.242 

.248 

.254 

.260 

.266 

.273 

.279 

.285 

9 

.292 

.298 

.305 

.311 

.318 

.325 

•   .332 

.339 

.340 

.353 

10 

.360 

.367 

.375 

.382 

.389 

.397 

.405 

.412 

.420 

.428 

11 

.436 

.444 

.452 

.460 

.468 

.476 

.484 

.493 

.501 

.510 

12 

.518 

.  527 

.536 

.545 

.554 

.563 

.572 

.581 

.590 

.599 

13 

.608 

.618 

.627 

.637 

.646 

.650 

.666 

.676 

.686 

.696 

14 

.706 

.716 

.726 

.736 

.746 

.757 

.767 

.778 

.788 

.799 

15 

.810 

.821 

.832 

.843 

.854 

.865 

.876 

.887 

.899 

.910 

10 

.922 

.933 

.945 

.956 

.968 

.980 

.992 

1.004 

1.016 

1.028 

17 

1.040 

1.053 

1.065 

1.077 

1.090 

1.102 

1.115 

1.128 

1.140 

1.153 

IS 

1.166 

1.179 

1.192 

1.205 

1.219 

1.232 

1.245 

1.259 

1.272 

1.286 

19 

1.299 

1.313 

1.327 

1.341 

1.355 

1.369 

1.383 

1.397 

1.441 

1.426 

20 

1.440 

1 .  454 

1.469 

1.483 

1.498 

1.513 

1.528 

1.542 

1.557 

1.572 

21 

1 .  587 

1.603 

1.618 

1.633 

1.049 

1.664 

1.080 

1.695 

1.711 

1.726 

22 

1.742 

1.758 

1.774 

1.790 

1.800 

1.822 

1.839 

1.855 

1.871 

1.888 

23 

1.904 

1.921 

1.937 

1.954 

1.971 

1.988 

2.005 

2.022 

2.039 

2.056 

24 

2.073 

2.091 

2.108 

2.126 

2.143 

2.161 

2.178 

2.190 

2.214 

2.232 

25 

2.250 

2.268 

2.286 

2.304 

2.322 

2.341 

2.359 

2.378 

2.396 

2.415 

2r. 

2.433 

2.452 

2.471 

2.490 

2 .  509 

2.528 

2.547 

2.. 506 

2.585 

2.605 

27 

2.624 

2.644 

2.663 

2.683 

2.703 

2.722 

2.742 

2.762 

2.782 

2.802 

28 

2.822 

2.842 

2.863 

2.883 

2.903 

2.924 

2.944 

2.965 

2.986 

3.006 

29 

3.027 

3.048 

3.069 

3.090 

3.111 

3.133 

3.154 

3.175 

3.197 

3.218 

30 

3.240 

3.261 

3.283 

3.305 

3.327 

3.349 

3.371 

3 .  393 

3.415 

3.437 

31 

3.459 

3.482 

3.. 504 

3.527 

3.549 

3.572 

3.595 

3.617 

3.640 

3.663 

32 

3.686 

3 .  709 

3.732 

3.750 

3.779 

3.802 

3.820 

3.849 

3.873 

3.896 

33 

3.920 

3.944 

3.968 

3.092 

4.010 

4.040 

4.004 

4.088 

4.112 

4.137 

34 

4.161 

4.186 

4.210 

4.235 

4.200 

4.285 

4.309 

4.334 

4.359 

4.385 

35 

4.410 

4.435 

4.460 

4.486 

4.511 

4.537 

4.562 

4.588 

4.614 

4.639 

36 

4.665 

4.691 

4.717 

4.743 

4.769 

4.790 

4.822 

4.848 

4.875 

4.901 

37 

4.928 

4.955 

4.981 

5.008 

5.035 

5.062 

5.089 

5.116 

5.143 

5.171 

38 

5.198 

5.225 

5.253 

5.280 

5.308 

5.336 

5.363 

5.391 

5.419 

5.447 

39 

5.475 

5.. 503 

5.532 

5.560 

5.588 

5.616 

5.645 

6.673 

5.702 

5.731 

40 

5.760 

5.788 

5.817 

5.846 

5.875 

5.904 

5.934 

5.963 

5.992 

6.022 

41 

6.051 

6.081 

6.110 

6.140 

0.170 

6.200 

0.230 

0.200 

6.290 

6.320 

42 

6.350 

6.380 

6.411 

0.441 

6.471 

6.502 

6.533 

6.503 

0.594 

6.625 

43 

6.656 

6 .  687 

6.718 

6 .  74u 

6.780 

6.812 

6.843 

6.874 

6.906 

6.937 

44 

6.969 

7.001 

7.033 

7.064 

7.096 

7.128 

7.160 

7.193 

7.225 

7.257 

45 

7.290 

7.322 

7.354 

7.387 

7.420 

7.452 

7.485 

7.518 

7.551 

7.584 

46 

7.617 

7.650 

7.683 

7.717 

7.750 

7.784 

7.817 

7.851 

7.884 

7.918 

47 

7.952 

7.986 

8.020 

8.054 

8.088 

8.122 

8.156 

8.190 

8.225 

8.259 

48 

8.294 

8.328 

8.363 

8.404 

8.433 

8.467 

8.502 

8.537 

8.573 

8.608 

49 

8.643 

8.678 

8.714 

8.749 

8.785 

8.820 

8.856 

8.892 

8.927 

8.963 

50 

8.999 

9.035 

9.072 

9.108 

9.144 

9.180 

9.217 

9.253 

9.290 

9.326 

TABLES  USED  IN  FOREST  MENSURATION 


497 


TABLE  LXXXII 

Breast-high  Form  Factors 

For  Various  Heights  and  Form  Classes 

Total  Cubic  Volume  of  Stem 


Form  Ci 

ASS 

Height 

Height 

in 
feet 

0.50 

0.525 

lo.. 

0.575 

0.60 

'o.62o 

0.65 

0.675 

0.70 

0.725 

0.75 

0.775 

0.80 

in 

feet 

(5-foot 

1 

1 

1 

1 

(5-foot 

classes) 



classes) 

Bre 

\ST-HiGH  Form  Factor 

20 

0.524 

0.532 

0.541 

0,548 

0.559 

0.569 

0.581 

0.592 

0.607 

0.620 

0.641 

0.661 

0.683 

20 

25 

472 

482 

494 

504 

517 

530 

545 

560 

577 

595 

614 

635 

657 

25 

30 

443 

454 

466 

478 

494 

508 

524 

541 

559 

579 

598 

621 

643 

30 

35 

424 

436 

449 

464 

478 

494 

511 

528 

547 

568 

588 

611 

635 

35 

40 

409 

422 

437 

452 

468 

483 

501 

518 

537 

559 

580 

603 

628 

40 

45 

398 

412 

427 

442 

459 

474 

493 

510 

530 

552 

574 

597 

623 

45 

50 

389 

404 

420 

435 

451 

468 

487 

504 

524 

546 

569 

592 

619 

50 

55 

583 

397 

414 

429 

445 

463 

482 

499 

519 

542 

565 

588 

615 

55 

60 

378 

392 

409 

424 

441 

459 

477 

495 

515 

538 

562 

584 

612 

60 

65 

373 

388 

405 

420 

437 

455 

473 

492 

512 

535 

559 

581 

609 

65 

70 

369 

385 

401 

417 

434 

452 

470 

489 

509 

532 

556 

579 

606 

70 

75 

366 

382 

398 

415 

431 

449 

467 

487 

507 

529 

553 

577 

604 

75 

80 

364 

380 

395 

412 

429 

446 

465 

485 

505 

527 

550 

575 

603 

80 

85 

361 

378 

393 

410 

427 

444 

463 

483 

503 

525 

548 

573 

601 

85 

90 

359 

376 

392 

409 

425 

442 

461 

481 

501 

523 

546 

571 

600 

90 

95 

357 

374 

390 

407 

424 

441 

460 

479 

500 

522 

545 

570 

598 

95 

100 

356 

373 

389 

405 

423 

440 

459 

478 

499 

521 

544 

569 

597 

100 

105 

354 

371 

387 

404 

421 

439 

457 

477 

498 

520 

543 

568 

596 

105 

110 

353 

370 

386 

403 

420 

437 

456 

476 

4971 

519 

542 

567 

595 

110 

115 

352 

368 

385 

402 

419 

436 

455 

475 

495 

518 

541 

566 

594 

115 

.0 

350 

367 

384 

401 

417 

434 

453 

474 

494 

516 

540 

565 

593 

120 

*  From  table,   Massatabeller  fiir  Traduppskattning.     Tor  Jonson,  Stockholm,  Sweden,  1918, 
p.  66,  by  conversion  of  height  in  meters  to  height  in  feet. 


498 


APPENDIX  C 


TABLE  LXXXIII  * 

Weights  per  Cord  of  Timber  op  Various  Species — 7-  to  8-inch  Wood 
Hardwoods 


Species 


Pounds, 

Pounds, 

green 

seasoned 

4150 

2600 

4050 

365) 

4700 

3300 

4150 

3800 

4300 

3800 

4150 

3600 

4150 

3450 

4150 

3750 

4600 

4300 

4250 

2500 

3850 

2500 

3700 

2450 

4950 

4050 

4600 

3550 

5300 

4400 

5200 

4100 

4400 

2350 

4500 

3350 

4150 

2500 

4150 

3350 

2950 

2600 

4850 

2850 

5500 

3000 

4150 

2250 

4500 

3200 

5850 

5050 

4950 

4400 

5850 

3450 

4750 

4250 

5050 

3500 

4700 

3250 

4050 

3350 

6300 

4900 

5950 

3450 

4150 

3250 

Species 


Pounds,    Pounds, 
green      seasoned 


Alder,  red 

Ash,  Biltmore 

Ash,  black 

Ash,  blue 

Ash,  green 

Ash,  Oregon 

Ash,  pumpkin 

Ash,     white      (forest 

growth) 

Ash,     white     (second 

growth) 

Aspen 

Aspen,  large  tooth .  . 

Basswood 

Beech 

Birch,  paper 

Birch,  sweet 

Birch,  yellow 

Bird's  eye,  yellow. .  . 
Buckthorn,  cascara .  . 

Butternut 

Cherry,  black 

Chqrry,  wild  red 

Chestnut 

Chinquapin,  Western 
Cottonwood,  black..  . 

Cucumber  tree 

Dogwood,  flowering . 
Dogwood,  Western.  . 

Elder,  pale 

Elm,  cork 

Elm,  slippery 

Elm,  white 

Gum,  black 

Gum,  blue ^ . 

Gum,  cotton 

Gum,  red 


Hackberry 

Haw,  pear 

Hickory,  big  shell  bark 
Hickory,  butternut..  . 
Hickory,  mockernut.. 
Hickory,  nutmeg .... 

Hickory,  pig  nut 

Hickory,  shagbark .  .  . 

Hickory,  water 

Holly,  American 

Hornbeam 

Laurel,  California..  .  . 
Laurel,  mountain .... 

Locust,  black 

Locust,  honey 

Madrona 

Magnolia,  evergreen  . 

Maple,  Oregon 

Maple,  red 

Maple,  silver 

Maple,  sugar 

Oak,  burr 

Oak,  C  a  1  i  f  or  n  i  a, 

black 

Oak,  canyon  live .... 

Oak,  chestnut 

Oak,  cow 

Oak,  laurel 

Oak,  Pacific  post 

Oak,  post 

Oak,  red 

Oak,  Spanish  highland 
Oak,  Spanish  lowland 

Oak,  water 

Oak,  white 

Oak,  willow 

Oak,  yellow 


4500 
5650 
5650 
5750 
5750 
5500 
■5750 
5750 
6200 
5150 
5400 
4850 
5600 
5200 
5850 
5400 
5600 
4250 
4600 
4150 
5050 
5600 

5900 
6400 
5600 
5850 
5850 
6100 
5650 
5750 
5600 
6050 
5650 
5600 
6050 
5650 


3500 
4550 
4800 
4550 
4900 
4000 
5050 
4850 
4300 
3750 
4900 
3650 
4550 
4550 
4750 
4000 
3250 
3200 
3450 
3200 
4100 
4200 

3650 
5200 
4300 
4650 
4400 

4500 
4100 
3900 
4600 
4200 
4500 
4300 
4100 


♦From  General  Orders  No.  63,  War  Department,    p.  4, 


TABLES  USED  IN  FOREST  MENSURATION 


499 


TABLE  LXXXIU— Continued 
Hardwoods — Continued 


Species 


Pounds,  I  Pounds,  i 
green    ,  seasoned| 


Species 


Pounds,  !  Pounds, 
green    :  seasoned 


Poplar,  yellow 

Rhododendron,  great 

Sassafras 

Service  berry 

Silver-bell  tree 

Sourwood 


Sumach,  staghorn .  .  .  j     3700 

Sycamore 

Umbrella,  Eraser.  .  .  . 

Willow,  black 

Willow,  Western  black 
Witch  hazel 


3200 


4700  3400 

4250  2900 

4600  2400 

4600  [  2900 

5300  t  4300 


Conifers 


Cedar,  incense .... 
Cedar,  Port  Orford. 
Cedar,  Western  red 

Cedar,  white 

Cypress,  bald 

C3T)ress,  yellow.  .  . 
Douglas    fir.     Pacific 

Northwest 

Douglas  fir,  mountain 

type •■ 

Fir,  Alpine 

Fir,  amabilis 

Fir,  balsam 

Fir,  Noble 

Fir,  white 

Hemlock,  black 

Hemlock,  Eastern.  .  . 
Hemlock,  Western . . . 

Larch,  Western 

Pine,  Cuban 


4150 

1! 

2400 

3500 

2900 

2450 

2100   1 

2500 

1950 

4300 

3200 

3150 

3400 

3250 

3100 

2900 

2500 

2050 

4250 

2700 

4050 

2350 

2800 

2600   I 

5050 

2400 

4050 

3000 

4350 

3100 

4200 

2900 

4300 

3500 

4750 

4200 

Pine,  jack 

Pine,  Jeffrey 

Pine,  loblolly 

Pine,  lodgepole 

Pine,  longleaf 

Pine,  Norway 

Pine,  pitch 

Pine,  pond 

Pine,  shortleaf 

Pine,  sugar 

Pine,  Table  Mountain 
Pine,  Western  white. . 
Pine,  Western  yellow. 

Pine,  white 

Spruce,  Englemann.  . 

Spruce,  Sitka 

Spruce,  white 

Tamarack 

Yew,  Western 


4500 

4250 

4750 

3500 

4550 

3800 

4850 

4400 

4500 

4500 

4850 

3500 

4150 

3500  I 

3500  I 

3250  [ 

3300 

4250 

4850 


2800 
2600 
3600 
2700 
3950 
3200 
3200 
3750 
3500 
2500 
3450 
2800 
2650 
2500 
2200 
2400 
2650 
3550 
4200 


Two  pounds  of  air-dried  wood  are  equivalent  to  1  pound  of  average  hard  coal. 
The  above  table  indicates  the  comparative  fuel  value  of  different  species  of  wood 
compared  with  coal.  For  anthracite,  the  equivalent  is  2.5  pounds  of  dry  wood 
to  1  pound  of  coal,  or  3|  pounds  green  wood  to  1  pound  coal. 


500 


APPENDIX  C 


TABLE 

The  Tiemann  Log  Rule  for  Saws 

This  log  rule  is  applied  to  the  diameter  inside  bark  at  middle  of 

on  mill  tallies,  for  1-inch  boards,  but  conforms  to  the  formula, 

TABLE 
Tiemann 


Middle 

diameter, 

Inches 


Length  of 


10 


12 


13 


11 
14 

17 
21 
25 
30 
35 

40 
46 
52 

58 
65 

72 
80 
88 
96 
105 

114 
123 
133 
143 

154 

165 
176 


Contents- 


1 

1 

1 

2 

2 

2 

2 

2 

3 

3 

3 

3 

4 

4 

5 

5 

6 

7 

5 

6 

7 

8 

8 

9 

10 

11 

7 

9 

10 

11 

13 

14 

16 

17 

10 

12 

14 

16 

18 

20 

22 

24 

13 

16 

19 

21 

24 

27 

29 

32 

17 

21 

24 

28 

31 

34 

38 

41 

21 

26 

30 

34 

39 

43 

47 

52 

26 

32 

37 

42 

47 

52 

58 

63 

31 

38 

44 

50 

57 

63 

69 

76 

37 

45 

52 

60 

67 

74 

82 

89 

43 

52 

61 

69 

78 

87 

95 

104 

50 

60 

70 

80 

90 

100 

110 

120 

57 

69 

80 

91 

103 

114 

126 

137 

65 

78 

91 

104 

116 

129 

142 

155 

73 

87 

102 

116 

131 

145 

160 

175 

81 

98 

114 

130 

146 

162 

179 

195 

90 

108 

126 

144 

162 

180 

199 

217 

100 

120 

140 

160 

179 

199 

219 

239 

110 

132 

153 

175 

197 

219 

241 

263 

120 

144 

168 

192 

216 

240 

264 

288 

131 

157 

183 

209 

236 

262 

288 

314 

142 

171 

199 

228 

256 

284 

313 

341 

154 

185 

216 

246 

277 

308 

339 

370 

166 

200 

233 

266 

299 

332 

366 

399 

179 

215 

251 

286 

322 

358 

394 

430 

192 

231 

269 

308 

346 

384 

423 

461 

206 

247 

288 

329 

371 

412 

453 

494 

220 

264 

308 

352 

396 

440 

484 

528 

3 

7 

12 
18 
26 
35 
45 

56 
68 
82 
97 
113 

130 
148 
168 
189 
211 

235 
259 

285 
312 
340 

370 
400 
432 
465 
500 

535 
572 


TABLES  USED  IN  FOREST  MENSURATION 


501 


LXXXIV 

Cutting  a  ^-inch  Kerf 

log,  by  caliper  scale  with  deduction  of  widths  of  bark.     It   is   based 

L 


B.M.  =  (0.75Z)2-2Z)) 


16" 


LXXXIV 

Log  Rule 


Log — Feet 

14    15 

16 

17 

18 

19 

20 

21 

-1 

23 

24 

Board  Feet 

1 

1 

1  1 

1 

1 

1 

1 

1 

1 

1 

1 

4 

4 

4 

4 

4 

5 

5 

5 

6 

6 

6 

8 

8 

9 

9 

10 

10 

11 

11 

12 

13 

13 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

22 

20 

21 

23 

24 

26 

27 

28 

30 

31 

33 

34 

28 

30 

32 

34 

36 

38 

40 

42 

44 

46 

48 

37 

40 

43 

45 

48 

51 

53 

56 

59 

61 

64 

48 

52 

55 

58 

62 

65 

69 

72 

76 

79 

82 

60 

64 

69 

73 

77 

82 

86 

90 

95 

99 

103 

74 

79 

84 

89 

94 

100 

105 

110 

116 

121 

126 

88 

94 

101 

107 

113 

120 

126 

132 

139 

145 

151 

104 

112 

119 

126 

134 

141 

149 

156 

164 

171 

178 

121 

130 

139 

147 

156 

165 

173 

182 

191 

199 

208 

140 

150. 

160 

170 

180 

190 

200 

210 

220 

230 

240 

160 

171 

183 

194 

206 

217 

228 

240 

251 

263 

274 

181 

194 

207 

220 

233 

246 

259 

272 

285 

298 

310 

201 

218 

233 

247 

262 

276 

291 

305 

320 

335 

349 

228 

244 

260 

276 

292 

309 

325 

341 

358 

374 

390 

253 

271 

289 

307 

325 

343 

361 

379 

397 

415 

433 

279 

299 

319 

339 

359 

379 

399 

419 

439 

459 

478 

307 

329 

351 

373 

395 

417 

438 

460 

482 

504 

526 

336 

360 

384 

408 

432 

456 

480 

504 

528 

552 

576 

366 

393 

419 

445 

471 

497 

523 

550 

576 

602 

628 

398 

427 

455 

483 

512 

540 

569 

597 

626 

654 

682 

431 

462 

493 

524 

554 

585 

616 

647 

678 

708 

739 

466 

499 

532 

565 

598 

632 

665 

698 

732 

765 

798 

501 

537 

573 

609 

644 

680 

716 

752 

788 

823 

859 

538 

577 

615 

653 

692 

730 

769 

807 

846 

884 

922 

576 

618 

659 

700 

741 

782 

823 

865 

906 

947 

988 

616 

660 

704 

748 

792 

836 

880 

924 

1  968 

1012 

1056 

502 


APPENDIX  C 


TABLE  LXXXV 
TiEMANN  Log  Rule 
Reduced  to  end  measurement  assuming  a  taper  of  1  inch  to  8  feet. 


Length  of  Log — Feet 

Small 

end 

1        1         1 

diameter, 

6 

8        10       12       14 

16 

Inches 

1         1         ' 

Contents  of  Log — Board  Feet 

4 

2 

3 

4 

6 

7 

9 

5 

4 

6 

8 

10 

12 

15 

6 

7 

9 

12 

16 

19 

23 

7 

10 

14 

18 

22 

27 

32 

8 

13 

19 

24 

30 

36 

43 

9 

18 

24 

31 

39 

47 

55 

10 

22 

31 

40 

49 

59 

69 

11 

28 

38 

49 

60 

72 

84 

12 

34 

46 

59 

72 

86 

101 

13 

40 

55 

70 

86 

102 

119 

14 

47 

64 

82 

100 

119 

139 

15 

55 

75 

95 

116 

138 

160 

16 

63 

86 

109 

133 

157 

183 

17 

72 

98 

124 

151 

178 

207 

18 

81 

110 

139 

170 

201 

233 

19 

91 

123 

156 

190 

224 

260 

20 

101 

137 

174 

211 

249 

289 

21 

112 

152 

192 

233 

276 

319 

22 

124 

167 

212 

257 

303 

351 

23 

136 

184 

232 

282 

332 

384 

24 

149 

201 

253 

307 

363 

419 

25 

162 

218 

276 

334 

394 

455 

26 

176 

237 

299 

362 

427 

493 

27 

190 

256 

323 

392 

461 

532 

28 

205 

276 

348 

422 

497 

573 

29 

221 

297 

374 

453 

533 

615 

30 

237 

318 

401 

486 

572 

659 

31 

253 

341 

429 

519 

611 

704 

32 

271 

364 

458 

554 

652 

751 

TABLES  USED  IN  FOREST  MENSURATION  503 


TABLE  LXXXVI 

ScRiBNER  Decimal  C  Log  Rule  for  Saws  Cutting  a  J-inch  Kerf 

This  log  rule  disregards  taper,  and  is  applied  at  small  end  of  log, 
inside  bark.  It  is  based  on  diagrams  of  1-inch  boards,  values  not  made 
regular  by  curves,  and  deduction  for  slab  too  large  above  28  inches. 

The  Decimal  form  is  given,  with  values  of  the  original  rule  rounded 
off  to  the  nearest  10  board  feet  and  the  cipher  dropped.  To  read  in 
board  feet,  add  the  cipher.  Decimal  C  values  are  given,  as  in 
Table  XII,  §  68.  Values  above  44  inches  adopted  by  the  U.  S.  Forest 
Service. 


504 


APPENDIX  C 


TABLE  LXXXVI 
ScRiBNER  Decimal  C  Log  Rule 


Diam- 

Length—Feet 

Diam- 

eter, 

6  1 

7 

8  j 

9 

10 

11 

12 

13 

14 

15 

16 

eter, 

Inches 

Contents— Board  Feet 

Inches 

6 

0.5 

0.5 

0.5 

0.5 

1 

1 

1 

1 

1 

1 

2 

6 

7 

0.5 

1 

1 

1 

1 

2 

2 

2 

2 

2 

3 

7 

8 

1 

1 

1 

1 

2 

2 

2 

2 

2 

2 

3 

8 

9 

1 

2 

2 

2 

3 

3 

3 

3 

3 

3 

4 

9 

10 

2 

2 

3 

3 

3 

3 

3 

4 

4 

5 

6 

10 

11 

2 

2 

3 

3 

4 

4 

4 

5 

5 

6 

7 

11 

12 

3 

3 

4 

4 

5 

5 

6 

6 

7 

7 

8 

12 

13 

4 

4 

5 

5 

6 

7 

7 

8 

8 

9 

10 

13 

14 

4 

5 

6 

6 

7 

8 

9 

9 

10 

11 

11 

14 

15 

5 

6 

7 

8 

9 

10 

11 

12 

12 

13 

14 

15 

16 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

16 

17 

7 

8 

9 

10 

12 

13 

14 

15 

16 

17 

18 

17 

18 

8 

9 

11 

12 

13 

15 

16 

17 

19 

20 

21 

18 

19 

9 

10 

12 

13 

15 

16 

18 

19 

21 

22 

24 

19 

20 

11 

12 

14 

16 

17 

19 

21 

23 

24 

26 

28 

20 

21 

12 

13 

15 

17 

19 

21 

23 

25 

27 

28 

30 

21 

22 

13 

15 

17 

19 

21 

23 

25 

27 

29 

31 

33 

22 

23 

14 

16 

19 

21 

23 

26 

28 

31 

33 

35 

38 

23 

24 

15 

18 

21 

23 

25 

28 

30 

33 

35 

38 

40 

24 

25 

17 

20 

23 

26 

29 

31 

34 

37 

40 

43 

46 

25 

26 

19 

22 

25 

28 

31 

34 

37 

41 

44 

47 

50 

26 

27 

21 

24 

27 

31 

34 

38 

41 

44 

48 

51 

55 

27 

28 

22 

25 

29 

33 

36 

40 

44 

47 

51 

54 

58 

28 

29 

23 

27 

31 

35 

38 

42 

46 

49 

53 

57 

61 

29 

30 

25 

29 

33 

37 

41 

45 

49 

53 

57 

62 

66 

30 

31 

27 

31 

36 

40 

44 

49 

53 

58 

62 

67 

71 

31 

32 

28 

32 

37 

41 

46 

51 

55 

60 

64 

69 

74 

32 

33 

29 

34 

39 

44 

49 

54 

59 

64 

69 

73 

78 

33 

34 

30 

35 

40 

45 

50 

55 

60 

65 

70 

75 

80 

34 

35 

33 

38 

44 

49 

55 

60 

66 

71 

77 

82 

88 

35 

36 

35 

40 

46 

52 

58 

63 

69 

75 

81 

86 

92 

36 

37 

39 

45 

51 

58 

64 

71 

77 

84 

90 

96 

103 

37 

38 

40 

47 

54 

60 

67 

73 

80 

87 

93 

100 

107 

38 

39 

42 

49 

56 

63 

70 

77 

84 

91 

98 

105 

112 

39 

40 

45 

53 

60 

68 

75 

83 

90 

98 

105 

113 

120 

40 

41 

48 

56 

64 

72 

79 

87 

95 

103 

111 

119 

127 

41 

42 

50 

59 

67 

76 

84 

92 

101 

109 

117 

126 

134 

42 

43 

52 

61 

70 

79 

87 

96 

105 

113 

122 

131 

140 

43 

44 

56 

65 

74 

83 

93 

102 

111 

120 

129 

139 

148 

44 

45 

57 

66 

76 

85 

95 

104 

114 

123 

133 

143 

152 

45 

46 

59 

69 

79 

89 

99 

109 

119 

129 

139 

149 

159 

46 

47 

62 

72 

83 

93 

104 

114 

124 

134 

145 

155 

166 

47 

48 

65 

76 

86 

97 

108 

119 

130 

140 

151 

162 

173 

48 

49 

67 

79 

90 

101 

112 

124 

135 

146 

157 

168 

180 

49 

60 

70 

82 

94 

105 

117 

129 

140 

152 

164 

175 

187 

50 

TABLES  USED  IN  FOREST  MENSURATION  505 


TABLE  LXXXVII 

Index  to  Standard  Volume  Tables 

Standard  volume  tables  (§  140)  have  been  constructed  by  the 
U.  S.  Forest  Service,  by  state  forestry  departments,  by  forest  schools, 
and  in  some  instances  by  private  corporations,  or  individuals. 

This  index  is  intended  to  include  such  of  these  tables  as  are  of 
value  for  future  timber  estimating,  and  can  be  obtained  in  pubHshed 
form,  or  from  the  U.  S.  Forest  Service.  The  index  briefly  describes 
each  table  under  the  standard  headings  to  enable  the  estimator  to 
decide  whether  or  not  it  is  suitable  for  his  purposes.  The  final  column 
gives  the  Forest  Service  designation  of  such  tables  as  have  not  so  far 
been  published. 


506 


APPENDIX  C 


Hardwoods 


TABLE 


Species 


Unit  of  measure- 
ment 


Log  rule 


Aspen       .... 

Aspen       .... 

Aspen       .... 
Aspen       .... 
Ash,  black 
Ash,  black 
Ash,  black 
Ash,  green     . 
Ash,  green     . 
Ash,  green     . 
Ash,  gieen     . 
Ash,  green 
Ash,  green     . 
Ash,  white 
Ash,  white 
Ash,  white 
Ash,  white 
Ash,  white 
Ash,  white 
Ash,  white 

Ash,  white 
Ash,  white 

Basswood.  .  . 
Beech  .... 
Beech     

Beech     

Beech     

Beech     

Beech 

Beech 

Birch,  paper. 
Birch,  paper. 
Birch,  paper. 
Birch,  paper. 
Birch,  paper . 
Birch,  paper. 
Birch,  paper . 
Birch,  yellow 

Birch,  yellow 
Birch,  yellow 
Birch,  yellow 
Chestnut.  .  .  . 
Chestnut .  .  .  . 

Chestnut.  .  .  . 
Cottonwood . 
Cottonwood . 


New  Hampshire 

Maine 

Maine 

Utah 

General 

General 

General 

General 

General 

General 

General 

General 

General 

General 

General 

General 

General 

General 

General 

Eastern  U.  S. 

Vermont 
Vermont 

Lake  States 

Vermont 

Vermont 

Michigan 
Pennsylvania 
New  Hampshire 
Pennsylvania 
Michigan 
New  Hampshire 
New  Hampshire 
Maine,  N.  Hamp. 
Maine,  N.  Hamp. 
Maine,  N.  Hamp. 
Maine,  N.  Hamp. 
Maine,  N.  Hamp. 
Vermont 

Vermont 

New  Hampshire 

Lake  States 

Connecticut 

Connecticut 

Connecticut 
Mississippi  Valley 
Mississippi  Valley 


25-50  yrs. 


Over  75  yrs. 
Over  75  yrs. 
Over  75  yrs. 
Under  75  yrs. 
Over  75  yrs. 
Under  75  yrs. 
Over  75  yrs. 
Under  75  yrs. 
Over  75  yrs. 
Under  75  yrs. 
Over  75  yrs. 
Under  75  yrs. 
Over  75  yrs. 
Under  75  yrs. 
Over  75  yrs. 


Second  growth 
Second  growth 


45-60  yrs. 
45-60  yrs. 


Second  growth 
Second  growth 


Second  growth 
Second  growth 

Second  growth 
Second  giowth 
Second  growth 


Cubic  ft.  peeled 

merch. 
Cubic  ft.  peeled 

merch. 
Cords 
Board  ft. 

Cu.  ft.,  peeled  total 
Cords 
Board  feet 
Cu.  ft.,  peeled  total 
Cu.  ft.,  peeled  total 
Cords 
Cords 
Board  feet 
Board  feet 
Cu.  ft.,  peeled  total 
Cu.  ft.,  peeled  total 
Cords 
Cords 
Board  feet 
Board  feet 
Cu.    ft.   of   branch 

wood 
Cu.  ft.,  with  limbs 
Bd.  ft.  and  cu.  ft.  in 

tops 
Board  feet 
Cu.  ft.,  with  limbs 
Bd.  ft.  and  cu.  ft.  in 

tops 
Cubic  feet 
Cubic  feet 
Board  feet 
Board  feet 
Board  feet 
Cubic  ft.,  merch. 
Board  feet 
Cu.  ft.,  total 
Cubic  ft.,  merch. 
Board  feet 
Cubic  ft.,  merch. 
Board  feet 
Cu.   ft.,  total  with 

limbs 
Board  feet 
Board  feet 
Board  feet 
Cu.  ft.,  merch.  O.B. 
Board  feet 

Cubic  feet  merch. 
Cu.  ft., peeled  total 
Board  feet 


Scribner  Dec  C. 


Scribner  Dec.  C. 


Scribner  Dec.  C. 
Scribner  Dec.  C. 


Scribner  Dec.  C. 
Scribner  Dec.  C. 


Scribner  Dec.  C. 


Scribner  Dec.  C. 
Scribner  Dec.  C. 
Scribner  Dec.  C. 


Mill  tally 


New  Hampshire 
New  Hampshire 


Scribner  Dec.  C. 
Scribner  Dec.  C. 


International 
i"  kerf 


Scribner  Dec.  C. 


TABLES  USED  IN  FOREST  MENSURATION 


507 


LXXXVII 


Hardwoods 


D.B.H. 

(Inches) 


Height. 

(Feet) 


30-  90 

30-  90 
1-4  log 
60-110 
60-110 
2-  6  log 
40^100 
60-130 
40-100 
60-130 
40-100 
60-130 
20-  90 
50-150 
20-  90 
50-120 
U-5  1og 


40-  90 
40-  90 

2-^ 
30-  70 
30-  70 

40-100 

70-110 

^3|log 

2-4  log 

1-4^  log 

10-50  used 

10-50  used 

50-  90 

12-60  used 

12-60  used 

50-  90 

50-  90 

40-  70 

40-  70 
J-3i  log 
U-3i  log 
20-  90 
50-   90 

50-  90 
50-150 
80-150 


Top 
diameter. 
(Inches) 


6-10 
6-10 


6-18 
2 


6-15 
6-21 
6-17 
6  21 
6-15 
4-10 
4-10 


6-21 

6-17 

2 

7-12 


Baals. 
Trees 


487 
423 
475 


1911 

1911 
1913 
1915 
1915 
1915 
1915 
1915 
1915 
1915 
1915 
1915 
1915 
1915 
1915 
1915 
1915 
1915 
1915 

1914 
1914 

1915 
1914 
1914 

1915 
1909 
1915 
1915 
1915 
1905 
1905 
1909 
1909 
1909 

1909 
1914 

1914 
1915 
1915 
1912 
1912 

1905 
1910 
1910 


U.  S.  F.  S. 
designation 


Bui.  36,  U.  S.  Forest  Se 
Bui.  93,  U.  S.  Forest  Service 


Bui.  299,  U.  S 


Dept.  Agr. 


Bui.  176,  Vt.  Agr.  Exp.  .Sta. 


Bui.  285,  U.  S.  Dept.  Agr. 
Bui.  176,  Vt.  Agr.  Exp.  Sta. 


Bui.  285,  U.  S.  Dept.  Agr. 

Bui.  36,  U.  S.  Forest  Service 
Circ.  163,  U.  S.  Forest  Service 

Circ.  163,  U.  S.  Forest  Service 

Bui,  285,  U.  S.  Dept.  Agr. 
Bui.  96,  U.  S.  Forest  Service 

N.  H.  Forestry  Com.  Report 


W94-V8 

W94-V8 


508 


APPENDIX  C 


TABLE  LXXXVII 


Hardwoods — Continued 


Species 

Locality 

Tree  class 

Unit  of  measure- 
ment 

Log  rule 

Eucalyptus 

California 

Plantations 

Cubic  feet 

(Blue  gum) 

Eucalyptus 

California 

Plantations 

Board  feet 

Scribner  Dec.  C. 

(Blue  gum) 

Gum,  red       

Southern  States 

Under  75  yrs. 

Board  feet 

Scribner  Dec.  C. 

Gum,  red       

Southern  States 

Over  75  yrs. 

Board  feet 

Scribner  Dec.  C. 

Gum,  red       

Southern  States 

Over  75  yrs. 

Board  feet 

Scribner  Dec.  C. 

Hickories     

Eastern  States 

Cubic  ft.,  merch. 

Hickories     

Eastern  States 

Cubic  ft.,  total 

Maple,  red 

Massachusetts 

Second  growth 

Cubic  ft.,  merch. 

Maple,  red 

Maple,  sugar 

Maple,  sugar 

Second  growth 
Second  growth 
Second  growth 

Cords 

Cu    ft      with  limbs 

Bd     ft      cu     ft    in 

tops 

Lake  States 

Cu.  ft.,  merch.  O.B. 

Maple,  sugar 

cu.  ft.  in  tops 

Maple,  sugar 
Maple,  sugar 

Maple,  sugar   

Maple,  sugar 

Maple,  sugar 

Pennsylvania 
New  Hampshire 

Lake  States 

Board  feet 

Scribner  Dec.  C. 

Oak,  chestnut     

S.  Appalachians 

Over  75  yrs 

Board  feet 

Scribner  Dec.  C. 

Oak,  chestnut 

S.  Appalachians 

Over  75  yrs. 

Board  feet 

Scribner  Dec.  C. 

Oak   red             

New  Hampshire 
New  Hampshire 
S.  Appalachians 
S.  Appalachians 
S.  Appalachians 
Connecticut 

Oak    red                  .     . 

Second  growth 
Under  75  yrs. 
Over  75  yis. 
Over  75  yrs. 
Second  growth 

Board  feet 

Mill  tallies 

Oak   red 

Bo  aid  feet 

Scribner  Dec   C 

Oak   red 

Board  feet 

Scribner  Dec   C 

Oak   red 

Scribner  Dec   C 

Oak,  red,  scarlet  and 

Cubic  ft.,  merch. 

black 

Oak,  red,  scarlet  and 

Connecticut 

Second  giowth 

Board  feet 

International 

black 

y  kerf 

Oak,  white 

Connecticut 

Second  growth 

Cu.  ft.,  merch.  O.B. 

Oak,  white 

Connecticut 

Second  growth 

Board  feet 

International 
kerf 

Oak,  white 

New  York 

Second  growth 

Cu.  ft.,  merch.  O.B. 

S.  Appalachians 
S.  Appalachians 

PQplar,  yellow 

1-50  yrs. 

Board  feet 

Scribner  Dec.  C. 

Poplar,  yellow 

S.  Appalachians 

51-100  yrs. 

Board  feet 

Scribner  Dec.  C. 

Poplar,  yellow 

S.  Appalachians 

Under  100  yrs. 

Board  feet 

Mill  tallies 

Poplar,  yellow 

S.  Appalachians 

Over  100  yrs. 

Board  feet 

Mill  tallies 

Poplar,  yellow 

Poplar,  yellow 

Virginia 
Virginia 

Second  growth 
Second  growth 

Cubic  feet    total 

Board  feet 

Scribner  Dec.  C. 

TABLES  USED  IN  FOREST  MENSURATION 


509 


— Continued 


Hardwoods — Continued 


Height. 


Top 
diameter 
finches)  (Feet)  (Inches) 


2-23 
7-24 

8-32 

8-48 
8-48 
5-28 
5-18 
2-17 
3-17 
2-15 
7-14 

6-30 
10-28 

10-28 
7-32 


8-40 
8-40 
5-20 
5-20 
8-25 
8-44 


2-16 
9-16 


10-40 
7-26 
9-30 
7-26 

10-40 
5-20 
7-20 


50-160 

1-6  log 
1-7  log 
80-140 
5-65  used 
40-  90 
20-  80 
20-  80 
40  -80 
40-  80 

50-100 
70-110 

2i-4  log 
i-4  log 
lJ-4  log 
2-5  log 
1-1 1  log 
1-5  log 
40-110 
10-50  used 
10-50  used 
40-100 
1-5  log 
40-130 
20-  80 

50-  80 

20-  80 
50-  70 

20-  60 

1-5  log 
1-5  log 
1-6  log 
1-5  log 
2-6  log 
50-100 
40-100 


Basis. 
Trees 


6-13 
6-23 
6-23 
4-20 

2 
2 


6-17 
6-16 

6-16 
6-21 
6-17 
6-13 
7-22 
6-20 
6-20 
5-  9 
5-  9 
6-13 
6-22 
6-22 
2 

7-10 

2 


6-  8 
6-14 
6-  8 
6-17 


332 
1740 
1740 
630 
365 
397 
397 
222 
222 

305 
41 

41 
360 

278 
278 
278 
2232 
2232 


1300 
1300 
441 

175 

293 

26 

349 

1436 
489 
102 


407 
491 
480 


1906 

1904 
1904 
1904 
1910 
1910 
1915 
1915 
1914 
1914 

1915 
1915 

1915 
1915 
1915 
1915 
1915 
1913 
1913 
1905 
1905 
1914 
1914 
1914 
1913 

1913 

1913 
1913 

1905 

1903 
1913 
1913 
1913 
1913 
1907 
1907 


Bui.  80,  U.  S.  Forest  Service 

Bui.  80 

Bui.  285,  U.  S.  Dept.  Agr. 

Bui.  176,  Vt.  Agr.  Exp.  Sta. 


Bui.  285,  U.  S.  Dept.  Agr. 


Bui.  285.  U.  S.  Dept.  Agr 

N.H.  Forestry  Com.  Report 
"       and  Bui.  36,  U.  S.  For.  Serv. 

Bui.  96,  U.  S.  Forest  Service 


Bui.  36,  U.  S.  Forest  Service 


Bui.  36,  U.  S.  Forest  Service 


U.  S.  F.  S. 
designation 


G93-V2-3 


G71-V5 
G71-V7 
G71-V8 


Q68-V19 
Q68-V20 


Q61-V18 
Q61-V15 
Q61-V16 


Q82-V1 

W82-V24 

W82-V25 

W82-V26 

W82-V28 


510 


APPENDIX  C 


TABLE  LXXXVII 


Conifers 


Spec 


Cedar,  incense 

Cedar,  incense 

Cedar,  incense 

Cedar,  western  red. 

Cedar,  western  red. 
Cedar,  western  red. . 

Cypress 

Cypress 

Douglas  fir 

Douglas  fir 

Douglas  fir 

Douglas  fir 

Douglas  fir 

Douglas  fir 

Douglas  fir 

Douglas  fir 

Fir,   Amabilis 

Fir,  balsam 

Fir,  balsam 

Fir,  balsam 

Fir,  balsam 

Fir,  balsam 

Fir,  balsam 

Fir,  balsam 

Fir,  balsam 

Fir,  balsam 

Fir,  balsam,  western, 

Fir,  red 

Fir,  red 

Fir,  red 

Fir,  red 

Fir,  white 

Fir,  white 

Fir,  white 

Fir,  white 

Fir,  white 

Hemlock 

Hemlock 

Hemlock 

Hemlock 

Hemlock 

Hemlock 

Hemlock 

Hemlock 

Hemlock,  western.  . 
Hemlock,  western.    . 

Juniper 

Juniper 

Larch,  western 


California 
California 
California 
Puget  Sd.,  Wash. 

Idaho 
Idaho 

South  Carolina 

South  Carolina 
Washington,  Oregon 
Washington,  Oregon 
Oregon 
California 
California 
New  Mexico 
Montana,  Idaho 
Montana,  Idaho 

Washington,  Oregoi 
New  York,  Maine 
New  York 

Maine 

New  Hampshire 

New  York,  Maine 

New  Hampshire 

Northeast 

Northeast 

Quebec 

Idaho,  Montana 

California 
California 
California 
California 
California 
California 
California 
California 
California 
New  Hampshire 

Mich.,  Wis. 
New  Hampshire 
Wis.,  Mich. 
Wis.,  Mich. 
Wis.,  Mich. 
Wis.,  Mich. 
Wis.,  Mich. 
Washington 
Washington 
Utah,  Arizona 
Utah,  Arizona 
Montana 


Tree  class       1 


Unit  of  measure- 
ment 


Second  growth 


Cubic  feet,  total 
Board  feet 
Board  feet 
Board  feet 

Board  feet 
Board  feet 

Board  feet 

Board  feet 
Cu.  ft.,  peeled  total 
Board  feet 
Board  feet 
Board  feet 
Board  feet 
Board  feet 
Board  feet 
Board  feet 

Board  feet 
Cubic  feet,  total 
Cubic  feet,  peeled 

merch. 
Cubic  feet,  peeled 

merch. 
Cubic  feet,  peeled 

merch. 
Cords 
Cords 
Board  feet 
Board  feet 
Board  feet 
Board  feet 

Cubic  feet,  total 
Cubic  feet,  cords 
Board  feet 
Board  feet 
Cubic  feet 
Board  feet 
Board  feet 
Board  feet 
Board  feet 
Cubic  feet,  merch. 

Cu.  ft.,  merch.  O.B. 
Board  feet 
Board  feet 
Board  feet 
Board  feet 
Board  feet 
Board  feet 
Board  feet 
Cubic  feet,  total 
Cubic  feet,  total 
Cords  with  branches 
Cubic  feet,  total 


Scribner  Dec.  C. 
Scribner  Dec.  C. 
Scribner  Dec.  C. 

Scribner  Dec.  C. 
Scribner  Dec.  C. 

Scribner  Dec.  C. 

Scribner  Dec.  C. 

Scribner  Dec.  C. 
Scribner  Dec.  C. 
Scribner  Dec.  C. 
Scribner  Dec.  C. 
Scribner  Dec.  C. 
Scribner  Dec.  C. 
Scribner  Dec.  C. 

Scribner  Dec.  C. 


Scribner  Dec.  C. 
Maine 
Quebec 
Scribner  Dec.  C. 


Scribner  Dec.  C. 
Scribner  Dec.  C. 

Scribner  Dec.  C. 
Scribner  Dec.  C. 
Scribner  Dec.  C. 
Scribner  Dec.  C. 


Mill  tally 
Scribner  Dec.  C. 
Scribner  Dec.  C. 
Scribner  Dec.  C. 
Scribner  Dec.  C. 
Vermont 
Scribner  Dec.  C. 


TABLES  USED  IN  FOREST  MENSURATION 


511 


-Continued 


CoNIi^ERS 


D.B.H.l       Height. 
(Feet) 


16-62 
14-60 
16-60 
10-50 

8-31 
10-42 

6-30 
at  20  ft. 
8-30 
2-44 
12-46 
10-76 
10-60 
10-60 
10-60 
7-37 
8-40 

12-50 
3-14 
6-16 


6-15 

3-14 
6-15 
7-16 
7-16 
6-22 


10-40 
10-50 
10-50 
10-50 
7-40 
7-44 
18-60 
12-60 
11-40 
6-17 


60-150 
2-9  log 
40  200 
Short,  me- 
dium, tall 
16  log 
19  log 

15  log 

16  log 
20-220 
2- 10  log 
2-15  log 
40-  200 
1-10  log 
1-9  log 
1-7  log 
1-9  log 

1-5^  log 
20-  80 
40-  80 


40-   60 

20-  80 
40-  60 
40-  80 
40-  90 
39-  91 
1-9  log 

40-150 
40-150 
40-150 
1-8  log 
40-170 
40-180 
3-10  logs 
90-220 
2-8  logs 
30-  70 


5-36 

30-100 

6-17 

30-  70 

8-38 

30-100 

8-38 

1-5  log 

10-50 

50-120 

8-50 

1-7  log 

8-30 

4-100 

12-60 

2-11  log 

6-40 

50-200 

3-23 

10-  20 

3-23 

10-   20 

11-44 

80-160 

Top 
diameter. 
(Inches) 


Basis. 
Trees  I 


1054 

8-11  1054 

8-11  1084 

1230 


6-7 

6-24 
6-25 


5.9-6.4 
4 


5.7-6. 

i.7-14. 
9-15 
6-  9 

4.4-6. 

4 
4.4-6. 
6-12 
6-12 
7-26 
6-17 


441 

437 
1747 

967 
1394 


1048 
855 


372 
2173 
947 


2171 
100 


1114 
322 

317 


317 
542 
542 

1402 

1370 
320 

1440 
335 
495 
495 

1324 


1918 
1918 
1918 


1910 
1914 

1915 

1915 
1911 
1911 
1905 
1913 
1913 
1917 

1914 

1917 
1904 
1914 


1914 

1914 
1914 
1914 
1914 
1911 
1914 


1912 
1912 
1912 
1905 
1905 

1913 
1913 
1905 

1915 
1905 
1915 
1915 
1915 
1915 
1910 
1912 
1900 
1900 
1900 
1907 


Bui.  604,  U.  S.  Dept.  Agr. 


Manual   for   Timber   Rcconnaisance 

Dist.  1,  U.  S.  Forest  Service 
Bui.  272,  U.  S.  Dept.  Agr. 


Circ.  175,  U.  S.  Forest  Service 


Circ.  175,  U.  S.  Forest  Service 


Manual  lor  Timber  Reconnaisance, 
Dist.  1,  U.  S.  Forest  Service 


U.  S.  F.  S. 
designation 


Bui.  55,  U.  S.  Dept.  Agr. 


For  Quar.,  IX,  593 
Manual  for  Timber  Reconnaissance, 
Dist.  1,  U.  S.  Forest  Service 


For.  Quar.,  XI,  362 
For.   Com.    N.   H.,    1905; 

U.  S.  Dept.  Agr. 
Bui.  152,  U.  S.  Dept.  Agr. 


Bui.  161,  Vt.  Agr.  Exp.  Sta. 
Circ.  197,  U.  S.  Forest  Service 


T6-V3 
T6-V3 


D1-V18 
D4-V32 
D4-  V31 
D1-V35-36 
D1-V29 

A8-V2 
A-35-V2 


A1-V4 

A1-V6-7 

A1-V2 

A1-V3 

A2-V3 

A2-V2 

A2-V5 

A2-V15 

A2-V17 


H6-V5 
H6-V4 


512 


APPENDIX  C 


TABLE  LXXXVII 


Conifers — Continued 


Species 


Locality 


Unit  of  measure- 


Log  rule 


Larch,  western Montana 

Larch,  western Montana 

Larch,  western Montana 


Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
•Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 
Pine, 


Jack  . . . . 
Jack  . . . . 
Jack  . . . . 
Jack  . . . . 
Jeffrey . .  . 
loblolly.  . 
loblolly.  . 
loblolly.  . 
loblolly .  . 
loblolly .  . 
loblolly .  . 
loblolly.  . 
loblolly .  . 
loblolly .  . 
loblolly .  . 
loblolly .  . 
lodgeptle 
lodgepole 
lodgepole 
lodgepole 
lodgepole 
lodgepole 
lodgepole 
lodgepole 
lodgepole 
lodgepole 
longleaf .  . 

red 

red 


red 

red 

red 

scrub .  .  .  . 
scrub .  .  .  . 
scrub.  .  . 
shortleaf . 
shortleaf . 
shortleaf. 
shortleaf . 
sugar ... 
sugar  .  .  . 
sugar  . . . 
white .  .  .  . 
white ... 
white .  .  .  . 
white .  .  .  . 
white .  .  .  . 
white .  .  .  . 
white'.  .  .  . 
white .  .  .  . 
white .  .  .  . 
white.  .  .  . 


Minnesota 

Minnesota 

Minnesota 

Minnesota 

California 

Maryland,  Virginia 

Maryland,  Virginia 

Maryland,  Virginia 

Maryland,  Virginia 

North  Carolina 

North  Carolina 

North  Carolina 

North  Carolina 

North  Carolina 

North  Carolina 

North  Carohna 

Montana 

Montana 

Montana 

Montana 

Montana 

Oregon 

Oregon 

Oregon 

Oregon 

Colorado,  Wyoming 

Alabama 

Minnesota 

Minnesota 

Minnesota 

Minnesota 

Minnesota 

Minnesota 

Maryland 

Maryland 

Maryland 

North  Carolina 

North  Carolina 

Arkansas 

Arkansas 

California 

California 

California 

New  Hampshire 

Massachusetts 

Massachusetts 

New  Hampshire 

Massachusetts 

Minnesota 

Minnesota 

Minnesota 

New  Hampphire 

S.  Appalachians 


Under  75  yrs. 
Over  75  yrs. 
Under  75  yrs. 
Over  75  yrs. 
Under  75  yrs. 
Over  75  yrs. 


Under  130  yrs. 
Over  200  yrs. 
Second  growth 
Second  growth 
Second  growth 


Second  growth 
Second  growth 
Second  growth 
Second  growth 
Second  growth 
Original 
Original 
Original 
Second  growth 
Under  75  yrs. 


Board  feet 
Board  feet 
Board  feet 

Cu.  ft.,  pe«led  total 
Cu.  ft.,  merch.  O.B. 
Board  feet 
Board  feet 
Board  feet 
Cu.  ft.,  merch.  O.B. 
Peeled 
Board  fee* 
Board  feet 
Cu.  ft. .peeled  merch. 
Board  feet 
Board  feet 
Board  feet 
Board  feet 
Board  feet 
Board  feet 
Cubic  feet,  merch. 
Board  feet 
Board  feet 
Cubic  ft.,  total  O.B. 
Board  feet 
Board  feet 
Poles 
Ties 

Board  feet 
Board  feet 
Board  feet 
Cu.  ft.,  peeled  total 
Board  feet 
Board  feet 
Cubic  feet,  total 
Board  feet 
Board  feet 
Cords  O.B. 
Cords,  peeled 
Cu.  ft.,  total  O.B. 
Cubic  feet,  merch. 
Board  feet 
Board  feet 
Board  feet 
Board  feet 
Board  feet 
Cubic  feet,  merch. 
Cu.  ft.,  total  O.B. 
Cu.  ft.,  merch  O.  B. 
Cords 
Board  feet 
Board  feet 
Board  feet 
Board  feet 
Board  feet 
Cubic  feet,  merch. 
Board  feet 


Scribner  Dec.  C. 
Scribner  Dec.  C. 
Scribner  Dec.  C. 


Scribner  Dec.  C. 
Scribner  Dec.  C. 
Scribner  Dec.  C. 


Scribner  Dec.  C. 
Mill  tallies 

Mill  tallies 
Mill  tallies 
Scribner  Dec.  C. 
Scribner  Dec.  C. 
Tiemann 
Tiemann 

Scribner  Dec.  C. 
Scribner  Dec.  C. 

Scribner  Dec.  C. 
Scribner  Dec.  C. 


Scribner  Dec.  C. 
Scribner 
Scribner  Dec.  C. 

Scribner  Dec.  C. 
Scribner  Dec.  C. 

Scribner 
Scribner 


Scribner  Dec.  C. 
Scribner  Dec.  C. 
Scribner  Dec.  C. 
Scribner  Dec.  C. 
Scribner  Dec.  C. 


Mill  tallies 
Mill  tallies 
Scribner 

Scribner  Dec.  C. 
Scribner  Dec.  C. 

Scribner  Dec.  C. 


TABLES  USED  IN  FOREST  MENSURATION 


513 


-Continued 


Conifers — Continued 


D.B.H. 

Height.        ^ 

Top 
iameter. 

«--     Date 

„  ^,.       .                               U.  S.  F.  S. 
Publication                                 . 

designation 

(Inches) 

(Feet) 

rinches) 

Trees 

12-42 

80-160 

.3-10.8 

1388 

1907 

Bui.  36,  U.  S.  Forest  Service 

L7-V2 

12-42 

3-8  log 

.3-10.8 

1394 

1907 

" 

L7-V4 

8-40 

1-9  log 

233 

1914 

Manual  for  Timber  Reconnaissance, 
Dist.  1,  U.  S.  Forest  Service 

2-20 

20-  80 

658 

1920 

Bui.  820,  U.  S.  Dept.  Agr. 

4-20 

20-   80 

3 

615 

1920 

8-20 

20-   80 

5.5 

288 

1920 

8-20 

1-4  log 

5.5 

288 

1920 

14-54 
3-20 

40-130 
15-   80 

6-16.4 
U 

413 
372 

1907 
1914 

P7-V1 

Bui.  11,  U.  S.  Dept.  Agr. 

3-20 

15-   80 

U 

372 

1914 

" 

7-20 

40-   80 

5.5 

372 

1914 

4-  8 

30-   70 

2.5 

Tapers 

1914 

6-30 

20-120 

3-5 

1915 

Bui.  24,  N.  Car.  Geol.  Survey 

7-22 

40-120 

5-11 

1915 

■' 

P76-V24 

14-36 

90-140 

7-15 

1915 

" 

P76-V28 

8-22 

40-120 

5-11 

1915 

" 

P76-V23 

14-36 

90-140 

7-15 

1915 

" 

P76-V27 

7-22 

40-120 

5-11 

1915 

P76-V21 

14-36 

90-140 

7-15 

1915 

P76-V25 

3-20 

30-100 

2  -3 

1915 

Bui.  234,  U.  S.  Dept.  Agr. 

7-24 

1-5  log 

6 

555 

1915 

10  + 

1-5  log 

6.2-6.6 

1808 

1915 

4-22 

30-    90 

644 

1907 

Circ.  126,  U.  S.  Forest  Service 

10-24 

50-100 

6 

1817 

1907 

7-22 

i-4J  log 
30-   70 

g 

549 

1913 

P0-V13 

3-4 

255 

1913 

P0-V14 

8-18 
9-18 
8-25 
7-36 

0-6  log 
J-3i  log 
i-5  log 
40-120 

9 

8 

8 

6-18 

2000 

P0-V12 

1913 

PO-Vll 

1971 
614 

1915 

P0-V28 

1904 

Bui.  36,  U.  S.  Forest  Service 

5-20 

40-100 

303 

1914 

Bui.  139,  U.  S.  Dept.  Agr. 

8-34 

30-120 

6 

4282 

1914 

8-34 

1-7  log 

6 

4282 

1914 

7-30 

40-120 
60-100 

613 

1905 

P31-V11 

7-18 

6 

259 

1909 

Bui.  36,  U.  S.  Forest  Service 

10-27 

70-100 

964 

1909 

2-12 

10-    75 

228 

1911 

Bui.  94,  U.  S.  Forest  Service 

4-12 

30-  75 

228 

1911 

2-12 

20-  70 

228 

1905 

Bui.  36,  U.  S.  Forest  Service 

6-20 

40-  90 

6-8 

317 

1915 

Bui.  308,  U.  S.  Dept.  Agr. 

6-20 

40-  90 

6-8 

317 

1915 

8-34 

40-120 

6-13 

3206 

1915 

" 

8-34 

U-6  log 

6-13 

3206 

1915 

10-80 

40-220 

8-16 

910 

1917 

Bui  426,  U.  S.  Dept.  Agr. 

10-80 

1-12  log 

8-16 

910 

1917 

■' 

10-80 

60-240 
30-120 

8- 16 

773 

1913 

P3-V13 

5-20 

5 

1578 

1905- 

Bui.  13,  U.  S.  Dept.  Agr. 

5-25 

30-  90 

4 

2000 

1908 

5-27 

30-  90 

4 

2000 

1908 

5-26 

30-120 

5 

1578 

I    1905 

"     and  Bui.  820,  U.  S.  Dept.  Agr. 

5-27 

30-  90 

4 

2000 

'    1908 

Bui.  13,  U.  S.  Dept.  Agr. 

8-40 

40-140 

6-14 

3899 

1    1910 

8-42 

40-110 

6 

1834 

1913 

P32-V40 

8-42 

lJ-7  log 

6 

1834 

!    1913 

P32-V39 

5-26 

30-120 

i          5 

1578 

;    1905 



P32-V25 

8-20 

40-  90 

!          6 

260 

'    1913 

P32-V42 

514 


APPENDIX  C 


TABLE  LXXXVII 


Conifers — Continued 


Species 


measure- 


Log  rule 


Pine,  white 

Pine,  western  white 
Pine,  western  white 
Pine,  western  white 

Pine,  western  white 
Pine,  western  yellow 
Pine,  western  yellow 
Pine,  western  yellow 
Pine,  western  yellow 
Pine,  western  yellow 
Pine,  western  yellow 
Pine,  western  yellow 
Pine,  western  yellow 
Pine,  western  yellow 
Pine,  western  yellow 
Pine,  western  yellow 
Pine,  western  yellow 
Pine,  western  yellow 
Pine,  western  yellow 
Pine,  western  yellow 
Pine,  western  yellow 

Redwood  

Redwood   

Redwood  

Spruce,  black 

Spruce,  black 

Spruce,  red 

Spruce,  red 

Spruce,  red 

Spruce,  red 

Spruce,  red 

Spruce,  red 

Spruce,  red 

Spruce,  red 

Spruce,  red 

Spruce,  red 

Spruce,  red 

Spruce,  red 

Spruce,  red 

Spruce,  red 

Spruce,  red 

Spruce,  red 

Spruce,  red 

Spruce,  red 

Spruce,  red 

Spruce,  red 

Spruce,  red 

Spruce,  Englemann. 

Spruce,  Englemann. 
Spruce,  Englemann . 
Spruce,  Englemann. 
Spruce,  Englemann. 

Spruce,  white 

Spruce,  white 

Tamarack 


S.  Appalachians 

Idaho 

Idaho 

Idaho 

Idaho 

Black  Hills,  S.  Dak 

California 

Black  Hills,  S.  Dak 

Klamath,  Ore. 

Blue  Mts.,  Ore. 

Arizona 

Arizona 

Arizona 

Arizona 

California 

S.  Dakota,  Idaho 

Montana 

Montana 

Montana 

Montana 

Colorado 

California 

California 

California 

Quebec 

Quebec 

Maine 

New  Hampshire 

New  Hampshire 

New  Hampshire 

New  Hampshire 

New  York 

West  Virginia 

New  York 

New  York 

Maine 

Maine 

Maine 

Maine 

New  Hampshire 

New  Hampshire 

New  Hampshire 

New  Hampshire 

New  York 

New  York 

West  Virginia 

West  Virginia 

Colorado,  Utah 

Colorado,  Utah 
Colorado,  Utah 
Colorado,  Utah 
Idaho,  Montana 

Quebec 
Quebec 
Minnesota 


Under  75  yrs. 


Sprouts 
Sprouts 
Original 


Old  field 
Old  field 
Original 
Original 
Original 
Original 
Original 
Original 


Board  feet 
Board  feet 
Board  feet 
Board  feet 

Cubic  feet 
Cubic  feet,  total 
Cubic  feet,  total 
Board  feet 
Board  feet 
Board  feet 
Board  feet 
Board  feet 
Board  feet 
Board  feet 
Board  feet 
Board  feet 
Board  feet 
Board  feet 
Board  feet 
Board  feet 
Board  feet 
Cu.  ft.,  total  O.B. 
Board  feet 
Board  feet 
Cubic  feet 
Board  feet 

Cubic  feet,  merch. 

Cubic  ft.  total  O.B. 

Cu.  ft.,  merch.  O.B. 

Cu.  ft.,  merch.  O.B. 

Cubic  feet,  peeled 

Cu.  ft.,  merch.  O.B. 

Cu.  ft.,  merch.  O.B. 

Standards 

Standards 

Board  feet 

Board  feet 

Board  feet 

Board  feet 

Board  feet 

Board  feet 

Board  feet 

Board  feet 

Board  feet 

Board  feet 

Board  feet 

Board  feet 

Cubic  feet,  merch. 
peeled 

Board  feet 

Board  feet 

Board  feet 

Board  feet 

Cubic  feet,  merch. 
Board  feet 
Cubic  feet,  total 


Scribner  Dec.  C. 
Scribner  Dec.  C. 
Scribner  Dec.  C. 
Scribner  De"c.  C. 


Scribner 
Scribner 
Scribner 
Scribner 
Scribner 
Scribner 
Scribner 
Scribner 
Scribner 
Scribner 
Scribner 
Scribner 
Scribner 
Scribner 


Dec.  C. 
Dec.  C. 
Dec.  0. 
Dec.  C. 
Dec.  C. 
Dec.  C. 
Dec.  C. 
Dec.  C. 
Dec.  C. 
Dec.  C. 
Dec.  C. 
Dec.  C. 


Scribner  Dec.  C. 
Spaulding 


Quebec 


Dimick 
Dimick 
Maine 
Maine 

Scribner  Dec.  C. 
Scribner  Dec.  C. 
New  Hampshire 
New  Hampshire 
Scribner  Dec.  C. 
Scribner  Dec.  C. 
Scribner  Dec.  C. 
Scribner  Dec.  C. 
Scribner  Dec.  C. 
Scribner  Dec.  C. 


Scribner  Dec.  C. 
Scribner  Dec.  C. 
Scribner 
Scribner  Dec.  C. 


TABLES  USED  IN  FOREST  MENSURATION 


515 


— Continued 


Conifers — Continued 


Diam- 
eter. 

(Inches) 

Height. 
(Feet) 

Top 

diameter. 
(Inches) 

Basis. 
Trees 

Date 

Publication 

U.  S.  F,  S. 
designation 

&-20 
8-36 

U-3^  log 
30-160 

6 
6-8 

260 

1913 

P32- V41 

1791 

1908 

Bui.  36,  U.  S.  Forest  Service 

P2-V3 

8-36 

2-10  log 

6-8 

1791 

1908 

P2-V4 

8-60 

1-9  log 

306 

1914 

Manual  of  Timber   Reconnaissance, 
Dist.  1,  U.  S.  Forest  Service 

8-44 

80-190 

1790 

1914 

Bui.  36,  U.  S.  Forest  Service 

P2-V5 

8-25 

30-    90 

1004 

1908 

Circ.  127,  U.  S.  Forest  Service 

12-48 

50-160 

710 

1908 

8-25 

40-100 

1419 

1910 

P4-V31 

12-50 

2-8ilog 

6-14 

823 

1917 

Bui.  418,  U.  S.  Dept.  Agr. 

10-42 

2-8|  log 

6-16 

1536 

1917 

10-50 
10-50 
12-40 

30-150 
1-8  log 
40-120 

g 

6099 
6099 
1822 

P4-  V43 

8 
8.3-17 

P4  V41 

1911 

Bui.  101,  U.  S.  Forest  Service 

12-40 

1-6  log 

8.3-17 

1822 

1911 

12-70 

60-220 

8-14 

2396 

1911 

P4-V30 

12-50 

2-10  log 
1-8  log 
30-140 

8 

1193 

1913 

P4-  V42 

10-40 

6-10 

427 

1913 

P4   V5 

10-40 

6^  10 

427 

1913 

P4-V36 

8-40 

lJ-8  log 
30-140 

2822 

1916 

P4-V37 

8-40 

6-18 

2438 

1916 

P4-V38 

12-43 

1-6^  log 
30-  90 

6.1-10.6 

2167 

1916 

P4-V61 

6-24 

883 

1900 

R1-V3 

7-24 

30-  90 

6-7 

763 

1900 

R1-V2 

20-112 

55-180 

503 

1917 

Timberman,  Dec,  1917,  p.  38 

7-20 

46-  89 

4 

317 

1911 

For.  Quar.,  Vol.   IX,  p.  591 

6-20 

13-  84 

4 

317 

1911 

6-25 

40-  90 

4.5 

246 

1920 

Bui.  544,  U.  S.  Dept.  Agr. 

6-14 

40-   70 

711 

1920 

6-18 

40-  80 

5 

711 

1920 

5-28 

40-  90 

4 

1226 

1920 

6-14 

40-  70 

4-6 

711 

1920 

6-26 

30-100 

4.5 

1591 

1920 

6-34 

50-100 

4.5 

417 

1920 

8-26 

1-5  log 

6 

1507 

1920 

8-26 

30-100 

6 

1507 

1920 

7-25 

40-  90 

6 

241 

1920 

7-25 

1-4  i  log 

6 

241 

1920 

7-25 

40-  90 

6-9 

241 

1920 

7-25 

1-5  log 

6-9 

241 

1920 

8-26 

30-  80 

6 

668 

1920 

8-26 

1-4  log 

6 

668 

1920 

" 

8-26 

30-  80 

6 

668 

1920 

" 

8-26 

1-4  log 

6 

668 

1920 

" 

8-26 

30-100 

6 

1507 

1920 

" 

8-26 

1-5  log 

6 

1507 

1920 

" 

8-34 

50-110 

6 

416 

1920 

8-34 

1^6  log 

6 

416 

1920 

7-36 

40-120 

6-8 

676 

1910 

Circ.  170,  U.  S.  Forest  Service 

S2-V4 

8-30 

40-120 

6-8 

676 

1910 

S2-V1 

8-30 

1-6  log 

6-8 

671 

1910 

" 

S2-V5 

7-26 
8-40 

35-115 
1-9  log 

6 

2380 
189 

1915 

S2-V10 

1914 

Manual  for  Timber  Reconnaissance, 

Dist.  1,  U.  S.  Forest  Service     ■ 

7-25 

51-100 

4 

441 

1911 

1  For.  Quart.,  Vol.  IX,  p.  590 

6-25 

44-112 

4 

1351 

1911 

j                       '  •                     p.  592 

7-15 

60-100 

246 

1905 

I-35-V4 

516 


APPENDIX  C 


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520 


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APPENDIX  D 

BIBLIOGRAPHY 

List  of  the  most  important  works  dealing  with  Forest  Mensiu-ation,  in  English: 

Carter,  P.  J.     Mensuration  of  Timber  and  Timber  Crops.     Calcutta,  Ind,,  1893. 
Gary,    A.     Manual   for   Northern   Woodsmen.     Harvard   University,    Cambridge, 

1918. 
Cook,  H.  O.     Forest  Mensuration  of  the  White  Pine  in  Massachusetts.     Boston. 

1908.     Office  of  State  Forester. 
D'Arcy,  W.  E.     Preparation  of  Forest  Working  Plans  in  India.     Calcutta,  1898. 
Graves,  H.  S.     Forest  Mensuration,     John  Wiley  &  Sons.     New  York,  1908. 
Graves,  H.  S.     Woodsman's  Handbook.     Bui.  36,  U.  S.  Forest  Service,    1910. 
Mattoon,    W.   R.,   and   Barrows,    W.    B.     Measuring  and   Marketing   Woodlot 

Products.     Farmers'  Bui.  715,  U.  S.  Dept.  Agr.,  1916. 
McGregor,  J.  L.  L.     Organization  and  Valuation  of  Forests.     London,  1883. 
Mlodziansky,  a.  K.     Measuring  the  Forest  Crop.     Bui.  No.  20,  Div.  of  Forestry, 

U.  S.  Dept.  Agr.,  1898. 
PiNCHOT,  Gifford.     The  Adirondack  Spruce.     New  York,  1898. 
PiNCHOT,  G.,  and  Graves,  H.  S.     The  White  Pine.     New  York,  1896. 
ScHENCK,  C.  A.     Forest  Mensuration.     Sewanee,  Tenn.,  1905. 
ScHLiCH,  Wm.     Manual  of  Forestry,  Vol.  III.     London,  1911. 
WiNKENWERDER,  H.     Manual  of  E.xercises  in  Forest   Mensuration.     John  Wiley 

&  Sons.     New  York,  1921. 

List  of  the  most  important  works  dealing  with  Forest  Mensuration,  in  German. 
Selected  from  bibliography  published  in  "Forest  Men.suration,"  by  H.  S.  Graves, 
with  some  additions : 

Special  Works  ox  Forest  Mensuration 

Baur,  Franz.     Die  Holzmesskunde.     Berlin,  4th  ed.,  1891. 

Brehmann,  Karl.     Anleitung  zur  Aufnahme  der  Holzmasse.     Berhn,  1857. 

Anleitung  zur  Holzmesskunst.     Berlin,  1868. 

Fankhauser,   F.     Praktische  Anleitung    zur    Holzmassen- Aufnahme,   3d  edition, 
Bern,  1909. 

Heyer,  Gust.     Ueber  die  Ermittelimgen  der  Masse,  des  Alters  und  des  Zuwachses 
der  Holzbestiinde.     Dessau,  1852. 

Heyer,  Karl.     Anleitung  zu  forststatlschen  Untersuchungen.     Giessen,  1846. 

Klauprecht.     Die  Holzmesskunst.     Karlsruhe,  1842  and  1846. 

KoNiG,  G.     Die  Forst-Mathematik  mit  Anweisung   zur   Forstvermessung.     Gotha, 
1835.     Revised  by  Dr.  Grfebe,  1864. 

KuNZE,  M.  F.     Lehrbuch  der  Holzmesskunst.     Berhn,  1873. 

Langenbacher,  Ferd.     Forstmathematik.     Berlin,  1875. 

Lamgenb.^cher,  F.  L.,  und  Nossek,  E.  A.     Lehr-  und  Handbuch  der  Holzmess- 
kunde.    Leipzig,  1889. 

MtJLLER,  Udo.     Lehrbuch  der  Holzme.s.skunde.     Leipzig,  2d  edition,  1915. 

Schwappach,  Adam.     Leitfaden  der  Holzmesskunde.     Berlin,  1903. 

521 


522  APPENDIX  D 

Smalian,  L.     Beitrag  zur  Holzmesskunst.     Stralsund,  1837. 

Anleitung  zur  Untersuchung  des  Waldzustandes.     Berlin,  1840. 

Statz,  Paul.     Die  Abstandszahl,  ihre   Bedeutung  fur  die  Forsttaxation,  Bestandes- 

erziehung  und  Bestandespflege,  Freiburg,  1909. 
Tkachenko,  M.     Das  Gesetz  des  Inhalts  der  Baumstamme  una  seine  Bedeutung 

fiir  die  Massen-  und  Sortimentstafeln.     Berlin,  1912. 

WoKKS  ON  Forest  Management  Containing  Chapters  on  Forest 
Mensuration 

BoRGGREVE,  B.     Die  Forstabschatzung.     Berlin,  1888. 

von  Fischbach,  C.     Lehrbuch  der  Forstwissenschaft.     Berlin,  1886. 

Graner,  F.     Die  Forstbetriebseinrichtung.     Tubingen,  1889. 

VON  Guttenberg,  a.  F.     Forstbetriebsienrichtung.     Wien  and  Leipzig,  1903. 

Hess,    R.     Encyclopedie   und   Methodologie   der   Forstwissenschaft.     Nordlingen, 

1885. 
Heyer,  Gust.     Waldertragsregelung.     Leipzig,  1893. 
JuDEicH,  F.  Die  Forsteinrichtung.     Dresden,  1893. 

LoREY,  TuiSKO.     Handbuch  der  Forstwissenschaft.     3d  edition,  Tubingen,  1913. 
Stotzer,  H.     Die  Forsteinrichtung.     Frankfurt,  1898. 
Weber,  Rudolf.     Lehrbuch  der  Forsteinrichtung.     Berlin,  1891. 
Weise,  W.     Ertragsregelung.     Berlin,  1904. 

List  of  the  most  important  works  dealing  with  Forest  Mensuration,  in  French. 
From  bibliography  published  in  "'Studies  of  French  Forestry,"  by  T.  S.  Woolsey,  Jr.: 

L'amenagement  des  forets  (2d  Edit.).     Puton.     Paris,  1874. 

Notice  sur  les  dunes  do  la  Coubre.     Vasselot  de  Regne.     Paris,  1878. 

Amenagement  des  forets-Estimation.     Fallotte.     Carcassonne,  1879. 

La  methode  du  controle  de  Gurnaud.     Grandjean.     Paris,  1885. 

L'art  forestier  et  le  controle.     Gurnaud.     Besangon,  1887. 

L'amenagement  des  forets  (V.  Edit.).     Tassy.     Paris,  1887. 

Traite  d'economie  forestiere.     Puton.     Paris,  1888. 

Cours  d'amenagement  professe  a  I'Ecole  forestiere  (1885-1886)  2  cahiers.     Reuss. 

Nancy,  1888. 
Diagrammes  et  calculs  d'accroissement.     Bartet.     Nancy,  1889. 
Guide  theorique  et  pratique  de  cubage  des  bois.     Frochot.     Paris,  1890. 
La  methode  du  controle  a  I'Exposition  de  1889.     Gurnaud.     Paris,  1890. 
Note  sur  une  nouvelle  methode  forestiere  dite  du  controle  de  Gurnaud.     de  Blonay. 

Lausanne,  1890. 
Traite  d'economie  forestiere.     Amenagement.     Puton.     Paris,  1891. 
Le  traitement  des  bois  en  France.     Broillard.     Paris,  1894. 
Estimations  et  exploitabilites  forestieres.     Bizot  de  Jontenz.     Gray,  1894. 
Notes  pour  la  vente  et  Tachat  des  forets.     Galmiche.     BesanQon,  1897. 
Notes  forestieres — Cubage,  estimation,  etc.     Devarenne.     Chaumont,  1889. 
Economic  forestiere.     Huffel.     Paris,  1904-07. 
Cubage  des  bois  sur  pied  et  abattus  manuel  pratique.     Berger,  Levrault  et  al.      Paris, 

1905. 
Mathematiques  et  Nature.     Broillard.     Besangon,  1906. 
Aide  memoire  du  forestier-Sylviculture.     Demorlaine.     Besangon,  1907. 


INDEX 


PAGE 

Abney  clinometer 239 

Abnormal  cross  sections 17 

plots,  rejection,  yield  tables 404 

Absolute  form  factors 212 

quotient 207 

versus  relative  accuracy  in  mensuration 3 

Accuracy  in  timber  estimating,  limits  of 301 

of  results  in  timber  estimating,  choice  of  system  for 261 

of  timber  estimates,  methods  of  improving 288 

of  volume  tables,  checking 189 

of  yield  predictions 412 

Accurate  formula  log  rules 65 

log  rules,  need  for 50 

Acre,  area  of 6 

Actual  density  of  stocking,  determination  of 413 

estimate  or  measurement  of  the  dimensions  of  every  tree  of  merchant- 
able size 257 

Adirondack  standard  or  market 28 

Adoption  of  a  standard  log  length  for  volume  tables 182 

Advantages  of  graphic  plotting  of  data 166 

Age,  as  affected  by  suppression 341 

average,  definition  and  determination 337 

classes,  group  form,  separation 418 

in  yield  tables 397 

economic 341 

from  annual  whorls 337 

groups,  yield  tables  for 412 

in  even-aged  versus  many-aged  stands,  the  factor  of 325 

of  average  trees  and  of  stand,  determining 339 

of  seedling 336 

of  stand,  determining 335,  339 

of  stands  relation  to  volume 449 

of  timber,  effect  on  methods  of  estimating 265 

of  trees,  determining 335 

separation  of,  in  yields 416 

Ake  log  rule 36 

Annual  increment  of  many-aged  stands 390 

whorls  of  branches  as  an  indication  of  age 337 

Applicability  of  Hoejer's  formula  in  determining  tree  forms 210 

523 


524  INDEX 


PAGE 

Application  of  graphic  method  in  constructing  volume  tables 169 

of  yield  tables  in  predicting  yields 322 

Appolonian  paraboloid 19 

Appraisal,  timber  as  distinguished  from  forest  survey 269 

Arbitrary  standards  in  constructing  log  rules 49 

Area  determination,  importance  in  timber  estimating 267 

for  age  groups  on  basis  of  diameter  groups 422 

for  two  age  groups  on  basis  of  average  age 419 

of  plots  in  yield  tables 397 

separation  of  in  yields 416 

imits,  size,  relation  to  per  cent  of  area  to  be  estimated 262 

Areas  determined  from  density  factor 416 

of  circles,  table  LXXVIII 490 

of  cross  sections 17 

of  crowns 423 

of  different  types,  separation,  method 290 

of  immature  timber,  growth  on 451 

separation  of,  effect  on  density 453 

Arkansas,  statute  log  rule 68 

Average  age,  basis  for  determining  volume  and  area  of  two  age  groups 419 

definition  and  determination 337 

Average  board-foot  volume,  tree  containing 311 

diameter  growth,  determination 346 

heights  of  timber  and  site  classes 291 

heights  of  tfees  based  on  diameter 258 

log  method  of  estimating 143 

stand  per  acre  from  partial  estimate 260 

trees,  age,  determining 339 

trees,  volume  and  diameter,  determination  of 338 

Averages  employed  in  timber  estimating,  six  classes  of 258 

Ballou  log  rule 75 

Barbow  cruising  compass 248 

Bark  as  a  waste  product 13 

as  affecting  diameter  in  volume  tables 150 

marks,  log 99 

measurement  in  cords 134 

volume  of 163 

width,  measurement  for  volume 161 

Basal  area,  definition 7 

areas,  table  LXXVIII 490 

use  in  predicting  yields 415 

Base  line 281 

Basis  for  board-foot  volume  tables 182 

for  cordwood  converting  factors 127 

of  determining  dimensions  of  the  frustum 219 

Baughman  log  rules 72 

Bangor  log  rule 85 

Baur's  method  of  constructing  yield  tables 396 

Baxter  log  rule 67 


INDEX  525 


PAGE 


Beaumont  log  rule ^^ 

Big  Sandy  Cube  rule 33 

Billets,  definition ^^ 


measurement . 


122 


products  made  from 1* 

Biltmore  pachymeter 248 

stick 230 

errors  in  use  of 232 

Table  XXXVIII 232 

graduation 233 

Table  XXXIX 233 

Blank  areas,  separation  in  estimating 289 

Blodgett  foot 3^ 

or  New  Hampshire  log  rule 30 

Board-feet,  basis  of  application  to  standing  timber 139 

errors  in  use  of  cubic  rules  for 42 

frustum  form  factors  for  merchantable  contents  in 218 

log  rules  expressed  in,  but  based  directly  upon  cubic  contents 34 

merchantable  form  factors  for 225 

volume  tables  for 1^2 

Board-foot  contents,  construction  of  log  rules  for 58 

middle  diameter  as  a  basis  for 46 

of  logs 40 

rules  of  thumb 252 

converting  factors  for  various  piece  products,  Table  LXXVI 478 

log  rules,  limitations  to  conversion  of 83 

necessity  for 4U 

rules,  formula  based  on  cubic. contents 35 

volume  tables,  construction  of 188 

volume,  tree  containing  average 311 

measure,  definition 

log  scaling  for 88 

Bole,  in  volume  tables 

Bolts,  definition 

measurement 

products  made  from 

Borer,  increment f^^ 

Bomidaries,  determination  in  timber  estimating 267 

85 
BojTiton  log  rule ° 

Branch  wood  or  lapwood  in  volume  tables 

Breakage 

Breast-high  form  factors ^ 

,  Table  LXXXII 497 

22 
Brejinann's  formula 

British  Columbia  log  rule 

Brubaker  log  rule 

Brush,  effect  on  width  of  strips 

Bulk  products,  forms  of 

Business,  definition 

Butt  rot 


526  INDEX 


PAGE 

Calcasieu  log  rule 36 

Calciilation  of  true  frustum  form  factor 221 

of  volumes  of  frustums 221 

California  log  rule 75 

Caliper  scale 97 

definition 23 

Calipers,  description  and  method  of  use 227 

Canada,  Dominion  forestry'  branch,  log  rule 73 

Canadian  log  rules 76 

Carey  log  rule 66 

Cat  faces 115 

Cedar,  western  red,  poles 469 

white,  poles 467 

Center  rot 108 

Chain,  imit  of  measurement,  definition 6 

Champlain  log  rule 65 

Chandler,  B.  A 220 

Chapin  log  rule 85 

Character  and  utility  of  frustum  form  factors 219 

of  crown  tree  for  volume  tables 157 

of  growth  per  cent 318 

Chart  of  growth  studies 328 

Check  estimating 308 

Checking  the  accuracy  of  volume  tables 189 

Check  scaling 117 

Checks,  heart 112 

surface 115 

Chestnut  oak,  height  growth,  Milford,  Pa.,  Table  LVII 371 

volume  growth,  cubic.  Table  LVIII 376 

poles,  minimum  circumference.  Table  LXXII 472 

Choice  of  a  board-foot  log  rule  for  a  imiversal  standard 84 

system  for  timber  estimating  with  relation  to  accuracy  of  results.  .  . .  261 

of  units  in  timber  estimating 140 

Christen  hjTisometer 243 

Circular  plots,  sizes.  Table  XLII 286 

Classification  and  averaging  of  tree  volumes  according  to  diameter  and  height 

classes 163 

of  tree,  measurements  required  in  volume  tables 156 

of  trees  by  diameter 151 

height  in  volume  tables 151 

Clement's  log  rule 66 

CHck's  log  rule 66 

Clinometer,  Abney 239 

Codominant  tree,  definition 158 

Columbia  River  Log  ScaUng  and  Grading  Bureau  log  grades 460 

Combination  log  rules 76 

volume  tables  for  two  or  more  products 193 

Common  grades  of  lumber 457 

Comparison  of  gro\vth  for  diameter  classes 360 

of  log  rules  based  on  cubic  contents,  Table  II 37 


INDEX  527 

PAGE 

Comparison  of  log  rules  based  on  diameter  at  middle  and  at  small  end  of  log. .  26 

on  formulae 61 

of  scaled  and  cubic  contents  by  different  log  rules 36 

Compass,  hand 276 

staff 277 

Composition  of  stands  as  to  species,  effect  on  yield 393 

Computation  of  volume  of  the  tree 161 

Cone 19 

Connecticut  River  log  rule 68 

Constantine  log  rule 34 

Construction  and  use  of  local  volume  tables 174 

of  board-foot  volume  tables 188 

of  a  log  rule,  standardization  of  variables  in 49 

of  log  rules  based  on  diagrams 72 

mathematical  formulae 59 

for  board-foot  contents 58 

for  mill  talUes 78 

of  standard  volume  tables  for  total  cubic  contents 154 

of  volume  table  from  frustum  form  factors 224 

of  yield  table  with  site  classes  based  directly  on  yields  per  acre. . .  406 

on  height  growth 401 

based  on  crown  space,  for  many-aged  stands 422 

tables,  Baur's  method 396 

Contents  of  standing  trees,  rules  of  thumb  for  estimating 251 

solid,  of  logs,  formulae 20 

Conversion  of  board-foot  log  rules,  limitations  to 83 

of  International  rule  ^-inch  saw  kerf  for  other  widths  of  kerf.  Table 

XIII 81 

of  log  rules  with  i-inch  saw  kerf  to  other  widths  of  kerf.  Table  XIV .  .  82 
of  values  of  a  standard  rule  to  apply  to  different  widths  of  saw  kerf 

and  thickness  of  lumber 80 

of  volume  tables  for  cubic  foot,  to  cords 180 

Converter  poles 473 

Converting  factors,  cordwood  basis  for 127 

for  cordwood.  Table  XX 129 

for  log  rules 27 

for  sticks  of  different  diameters 129 

lengths 128 

piece  products  to  board-feet 478 

standard  cordwood 128 

stacked  cords  to  board-feet,  factors  for 135 

Cook  log  rule 35 

Coordination  of  merchantable  heights  with  top  diameters 184 

Cord  foot 1 23 

,  long 121 

measure 121 

definition 7 

discounting  for  defects  in 133 

Cords,  conversion  of  volume  tables  from  cubic  feet  to 180 

Cord,  short 121 


528  INDEX 


PAGE 

Cord,  standard,  definition 7 

versus  short  cords  and  long  cords 121 

volume  tables  for 177 

to  board-feet,  factors  for  converting 133 

Cordwood  converting  factors,  basis  for 127 

standard 128 

log  rules 132 

methods  of  measurement 123 

rule,  Humphrey  caliper 132 

weight  as  a  measure  of 137 

Correction  factors  for  volume,  use  of 293 

of  average  stand  per  acre 260 

Cost  of  estimating  timber 302 

Count,  and  average  tree  in  estimating 259 

and  partial  tally  of  trees  in  estimating 259 

Cracks,  frost 112 

Crook  or  sweep,  deductions  for,  Table  XVIII 116 

in  scaling 116 

waste  from 51 

Crooked  River  log  rule 35 

Cross  sections,  abnormal 18 

diameters  and  areas 17 

Cross  ties 474 

volume  tables  for 191 

Crown  class  and  suppression  as  alTecting  height  growth 366 

definition 157 

effect  on  diameter  growth 353 

cover,  density  of 424 

of  tree,  character  for  volume  tables 157 

space,  yield  tables  based  on,  for  many-aged  stands 422 

spread  of  loblolly  pine,  Ala.,  Table  LXI 389 

Crowns,  areas  of 423 

width  of,  measurement 423 

Cruisers'  method,  Lake  States  estimating 283 

methods.  Southern  estimating 283 

Cuban  One  Fifth  log  rule 34 

Cube  Rule,  Big  Sandy 33 

Cubic  and  board  foot  contents  of  logs  compared,  Table  III 41 

contents  of  cylinders,  Table  LXXVII 480 

scaled  by  various  log  rules.  Table  II 37 

log  rules  based  directly  upon,  but  expressed  in  board-feet 34 

on 26 

of  logs,  measurement 16 

scaled  as  board  feet,  by  different  log  rules,  comparison .  .     36 

of  squared  timbers,  log  rules  for 33 

of  stacked  wood,  sohd 124 

rules  of  thumb 251 

total,  construction  of  standard  volume  tables  for 154 

weight  as  a  basis  of  measuring 33 

foot,  use  of,  in  log  scaling 31 


INDEX  529 

PAGE 

Cubic  measure,  definition 8 

in  log  measurements 28 

relation  to  true  board-foot  log  rules 39 

stacked,  definition 7 

measure  as  a  substitute  for 121 

meter  in  log  measurement 28 

rules  for  board-feet,  errors  in  use  of 42 

volume,  log  rules  based  on 28 

merchantable,  standard  volume  tables 177 

Cull  factor,  or  deductions  for  defects  in  timber  estimating 271 

in  log  scaling,  relation  to  grades  of  timber 458 

in  volume  tables 179 

Cumberland  River  log  rule 35 

Current  annual  growth 315 

growth,  compared  with  yield  tables  and  mean  annual  growth 445 

loblolly  pine,  diameter.  Table  LVI 363 

per  cent 429 

permanent  sample  plots  for  measurement  of 443 

spruce,  Adirondacks,  Table  LIV 360 

use  of  yield  tables  in  predicting 436 

height  growth 371 

periodic  growth  based  on  diameter  classes 358 

or  periodic  growth  of  stands,  measurement 436 

Curves,  harmonized,  for  volumes  based  on  height 170 

for  standard  volume  tables  based  on  diameter 169 

for  taper  tables,  based  on  D.  B.  H 200 

on  total  heights  of  tree 202 

original  based  on  height  above  stump 197 

Cut-over  areas,  application  of  yield  tables  based  on  age  to 441 

growth  on " 438 

Cylinder 19 

as  the  standard  of  scaling 90 

d'Aboville  method  for  determining  form  quotients 248 

Data  required  from  forest  survey  for  growth 447 

which  should  accompany  a  volume  table 188 

D.  B.  H.,  correlation  with  stump  growth 348 

definition 150 

merchantable  hmit  at 177 

Decades,  method  of  counting 343 

Decimal  C,  Scribner  log  rule 74 

rule,  Scribner 73 

values  below  12  inches,  Scribner  log  rule,  Table  XII 74 

Deducting  a  per  cent  of  total  scale 107 

Deductions  by  sectors 115 

by  slabs 114 

for  crook  or  sweep.  Table  XVIII 116 

for  defects  in  timber  estimating 271 

from  scale  for  unsound  defects 105 

from  sound  scale  versus  over-run 90 


530  INDEX 

PAGE 

Defect,  effect  upon  grades  of  logs 460 

Defective  logs,  merchantable 99 

scaling  of 105 

trees,  measurement  for  volume  tables 183 

Defects,  deductions  for,  in  timber  estimating 271 

exterior 113 

in  cord  measure,  discounting  for 133 

in  lumber 456 

interior 108 

or  cull  in  volume  tables 179 

sound  and  unsound 103 

unsoimd,  deductions  from  scale  for 105 

Degree  of  uniformity  of  stand  as  affecting  methods  employed  in  estimating ....  265 

Dendrometers 247 

Density  factor,  determination  of  areas  from 416 

factors,  application  in  prediction  of  growth  from  yield  tables 414 

for  mature  stands,  effect  of  separation  of  areas  of  immature 

timber 453 

of  crown  area 424 

of  stand,  effect  on  diameter  growth '. ; 352 

of  stocking  as  affecting  growth  and  yields 392 

of  stocking,  empirical 413 

of  stocking,  standard  for  normal 397 

Derby  log  rule 36 

Derivation  of  local  volume  table  from  standard  volume  tables 175 

of  standard  breast-high  form  factors 213 

Description  of  plot,  yield  tables 399 

Determination  of  what  constitutes  a  merchantable  log 99 

Determining  the  age  of  stands 335 

of  trees 335 

Diagrams,  construction  of  log  rules  based  on 72 

in  construction  of  log  rules 58 

use  of,  for  deductions  in  scaHng 106 

Diameter  alone,  versus  diameter  and  height  as  basis  of  volume  tables 152 

and  height  classes,  classification  and  averaging  of  tree  volumes  by ...  .  163 

at  middle  of  log,  scaUng  practice  based  on 97 

at  small  end  of  log,  scaUng  practice  based  on 91 

breast  high 150 

in  measuring  standing  trees 226 

Classes 227 

comparison  of  growth  for 360 

current  periodic  growth  based  on 358 

clasification  of  trees  by 151 

groups  as  basis  of  age  groups 422 

growth,  basis  for  determining 342 

computation  of 346 

correction  for  seedling  age 348 

effect  of  species  on 351 

in  even-aged  stands,  laws  of 354 

in  many-aged  stands,  laws  of 357 


INDEX  531 

PAGE 

Diameter  growth  of  trees  growing  in  stands,  factors  influencing 351 

on  sections,  measurement  of 342 

purpose  of  study 342 

relation  to  volume  growth 374 

spruce.  Table  LI 345 

harmonized  curves  for  volume  based  on 169 

in  determination  of  log  grades 459 

instruments  for  measuring 227 

of  average  trees,  determining 338 

of  log,  relation  to  per  cent  of  utilization  in  sawed  lumber 40 

tape 229 

Diameters,  abnormal 18 

and  areas  of  cross  sections 17 

bark  as  affecting,  in  volume  tables 150 

measured  at  ends  of  log 22 

at  middle  of  log 23 

point  of  measurement,  in  volume  tables 148 

scaling 92 

Dimensions  of  frustum,  basis,  in  form  factors 219 

of  stick,  effect  of,  on  solid  contents  of  stacked  wood 126 

of  tree  containing  average  board-foot  volume 311 

Diminishing  numbers,  law  of 318 

Direct  ocular  estimate  of  total  volume  in  stand 256 

Discounting  for  defects  in  cordwood  measure 133 

Distances  between  strips  in  estimating 264 

Doyle-Baxter  log  rule 77 

Doyle  log  rule 68 

rule,  errors  in,  effect  upon  scaling  and  over-run 70 

-Scribner  log  rule 76 

Dominant  tree,  definition 158 

Drew  log  rule 85 

Durability 466 

Dusenberry  log  rule 85 

Economic  age  of  trees 34I 

Edgings,  waste  from 50 

Effect  of  dimensions  of  stick  on  solid  contents  of  stacked  wood 126 

of  errors  in  Doj'le  rule  upon  scaling  and  over-nm 70 

of  irregular  piling  on  solid  contents  of  stacked  wood 124 

of  losses  versus  thinnings  upon  yields 324 

of  minimum  dimensions  of  merchantable  boards  upon  deductions  in  scaling  107 

of  seasoning  on  volume  of  stacked  wood 123 

of  variation  in  form  of  sticks  on  solid  contents 125 

Empirical  density  of  stocking 413 

yield  tables 396 

use  of 413 

English  system  of  measurement 6 

Errors  in  Doyle  rule,  effect  upon  scaling  and  over-run 70 

in  use  of  Biltmore  stick 232 

of  cubic  rules  for  board-feet 42 


532  INDEX 

PAGE 

Estimate,  ocular,    of  total  volume 256 

of  every  tree 257 

Estimates  covering  a  part  of  the  total  area 273 

extensive 308 

total  or  lOO.per  cent 271 

Estimating  a  part  of  the  timber  as  an  average  of  the  whole 257 

by  means  of  felled  sample  trees 310 

by  plots  arbitrarily  located 297 

contents  of  standing  trees,  rules  of  thumb 251 

log  as  the  unit  of 141 

quality  of  standing  timber 297 

strip,  systems  in  use 282 

timber,  choice  of  units  in 140 

cost 302 

tree  as  a  imit  in 144 

use  of  forest  types  in 288 

Estimation  of  standing  timber,  principles  underlying  the 255 

of  tree  dimensions,  ocular 234 

Evansville  log  rule 35 

Even-aged  stands,  laws  of  diameter  growth 354 

normal  yield  tables  for 395 

versus  many-aged  form  of  stands 388 

stands,  definition 337 

Extensive  estimates 308 

Extension,  Scribner  log  rule 74 

Exterior  defects 113 

Fabian's  log  rule 76 

Face,  lumber 456 

Factors  affecting  the  growth  of  stands 384 

determining  the  methods  used  in  timber  estimating 255 

width  of  strips 274 

for  converting  stacked  cords  to  board-feet 135 

Factory  or  shop  grades 457 

Faustmann  hypsometer 240 

Favorite  log  rule 85 

Felled  sample  trees,  methods  of  estimating 310 

Fence  stays 473 

Fifth  girth 25 

Finance,  forest,  relation  to  mensuration 3 

Finch  and  Apgar  log  rule 85 

Finished  lumber  grades 456 

Finishing  grades 457 

Fixed  or  variable  limits  for  top  diameters 183 

Florida,  statute  log  rule 68 

Forest  cover,  map 268 

finance,  relation  to  mensuration 3 

growth  determination  for,  coordination  of  forest  survey 447 

management,  relation  to  mensuration 3 

mensuration,  definition 1 


INDEX  533 

PAGE 

Forest  property,  definition 1 

Service  hypsometer 241 

standard  valuation  survey 282 

survey  as  distinguished  from  timber  estimating 268 

coordination  with  growth  determination  for  forest 447 

data  required  for  growth 447 

definition 5 

surveying,  as  a  part  of  the  forest  survey 270 

relation  to  mensuration 5 

survey,  timber  appraisal  distinguished  from 269 

total  increment  of,  inclusive  of  immature  stands 443 

types,  use  in  estimating 288 

valuation,  relation  to  timber  appraisal 269 

Forestry,  relation  to  growth  measurements 2 

Forests  composed  of  all  age  classes,  growth  per  cent  of 434 

having  a  group  form  of  age  classes 418 

Form  as  a  third  factor  affecting  volume 196 

class,  determination  from  form  point.  Table  XL 250 

classes  and  form  factors 205 

and  universal  volume  tables  as  applied  to  conditions  in  America. .  215 

based  on  form  quotient 206 

factor,  Riniker's  absolute 212 

factors 211 

absolute 212 

breast-high 212 

for  board-feet 225 

frustum,  character  and  utility 219 

merchantable 214 

normal 212 

standard  breast-high 213 

height 215 

of  logs,  the 18 

of  red  pine 210 

of  stands 388 

of  sticks,  effect  on  solid  cubic  contents 125 

of  trees  and  taper  tables 196 

Hoejer's  formula  for 209 

of  white  pine 210 

point  method  of  determining  form  classes,  Jonson 249 

position  of,  to  determine  form  class;  Table  XL 250 

quotient,  absolute 207 

as  the  basis  of  form  classes 206 

quotients,  d'Aboville  method  for  determining 248 

of  trees,  wind  pressure 208 

relation  to  volume  and  diameter  growth 374 

Formula  for  board-foot  rules  based  on  cubic  contents 35 

for  tree  form,  Hoejer's 209 

Ruber's 20-21 

log  rules 65 

log  rules,  inaccurately  constructed   67 


534  INDEX 


PAGE 

Formula,  Newton's 21 

prLsmoidal 21 

Schiffel's,  derivation 206 

use  in  computing  volume  of  tree 163 

Smalian's 20-21 

Formula;,  general,  for  all  log  rules 77 

in  construction  of  log  rules 58 

waste  from  saw  kerf 53 

Forties,  unit  of  estimating 263 

Forty,  definition 6 

Forty-five  log  rule 85 

Frost  cracks 112 

Frustum,  basis  of  determining  dimensions  of,  in  frustum  form  factors 219 

form  factor,  principle  of 278 

true,  calculation  of  the 221 

factors,  character  and  utility 219 

construction  of  volume  table  from 224 

for  merchantable  contents  in  board-feet 218 

Frustums 20 

volume,  calculation 221 

Full  and  scant  thicknesses  of  boards  as  affecting  over-run 49 

General  formulae  for  all  log  rules 77 

Girth  as  a  substitute  for  diameter  in  log  measurements 24 

Glens  Falls  standard 28 

Goble  log  rule 33 

Graded  log  rules 78 

applied  to  the  log,  in  estimating 299 

tables 195 

volume  tables 193 

apphed  to  tree  in  estimating 299 

Grades,  finishing 457 

of  lumber 455 

and  log  grades 103 

in  estimating,  method  based  on  sample  plots  and  log  tables .  300 

in  standing  timber 298 

re'ation  to  cull  in  log  scaling 458 

log 103 

Grading  rules,  Southern  yellow  pine 457 

Graduation  of  Biltmore  stick,  Table  XXXIX 233 

Graphic  method,  application  in  constructing  volume  tables 169 

of  determining  diameter  growth 347 

plotting  of  data;   its  advantages 166 

Graves,  H.  S.  Method  of  stem  analysis ■ 382 

Ground  rot 110 

Group  form  of  age  classes,  separation  of  areas 418 

Growth  and  yields,  density  of  stocking  as  affecting 392 

by  diameter  classes,  projection 361 

correlation  of  stump  with  D.  B.  H 269 

current  annual 315 


INDEX  535 

PAGE 

Growth  current  periodic,  based  on  diameter  classes 358 

data,  relative  utility  of  different  classes  of 327 

determination  for  forest,  co-ordination  of  forest  survey  with 447 

diameter,  purposes  of  study 342 

effect  of  treatment  on 391 

for  diameter  classes,  comparison  of 360 

increased,  method  of  determination 363 

loblolly  pine,  old  field,  diameter;   Table  LIII 350 

mean  annual 315 

of  stands  after  cutting,  increased 438 

reduced 439 

current  or  periodic,  measurement 436 

factors,  affecting 384 

prediction  by  growth  per  cent 432 

of  trees  as  basis  for  method  of  predicting  current  growth  of  stands 436 

in  diameter 342 

in  height 365 

in  volume 374 

on  areas  of  immature  timber 450 

on  even-aged  stands,  in  large  age  groups 412 

per  cent 316 

character 318 

definition 429 

determination 429 

in  forests  composed  of  all  age  classes 434 

in  quaUty  and  value 435 

to  determine  growth  of  stands  by  comparison  with  measured 

plots 433 

use  to  predict  growth  of  stands 432 

periodic 315 

annual 315 

prediction  by  projecting  past  growth  of  trees 323 

short  leaf  pine,  diameter.  La.,  Table  LV 362 

studies,  chart  of 328 

purpose  and  character 315 

volume  for  single  trees,  computation 289 

substitution  of  tapers  for 379 

Hand  compass,  use  in  strip  surveys 276 

Hanna  log  rule 75 

Harmonized  curves  for  standard  volume  tables  based  on  diameter 169 

for  volume,  based  on  height 170 

Heart  checks 112 

Height  classes,  tree  volumes  averaged  by 163 

classification  of  trees  by,  in  volume  tables 151 

growth  a  basis  for  site  qualities 386 

basis  for  site  classes  in  construction  of  yield  table 401 

chestnut  oak,  Milford,  Pa.,  Table  LVH 371 

current 371 

influences  affecting 365 


536  INDEX 

PAGE 

Height,  growth  of  trees  in 365 

,  measurement 368 

relations  to  diameter  growth 367 

substitution  of  curves  of  height  on  diameter 371 

harmonized  curves  for  volume  based  on 170 

of  seedlings,  western  yellow  pine,  Table  L 336 

of  stump 156 

total  measurement 156 

Heights,  measurement  of 235 

measuring,  technique 245 

of  timber,  average,  and  site  classes 291 

total  versus  merchantable 184 

Herring  log  rule 85 

Hewn  ties 474 

Heyer's  method,  xylometric  for  cordwood 132 

Hoejer's  formula  for  tree  form 209 

Holland  log  rule 76 

Hop  poles 473 

Hoppus,  or  Quarter  Girth  log  rule 25 

rule 34 

Horseshoe  method  of  estimating 284 

Hossf eld's  formula 22 

Huber's  formula 20 

in  measuring  branch  wood 177 

use  in  computing  volume  of  tree 162 

Humphrey  caliper  cordwood  rule 132 

Hybrid  log  rules 76 

Hypsometer,  ChrLsten 243 

Faustmann 240 

Forest  Service 241 

Klaussner 236 

Merritt 238 

Weise 240 

Winkler 241 

Hypsometers 235 

based  on  the  pendulum  or  plumb-bob 239 

Idaho,  statute  log  rule 73 

Immature  stands,  increment  of,  as  part  of  total  increment  of  forest 443 

timber,  growth  on 450 

Importance  of  area  determination  in  timber  estimating 267 

Increased  growth  of  stands  after  cutting 438 

method  of  determination 363 

Increment  borer 358 

use 336 

Index  yield  tables 396 

Influence  of  log  rule  on  deductions  for  defects 107 

Influences  affecting  height  growth 365 

over-run,  methods  of  manufacture 47 

the  log  rule  itself 47 


INDEX  537 

PAGE 

Inscribed  Square  log  rule 33 

Inspection  and  measurement  of  piece  products 477 

Instruments  for  measuring  diameter 227 

Interior  defects 108 

Intermediate  tree,  definition 158 

International  log  rule  for  J-inch  kerf,  Table  LXXX 493 

|-inch  kerf  log  rule , 63 

j-inch  kerf  log  rule 64 

Introduction  of  taper  into  log  rules 44 

Inventory  of  timber 268 

Isosceles  triangles  as  basis  of  height  measure 235 

Jack  Pine,  growth,  Minnesota,  Table  XLVII 318 

Jonson  form  point  method  of  determining  form  classes 249 

Tor 207 

Klaussner  hypsometer,  principle  of 235 

Knots,  rot  entering  from 112 

Lagging 474 

Lake  states,  cruisers'  method  of  strip  estimating 283 

Lapwood,  in  volume  tables 177 

Large  timber  on  the  Pacific  Coast,  methods  of  estimating 287 

Law  of  diminishing  numbers  as  affecting  growth  of  trees  and  stands 318 

Laws  of  diameter  growth  in  even-aged  stands,  based  on  age 354 

in  many-aged  stands,  based  on  diameter 357 

Leaning  trees,  height,  measurement 245 

Legal  status  of  scaler 119 

Lehigh  log  rule 35 

Lengths,  log 16 

scahng 91 

Licking  River  log  rule 86 

Limitations  of  taper  tables 204 

to  conversion  of  board-foot  log  rules 83 

Limits  of  accuracy  in  timber  estimating " 301 

Loblolly  pine  crown  spread,  Ala.,  Table  LX 389 

current  growth,  diameter,  Table  LVI 363 

old  field,  growth  in  diameter.  Table  LIII 350 

Local  volume  table,  form,  Table  XXXI 175 

tables,  definition 153 

derivation  from  standard  tables 175 

construction  and  use 174 

Log  as  the  unit  of  estimating 141 

brands 99 

grades 103 

defect,  effect  upon 460 

determination 459 

examples,  hardwoods 460 

softwoods 460 

purpose 455 

length,  standard  for  volume  tables 182 


538  INDEX 

PAGE 

Log  lengths 16 

merchantable,  what  constitutes  a 99 

rule,  Baxter 67 

British  Columbia 64 

Blodgett  or  New  Hampshire 30 

board-foot,  choice  of,  for  a  universal  standard 84 

Carey 66 

Champlain 65 

Clements' 66 

CUck's 66 

Doyle 68 

Doyle-Scribner 76 

for  round  edged  lumber,  Massachusetts 79 

influence  on  deductions  for  defects 107 

International  |-inch  kerf 63 

5-inch  kerf 64 

McKenzie 63 

Maine 76 

New  Brunswick 76 

New  Hampshire  or  Blodgett 30 

Preston 66 

Quebec 76 

Scribner : 73 

Scribner-Doyle 77 

Spaulding 75 

Tiemann 67 

Thomas'  accurate 66 

Wilson 66 

based  on  cubic  contents 26 

on  diagrams,  construction  of 72 

on  diameter  at  middle  and  at  small  end  of  log,  comparison ....  26 

on  formulae,  comparison  of 61 

on  mathematical  formula,  construction  of 59 

rules,  Baughman 72 

board-foot,  necessity  for 40 

Canadian 76 

comparison  of  scaled  cubic  contents  by  different 36 

definition 8 

expressed  in  board-feet  but  based  directly  upon  cubic  contents 34 

for  board-foot  contents,  construction  of 58 

for  cubic  contents  of  squared  timber 33 

formula,  accurate 65 

from  mill  taUies,  construction 78 

general  formulae  for  all 77 

graded 78 

applied  to  log,  in  estimating 299 

in  use,  based  on  cubic  volume 28 

need  for  more  accurate 50 

obsolete 36,  85 

taper,  introduction  of,  into 44 


INDEX  539 

PAGE 

Log  rules,  true  board-foot,  relation  to  cubic  measure 39 

run  or  average  log  method 143 

scale,  the 88 

scaling,  cull,  relation  to  grades  of  lumber 458 

for  board  measure 88 

use  of  cubic  foot  in 31 

stamps 99 

tables,  graded 195 

Logging  conditions 269 

Logs,  board-foot  contents 40 

defective,  scaling  of 105 

measurement  of  cubic  contents 16 

solid  contents  of,  formulae 20 

technique  of  measuring 22 

the  form  of 18 

Long  cord 122 

Losses  of  trees,  correction  for,  in  growth  prediction 437' 

versus  thinnings,  effect  upon  yields 324 

Lot,  area  unit,  definition 6 

Lumber,  defects 456 

grades  and  log  grades 455 

of 103 

Lumbering,  relation  to  timber  estimating '. 2 

Limberman's  Favorite  log  rule 85 

log  rule 35 

Lumber,  thicknesses  of,  conversion  of  values  of  a  standard  rule  to  apply  to 

different 80 

Maine  log  rule 76 

Management,  forest,  relation  to  mensuration 3 

Manufacture,  the  factor  of  waste  in 13 

Manufactured  products,  forms  of 11 

Many-aged  form  of  stands 388 

stands,  annual  increment  of 390 

application  of  yield  table  based  on  crown  space  to 425 

definition 337 

factor  of  age  in 325 

laws  of  diameter  growth 357 

yield  tables  based  on  crown  space  for 422 

Map,  forest  cover 268 

soil 268 

timber  tj^jes 268 

topographic 268 

Market,  cubic  standard 28 

Massachusetts  log  rule  for  round-edged  lumber 79 

Mathematical  formulaj,  construction  of  log  rules  based  on 59 

Mathematics,  relation  to  mensuration 3 

McKenzie  log  rule 63 

Mean  annual  growth 315 

per  cent 429 


540  INDEX 


PAGE 

Mean  diameters,  error  in  use  of 23 

end  formula,  use  in  computing  volume  of  tree 161 

sample  tree  method 311 

Measurement  of  bark  in  cords 134 

of  cordwood,  methods  of 123 

of  current  growth  on  permanent  sample  plots 443 

of  defective  trees  for  volume  tables 183 

of  diameter  growth  on  sections 342 

of  height  by  a  straight  stick  held  in  hand 235 

growth 368 

of  heights 235 

of  log  lengths 16 

of  permanent  sample  plots 312 

of  piece  products 466 

of  solid  contents  of  stacked  cords 132 

of  stacked  wood  cut  for  special  purposes 122 

of  standing  trees 226 

of  tree  diameters 227 

of  upper  diameters 247 

of  waste 179 

of  width  of  crowns 423 

systems  used  in  forest  mensuration 6 

Measurements  of  the  tree  required  for  classification  in  volume  tables 156 

required  for  tree  analyses 289 

on  each  plot,  in  yield  tables 398 

to  obtain  the  volume  of  the  tree.     Systems  used 158 

Measuring  and  predicting  the  current  or  periodic  growth  of  stands 436 

diameter,  instruments  for 227 

heights,  technique  of 245 

logs,  technique  of 22 

standing  timber  for  volume 226 

stick  for  log  lengths 16 

Medwiedew's  method 387 

Mensuration,  Forest,  definition 1 

Merchantable  boards,  minimum  dimensions,  effect  of,  in  making  deductions  in 

scaling 107 

Merchantable  contents  in  board-feet,  frustum  form  factors  for 218 

cubic  volume,  standard  volume  tables 177 

form  factors 214 

for  board-feet 225 

heights  as  a  basis  for  tree  classes 184 

coordination  with  top  diameters 184 

limit  in  tops  and  at  D.  B.  H 177 

log,  determination  of 99 

versus  used  length 178 

Merritt  h>'pso meter 238 

for  merchantable  heights 246 

Method  of  constructing  taper  tables 197 

of  counting  decades  for  growth 343 

of  deducting  sawdust  first,  construction  of  log  rules 59 


INDEX  541 


PAGE 

Method  of  deducting  slabs  first,  construction  of  log  rules 59 

of  determining  form  classes,  Jonson  form  point 249 

of  graded  log  rules  applied  to  the  log 299 

volume  tables  applied  to  tree 299 

of  mill-run  applied  to  stand 299 

of  running  strip  surveys 276 

of  separating  areas  of  different  types 290 

of  volume  growth  by  use  of  tapers 379 

Methods  of  estimating  dependent  on  use  of  plots  arbitrarily  located 297 

systematically  spaced 285 

Pacific  coast 284 

plots,  large  timber  on  the  Pacific  coast 287 

spruce  in  Northeast 287 

strip,  horseshoe 284 

Lake  States  timber  cruisers 283 

southern  timber  cruisers 283 

valuation  survey 282 

Yale  Forest  School 284 

which  utilize  types  and  site  classes 292 

of  height  measurement  based  on  similarity  of  isosceles  triangles 235 

of  right  triangles 238 

of  improving  the  accuracy  of  timber  estimates 288 

of  making  deductions  for  defects 105 

of  measurement  of  cordwood 123 

of  scaling  a  log,  effect  of.  Table  V 45 

of  timber  estimating 267 

of  training  required  to  produce  efficient  timber  cruisers 303 

used  in  constructing  log  rules  for  board-feet 58 

in  timber  estimating,  factors  determining  the 255 

Metric  system,  conversion  table.  Table  LXXIX 492 

of  measurement 6 

Middle  diameter  as  a  basis  for  board-foot  contents 46 

Mill  factor,  substitution  for  log  rules,  in  universal  tables 146 

grade  or  mill  scale  studies 461 

-run  as  basis  of  grades  in  standing  timber 299 

-scale  studies 461 

method  of  conducting 462 

not  a  check  on  scaling 118 

tallies,  construction  of  log  rules  from 78 

tally,  in  construction  of  log  rules 58 

Miller  log  rule 85 

Mine  ties 474 

timbers 473 

Miner  log  rule 35 

Minimum  dimensions  of  merchantable  boards,  effect  on  deductions  in  scaling. .  .  .  107 

size  of  merchantable  logs 99 

Minnesota,  statute  log  rule 73 

Mississippi,  statute  log  rule 68 

Mixed  species,  yield  tables  for  stands  of 408 

stands,  effect  on  yield 393 


542  INDEX 

PAGE 

Mlodjiansky,  A.  J.,  method  of  stem  analysis 382 

Moore-Beeman  log  rule 68 

National  forests,  log  rule 73 

Necessity  for  board-foot  log  rules 40 

Need  for  form  classes  in  volume  tables 205 

Neiloid 19 

Nevada,  statute  log  rule 73 

New  Brunswick  log  nile 76 

New  Hampshire  or  Blodgett  log  rule 30 

Newton's  formula 20-21 

Noble  and  Cooley  log  rule 35 

Normal  density 397 

form  factors 212 

jaeld  tables  for  even-aged  stands 395 

use  of,  by  reduction 413 

Northwestern  log  rule 86 

Number  and  width  of  strips,  relation 274 

of  trees  per  acre,  influence  on  yields 414 

required  for  a  volume  table 155 

Oak,  White  and  Red,  log  grades 460 

Obsolete  log  rules 36,  85 

Ocular  estimating 256 

estimation  of  tree  dimensions 234 

Old  Scribner  log  rule 73 

Ontario,  Doyle  rule,  over-run 71 

log  rule 68 

Orange  River  log  rule 36 

Oregon,  statute  log  rule 73 

Over-run,  definition  and  basis  of 46 

deductions  from  sound  scale  versus 90 

effect  of  errors  in  Doyle  rule  upon 70 

influences  affecting.     Methods  of  manufacture 47 

The  log  rule  itself 47 

-topped  tree,  definition 158 

Pace,  unit  of  measurement,  definition 6 

Pachymeter,  Biltmore 248 

Pacific  Coast  method  of  estimating 284 

Pacing,  use  in  estimating 262 

Paraboloid,  appolonian,  definition 19 

Parson's  log  rule 85 

Partial  area  estimates 273 

estimates 257 

Partridge  cordwood  rule 133 

log  rule 36 

Peck  in  cypress 113 

Peeled  or  solid-wood  contents,  volume  tables  for 176 

Pendulum,  or  plumb-bob,  hypsometers  based  on  the 239 

Penobscot  log  rule 85 


INDEX  543 

PAGE 

Per  cent  of  area  to  be  estimated,  relation  to  size  of  area 262 

of  total  area  required  in  estimating,  Table  XLI V 292 

scale  as  a  deduction  in  scaling 107 

of  waste  in  a  log,  total 55 

Periodic  annual  growth 315 

growth 315 

of  stands 436 

per  cent 429 

Permanent  sample  plots  for  measurement  of  current  growth 443 

measurement 312 

Personnel,  scaling 1 18 

Philippine  Islands,  log  measurement 28 

Piece,  as  a  unit  of  timber  estimating 140 

measure  definition 7 

products,  converting  factors  for  board  feet.  Table  LXXVI 478 

inspection  and  measurement 477 

measurement  of 466 

volume  tables  for 191 

Pihng 470 

dimensions.  Table  LXXV 473 

irregular,  effect  on  solid  cubic  contents  of  stacked  wood 124 

Pitch  seams 112 

Plots,  arbitrarily  located,  use  of  in  estimating 297 

permanent  sample,  measurement 312 

systematically  spaced,  in  estimating 285 

used  in  estimating 263 

Plotting,  graphic 166 

Plumb-bob,  hypsometers  based  on  the 239 

Point  of  measurement  of  diameters  in  volume  tables 148 

Pole  lagging 474 

ties 474 

Poles  and  saplings,  stand  table  for 454 

chestnut,  specifications 469 

growth  of 452 

small 471 

specifications 467 

Portland  log  rule 35 

Posts,  large  posts  and  small  poles 471 

Predicting  future  growth,  methods  of 320 

yields,  application  of  yield  tables  in 322 

Prediction  of  current  growth  of  stands,  methods 436 

of  growth  by  projecting  past  growth  of  trees  into  the  future 323 

from  yield  tables,  by  apphcation  of  density  factor 414 

in  even-aged  stands,  yield  tables  for 412 

of  stands,  by  growth  per  cent 432 

Pressler's  formula  for  volume  growth  per  cent 429 

Preston  log  rule 66 

Principle  of  the  Christian  hypsometer 243 

of  the  frustum  form  factor 218 

of  the  Klaussner  hypsometer 235 


544  INDEX 


PAGE 

Principles  underlying  the  estimation  of  standing  timber 255 

the  study  of  growth 315 

Prismoidal  formula 21 

Products,  forms  of,  into  which  the  contents  of  trees  are  converted 11 

made  from  bolts  and  billets 14 

volume  tables  for  two  or  more,  combination 193 

Projection  of  growth  by  diameter  classes 361 

Purpose  and  character  of  growth  studies 315 

and  derivation  of  tables  for  cubic  volume  of  trees 177 

Purposes  of  study  of  height  growth 365 

Qualities  of  site,  separation  in  field 448 

volume  growth  a  l)asis  for 385 

Quahty,  growth  per  cent 435 

of  site :  ...  384 

as  affecting  height  growth 366 

effect  on  diameter  growth 352 

of  standing  timber,  estimating 297 

Quarter  girth 25 

or  Hoppus  log  rule , 34 

section,  definition 6 

Quebec  log  rule 76 

Record  of  data  on  plots,  yield  tables 400 

of  timber 276 

Records,  scale 98 

Reduced  growth  of  stands  after  cutting 439 

Reduction  in  diameter,  in  scaling  defective  logs 105 

in  length,  in  scahng  defective  logs 105 

Reisig  method,  xylometric,  for  cordwood 132 

Relation  between  cubic  measure  and  true  board-foot  log  rules 39 

current  and  mean  annual  growth 316 

plots  and  area  covered.  Table  XLIII 286 

size  of  area  units  and  per  cent  of  area  to  be  estimated 262 

of  cubic  and  board-foot  contents  of  IG-foot  logs.  Table  III 41 

of  diameter  of  log  to  per  cent  of  utilization  in  sawed  lumber 40 

Relations  of  height  growth  and  diameter  growth 367 

Relative  diameter,  in  determining  growth  per  cent 430 

utility  of  different  classes  of  growth  data 327 

Re-manufactured  lumber,  grades 456 

Re-plotting  curves,  strip  method 173 

Resistance  to  wind  pressure  as  the  determining  factor  of  tree  form 208 

Retracing  boundaries 267 

Right  triangles,  in  measuring  heights 238 

Rnig  shake 109 

Riniker's  absolute  form  factor 212 

Ropp's  log  rule 86 

Rot,  butt 110 

center 108 

entering  from  knots 112 


INDEX  545 

PAGE 

Rot,  Stump 100 

Rough  lumber,  grades 456 

Round  products , 466 

-edged  lumber 14 

Massachusetts  log  rule  for 79 

Rules  of  thumb,  for  board-foot  contents 252 

for  cubic  contents 251 

for  estimating  the  contents  of  standing  trees 251 

Running  strip  surveys,  method  of 276 

Saco  River  log  rule 36 

St.  Croix  log  rule 68 

St.  Louis  Hardwood  log  rule 35 

Sample  plots,  permanent,  measurement 312 

for  measurement  of  current  growth 443 

trees,  methods  of  estimating 310 

Sap,  stained 115 

Sapwood,  volume 161 

Saplings,  growth  of 451 

Saw  1-erf,  and  slabbing,  deductions  in  certain  log  rules,  Table  IX 62 

as  affecting  over-run 48 

conversion  of  values  of  a  standard  rule  to  apply  to  different  widths  of  80 

waste  from 53 

Saw  kerfs  of  different  widths,  corrections  for 55 

Sawdust,  method  of  deducting 60 

Sawed  lumber,  superficial  contents 13 

Scale  book 99 

caliper 97 

definition 88 

records 98 

rule 88 

stick 88 

Scaler,  legal  status 119 

Scalers 118 

Scaling 88 

check 117 

cyhnder  as  the  standard  of 90 

diameters 92 

from  the  stump 118 

length  of  logs,  taper  as  limiting 43 

lengths 91 

of  defective  logs 105 

practice,  based  on  measurement  of  diameter  at  middle  of  log,  or  cahper 

scale 97 

practice,  based  on  ptieasurement  of  diameter  at  small  end  of  log 91 

in  different  logging  regions.  Table  XVII 94 

use  of  cubic  foot  in 28 

Schiffels'  formula,  derivation 206 

u.se  in  computing  volume  of  tree 163 

values,  Table  LXXXI 494 


546  INDEX 

PAGE 

Schneider's  formula  for  growth  per  cent  on  standing  trees 431 

Scribner  decimal  log  rule 73 

C  log  rule,  Table  LXXXVI 504 

Scribner  log  rule 73 

decimal  values,  Table  XII 74 

erroneously  termed 68 

extension 74 

Scribner-Doyle  log  rule 77 

Scribner's  log  and  lumber  book 68 

Seams 112 

pitch 112 

Seasoning,  effect  on  volume  of  stacked  wood 123 

Second  growth  hardwoods,  yield  table,  Central  New  England,  Table  LXII 409 

Section,  definition,  area  unit 6 

Sections,  measurement  of  diameter  growth  on 342 

Sectors,  deduction  by,  for  defects 115 

Seedling,  age  of 336 

Seedlings,  height,  western  yellow  pine,  Table  L 336 

Selection  of  trees  for  measurement  in  constructing  volume  tables 154 

Separation  of  factors  of  volume,  age  and  area 416 

of  site  qualities  in  field 448 

Seventeen  Inch  log  rule 33 

Shade,  effect  on  diameter  growth 353 

Shake HI 

Shingle  bolts,  definition 15 

measurement 122 

Shop  grades 457 

Short  cord 121 

Shortleaf  pine,  diameter  growth.  La.,  Table  LV 362 

Shrinkage 54 

Similar  triangles  as  basis  of  height  measure 235 

Simoney's  formula 22 

Site  classes  and  average  height  of  timber 291 

based  on  height  growth  for  construction  of  yield  table 401 

on  yields  per  acre,  for  yield  tables 406 

use  in  estimating 292 

classifications,  standards  based  on  height  of  tree  at  100  years,  Table  LX .  .  387 

factors,  or  quality  of  site 384 

qualities,  height  growth  a  basis  for 386 

separation  in  field 448 

volume  growth  a  basis  for 385 

Site  quality,  averaging  for  entire  area 449 

effect  on  diameter  growth 352 

Six  classes  of  averages  employed  in  timber  estimating 258 

Size  of  area  units,  relation  to  per  cent  of  area  to  be  estimated 262 

Slabbing  and  sawdust  deductions  in  10  log  rules.  Table  IX 62 

waste,  distribution,  Table  VII 56 

Slabs  and  edgings,  waste  from 50 

as  affecting  over-run 48 

deductions  by,  for  defects 114 


INDEX  547 

PAGE 

Slabs,  method  of  deducting : 59 

Smalian's  formula 20 

use  in  computing  tree  volumes 161 

SmaU  poles 471 

Soil  map 268 

Solid  contents,  effect  of  dimensions  of  stick  on 126 

of  irregular  piling  on 124 

of  variation  in  form  of  sticks  on 125 

of  logs,  formulae 20 

of  stacked  cords,  measvirement 132 

wood 124 

Table  XIX   127 

-wood  contents,  volume  tables  for 176 

Sound  scale,  deductions  from  versus  over-run 90 

Southern  timber  cruisers'  method  of  estimating 283 

yellow  pine,  grading  rules 457 

poles,  minimum  dimensions.  Table  LXXI 471 

Spaulding  log  rule 75 

Species  as  affecting  height  growth 365 

effect  on  diameter  growth 351 

Spoke  billets,  definition 15 

Spruce,  Adirondacks,  current  growth,  Table  LIV 360 

growth  on  cut-over  lands.  Table  LXVI 440 

diameter  growth  of  trees.  Table  LI 345 

in  Northeast,  on  large  tracts,  method  of  estimating 287 

Square  of  Three-fourths  log  rule 35 

Two-thirds  log  rule 35 

Squared  timbers,  log  rules  for  cubic  contents  of 33 

Squares,  definition 14 

Stacked  cords,  measurement  of  solid  contents 132 

cubic  measure,  definition 7 

measure  as  a  substitute  for  cubic  measure 121 

or  cord  measure 121 

wood,  sohd  cubic  contents  of 124 

Staff  compass 277 

Stained  sap 115 

Stamps,  log 99 

Stand,  determining  age  of 339 

per  acre,  estimated  by  eye 260 

table,  application  in  growth  studies 421 

for  poles  and  saplings 454 

tables 227 

uniformity  of,  as  affecting  methods  in  estimating 265 

Standard,  Adirondack 28 

breast-high  form  factors 213 

cord 121 

cordwood  converting  factors 128 

for  normal  density  of  stocking 397 

log  length  in  volume  tables 182 

of  scaling,  cyUnder  as  the 90 


548  INDEX 

PAGE 

Standard,  Twenty-two  Inch '. 29 

universal,  choice  of  a  board-foot  log  rule  for 84 

volume  table,  form,  Table  XXX 174 

tables,  construction,  by  curves 174 

definition 153 

for  cords 177 

for  merchantable  cubic  volume  and  cords 177 

for  total  cubic  contents,  construction  of 154 

harmonized  curves  for,  based  on  diameter 169 

Standardization,  need  of,  in  forest  measurements 10 

of  variables  in  construction  of  a  log  rule 49 

Standards  for  yield  tables 395 

in  constructing  log  rules 49 

of  site  classification  based  on  height  of  tree  at  100  years.  Table  LX .    387 

Standing  timber,  estimating,  principles  underlying 255 

units  of  measurement  for 139 

trees,  measurement 226 

rules  of  thumb  for  estimating  the  contents  of 251 

Stands,  form  of 388 

grown  under  management,  yield  tables  for 407,  427 

growth  of,  factors  affecting 384 

of  mixed  species,  yield  tables  for 408 

Stave  bolts 15 

Staves,  lengths 122 

Stem  analysis,  limitations  of  use 326 

of  a  tree.  Table  LIX 378 

purpose  and  appUcation 374 

Stereometric  measurement  of  cordwood 132 

Stillwell's  Vade  Mecum  log  rule 36 

Strip  estimating,  systems  in  use 282 

method  of  estimating 273 

of  replotting  curves 173 

surveys,  method  of  running 276 

Strips,  relation  of  width  and  number,  to  area  covered.  Table  XLI 274 

tying  in.     The  base  line 281 

used  in  estimating 263 

width  of,  factors  determining 274 

StuUs 473 

Stump,  height  of 156 

heights 178 

rot 110 

scaling • 118 

tapers,  Table  LII 350 

Stumpage  value,  definition.     Relation  to  forest  mensuration 3 

of    products   as   affecting   accuracy    sought   in    timber    esti- 
mating     266 

Substitution  of  mill  factor  for  log  rules  in  universal  tables 146 

of  taper  tables  for  tree  analysis 382 

Superficial  board-feet,  corre'ction  in  per  cents  for  lumber  sawed  less  than  one 
inch  thick,  Table  XVI 274 


INDEX  549 

PAGE 

Superficial  contents  of  lumber,  correction  of  log  rule  for 83 

of  sawed  lumber 13 


Suppressed  tree,  definition 158 

Suppression,  age  as  affected  by 341 

as  affecting  height  growth 366 

Surface  checks 115 

defects 115 

Survey,  forest,  as  distinguished  from  timber  estimating 268 

definition 5 

Surveying,  forest,  as  a  part  of  the  forest  survey 270 

relation  to  mensuration 5 

Sweep  in  scaling 116 

waste  from 51 

System  for  timber  estimating,  choice  of 261 

Systems  of  measurement  used  in  forest  mensuration 6 

of  strip  estimating  in  use 282 

used  in  taking  measurements  of  the  tree  for  volume .....' 158 

Tally  sheets 277 

unit  of  measurement,  definition 6 

Tape,  diameter 229 

Taper  as  a  factor  in  limiting  the  scaling  length  of  logs  for  board-foot  contents..  43 

definition 18 

introduction  into  log  rules 44 

tables 196 

definition  and  purpose 197 

limitations  of 204 

method  of  constructing 197 

substitution  for  tree  analysis 382 

Tapers,  standard,  as  basis  of  volume  tables 144 

substitution  for  volume  growth 379 

Tatarian  log  rule ,  36 

Technique  of  measuring  heights 245 

Tennessee  River  log  rule 35 

Texas,  Doyle  rule,  over-mn 71 

Third  and  Fifth  log  rule 35 

Thomas'  Accurate  log  rule 66 

Thurber  log  rule 68 

Tiemann  log  rule 67 

Table  LXXXIV 500 

comparison  with  BJodgett  rule 42 

reduced  to  small  end  diameters.  Table  LXXXV 502 

Timber  appraisal  as  distinguished  from  forest  survey 269 

cruisers,  training 303 

estimates,  accuracy,  methods  of  improving 288. 

estimating ....  9 

choice  of  system  for , 201 

of  imits  in .  140 

definition 2 


550  INDEX 

PAGE 

Timber  estimating,  factors  determining  the  methods  used  in 255 

forest  survey  as  distinguished  from 268 

importance  of  area  determination  in 267 

Umits  of  accuracy  in 301 

methods 267 

six  classes  of  averages  employed  in 258 

record  of 276 

types,  map 268 

Top  diameters,  co-ordination  of  merchantable  heights  with 184 

fixed  or  variable  limits 183 

versus  variable,  influence  on  frustum  form  factors 221 

Topographic  map 268 

Topography,  effect  on  methods  of  estimating 265 

Tops,  merchantable  limit  in : 177 

Tor  Jonson 207 

Total  growth  on  a  large  area,  factors 447 

height  of  tree,  measurement 156 

increment  of  a  forest  includes  that  of  immature  stands 443 

or  100  per  cent  estimates 271 

per  cent  of  waste  in  a  log 55 

versus  merchantable  contents  of  logs 16 

heights  as  a  basis  for  tree  classes 184 

yield 315 

Township,  definition 6 

Training  of  timber  cruisers 303 

Treatment,  effect  on  growth 391 

of  stand,  effect  on  diameter  growth 353 

Tree  analysis,  Umitations  of  use 326 

measurements  required  for 289 

purpose  and  application 374 

substitution  of  taper  tables  for 382 

substitution  of  volume  tables  for 375 

as  a  unit  in  estimating 144 

classes,  total  versus  merchantable  heights  as  a  basis  for 184 

diameters,  measurement 227 

dimensions,  ocular  estimation  of 234 

form,  Hoejer's  formula  for 209 

resistance  to  wind  pressure 208 

record,  in  connection  with  volume  tables 155 

volume,  computation 161 

systems  used  in  taking  measurements  of 158 

Trees  for  measurement,  selection  for  volume  tables 154 

standing,  measurement 226 

Trimming  allowance 92 

lengths,  in  measuring  trees  for  volume 161 

Truncated  cone 19 

neiloid 19 

paraboloid 19 

Twenty-two  Inch  standard 29 

Iwo-thirds  log  rule 34,  35 


INDEX  551 

PAGE 

Tying  in  the  strips.     The  base  line 281 

Types,  forest,  use  in  estimating 288 

method  of  separating  areas  of  different 290 

use  in  estimating 292 

Uniformity  of  stand  as  affecting  methods  in  estimating 265 

Units  of  measurement  for  standing  timber 139 

Universal  standard,  choice  of  a  board-foot  log  rule  for 84 

tables,  substitution  of  mill  factor  for  log  rules  in 146 

volume  table 144 

tables  and  form  classes 215 

Unsound  defects,  deductions  from  scale  for 105 

Unused  log  rules 85 

Upper  diameters,  measurement 247 

Use  of  correction  factors  for  volume 293 

of  cubic  rules  for  board  feet,  errors  in 42 

of  diagrams  for  deductions  in  scaling 106 

of  forest  types  in  estimating 288 

Used  length,  versus  merchantable 178 

Utilization  in  tops 183 

Valuation  survey,  forest  service  standard 282 

Value  growth  per  cent 435 

Vannoy  log  rule 68 

Variable  standards,  in  constructing  log  rules 50 

Vermont  log  rule 35 

Volume,  age  and  area,  separation  of,  in  yields 416 

and  age  of  stands,  relation 449 

and  area  for  age  groups  based  on  diameter  groups 422 

for  two  age  groups  on  basis  of  average  age 419 

and  diameter  of  average  trees,  determining 338 

correction  factors  for,  in  estimating 293 

form  as  a  third  factor  affecting 196 

growth  a  basis  for  site  qualities 385 

analysis,  utility 332 

for  single  trees,  computation 289 

of  trees  in 374 

per  cent,  Pressler's  formula 429 

of  bark 163 

of  standing  timber,  measurement 226 

of  tree,  computation 161 

system  used  in  taking  measurements 158 

table  based  on  mill  factors.  Table  XXVI 147 

data  which  should  accompany 188 

from  frustum  form  factors,  construction  of 224 

tables,  bark  as  affecting  diameter  in 150 

based  on  actual  volumes  of  trees 147 

on  standard  tapers  per  log 144 

board-foot,  construction 188 

standard  or  basis 182 


552  INDEX 

PAGE 

Volume,  tables,  checking  the  accuracy  of 189 

classification  of  trees  by  height,  in 151 

combination  for  two  or  more  products 193 

construction,  graphic  method 169 

conversion  from  cubic  feet  to  cords 180 

cords,  standard 177 

definition 144 

diameter  alone  versus  diameter  and  height  as  basis  of 152 

for  board-feet 182 

for  peeled  or  soUd-wood  contents 176 

for  piece  products 191 

for  railroad  cross  ties 191 

graded 193 

applied  to  tree  in  estimating 299 

local,  construction  and  use 174 

definition 153 

derivation  from  standard  tables 175 

need  for  form  classes  in 205 

point  of  measurement  of  diameters  in 148 

standard  definition 153 

for  total  cubic  contents,  construction 154 

for  merchantable  cubic  volume  and  cords 177 

substitution  for  tree  analysis 375 

universal 144 

Volumes,  tree,  classification  by  diameter  and  height 163 

of  frustums,  calculation 221 

of  trees,  actual,  volume  tables  based  on 147 

Warner  log  rule 86 

Waste,  definition  and  measurement 179 

from  crook  or  sweep 51 

from  saw  kerf 53 

from  slabs  and  edgings 50 

in  a  log,  total  per  cent  of 55 

in  manufacture,  factor  of 13 

in  tops  and  limbs 13 

or  cull,  effect,  mill-scale  studies 463 

slabbing  and  sawdust,  distribution.  Table  VII 56 

Weight  as  a  basis  of  measuring  cubic  contents 33 

as  a  measure  of  cordwood 137 

Weights  per  cord  for  various  species.  Table  LXXXIII 498 

Weise  hypsometer 240 

Western  red  cedar  poles 469 

minimum  dimensions.  Table  LXX 470 

West  Virginia,  statute  log  rule 73 

Wheeler  log  rule 86 

White  cedar  poles 467 

relation  between  circvunference  and  diameter.  Table  LXVIII  467 

log  rule 75 

pine,  yield  table,  Table  XLVIII 321 


INDEX  553 

PAGE 

Width  of  strips,  factors  determining 274 

single,  of  bark 161 

Wilcox  log  rule 86 

Wilson  log  nile 66 

Wind  pressure,  resistance  of,  in  tree  form 208 

Winkler  hj-psometer 241 

Wisconsin,  statute  log  rule 73 

Worm  holes 112 

Yale  Forest  School  method  of  estimating  in  southern  pine 284 

Yellow  pine.  Southern,  grading  rules 457 

poplar,  in  Tennessee,  yields  of  cordwood,  Table  LXV 426 

Yield  of  second  growth  hardwoods  in  central  New  England,  Table  LXII 409 

per  acre,  spruce,  cutting  to  various  diameter  limits.  Table  XLIX 322 

predictions,  accuracy  of,  factors  affecting 412 

table  based  on  crown  space,  method  of  construction 424 

construction  with  site  classes  based  on  height  growth 401 

on  yields  per  acre 406 

white  pine.  Table  XLVIII 321 

tables,  age  classes 397 

apphcation  in  predicting  yields 322 

area  of  plots 397 

based  on  crown  space  for  many-aged  stands 422 

on  age,  application  to  cut-over  areas 441 

construction 396 

definition  and  purpose 395 

empirical,  use  of 413 

example 321 

for  stands  grown  under  management 407,  427 

of  mixed  species 408 

measurements  required  on  each  plot 398 

normal,  for  even-aged  stands 395 

record  of  data  on  plot 400 

rejection  of  abnormal  plots 404 

standards  for 395 

use  of,  in  prediction  of  current  growth 436 

total 315 

Yields,  definition  and  purpose  of  study 320 

density  of  stocking  as  affecting 392 

effect  of  losses  versus  thinnings  upon 324 

of  cordwood  for  yellow  poplar  in  Tennessee,  based  on  crown  space.  Table 

LXV 426 

Younglove  log  rule 86 

Xylometers 132 

Xylometric  measurement  of  cordwood. 132 


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